introductory practical logic

INTRODUCTORY PRACTICAL
LOGIC
BENJAMIN J. BAYER
© 2010
Title page public domain/creative commons image credits:
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http://commons.wikimedia.org/wiki/File:Apollo_6_launch.jpg
http://commons.wikimedia.org/wiki/File:Aristotle_Altemps_Inv8575.jpg
http://www.flickr.com/photos/joshstaiger/273593601/
Extraordinary Popular Delusions and the Madness of Crowds, by Charles Mackay, 1841.
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http://commons.wikimedia.org/wiki/File:Goya_-_Caprichos_%2843%29_-_Sleep_of_Reason.jpg
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All images that appear in this book are either public domain, licensed for use in the creative commons, or
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INTRODUCTORY PRACTICAL LOGIC
BENJAMIN BAYER
August 24, 2010
I. INTRODUCTION .................................................................................................................................. 2
Chapter 1—What logic is, and why we need it .................................................................................. 2
II. SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS COUNTERPARTS ............ 23
Chapter 2—Logic and the basic requirements of good reasoning........................................................ 23
Chapter 3—Better known premises and the fallacy of begging the question ......................................... 41
Chapter 4—Relevance and the fallacy of subjectivism ...................................................................... 63
Chapter 5—Reliable and unreliable testimony ................................................................................. 86
Chapter 6—Reason, emotion, and emotionalism .............................................................................114
III. PROOF: LEGITIMATE AND ILLEGITIMATE DEMANDS FOR IT ......................................................143
Chapter 7—All the relevant evidence and proof..............................................................................143
Chapter 8—The fallacy of ignoring relevant evidence .....................................................................163
Chapter 9—Shifting the burden of proof and the argument from ignorance.........................................177
Chapter 10—The pseudo-proof of crackpot conspiracy theories ........................................................195
IV. THE ROLE OF MEANING IN LOGIC................................................................................................212
Chapter 11—The role of meaning, and fallacies of interpretation ......................................................212
Chapter 12—Rules of definition ...................................................................................................231
Chapter 13—Settling definitional disputes .....................................................................................261
V. INDUCTIVE LOGIC..........................................................................................................................277
Chapter 14—Induction and deduction ...........................................................................................277
Chapter 15—Inductive fallacies ...................................................................................................297
Chapter 16—Causal analysis .......................................................................................................316
VI. DEDUCTIVE LOGIC........................................................................................................................338
Chapter 17—Deductive validity and invalidity ...............................................................................338
Chapter 18—Categorical syllogisms .............................................................................................355
Chapter 19—Hypothetical and disjunctive syllogisms ..............................................................375
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§1: INTRODUCTION
Chapter 1:
Why we need logic, and what it is
Ben Bayer
Drafted January 20, 2010
Revised July 17, 2010
A. The practical imperative of logical thinking
At the beginning of his very practical book, Clear Thinking: A Practical
Introduction, Hy Ruchlis relays the following fascinating example. In the
early 1960s, military officers monitoring radar at a nuclear base in the Arctic
noticed a number of “blips” heading
their way. Some thought they were
under Soviet Russian attack. Since
this was the height of America’s “cold
war” with the U.S.S.R., it would not
have been out of character for the
Soviets to launch a sneak attack on a
forward American military base. If it
was an attack, the commanders of the
outpost had to respond with their own
Picture credit 1:
nuclear arsenal: it was their job to
http://commons.wikimedia.org/wiki/File:SPS-67_screen.jpg
ensure that any Soviet attack would be met with overwhelming retaliation.
So the base commanders attempted to contact the Pentagon in
Washington to verify whether the nation was really under attack. But they
couldn’t get through. Had Washington already been taken out by a
preemptive strike against the capital? If it had been, it was all the more
important that the base commanders launch a counterattack. In their view,
the Soviets could not be permitted to pulverize the whole nation just because
they’d been able to decapitate its leadership. But if the base commanders
were wrong and there was simply a glitch in communications—and this
wasn’t really a Russian nuclear attack—it would be a terrible miscalculation
to launch what would then be a first strike against Russia. What were they to
do?
Fortunately, one of the officers had his logical wits about him.
“Where is Khrushchev?” he asked, referring to the premiere of the Soviet
Union at the time. “In New York City, at the United Nations meeting,”
replied another. Now the wheels of logic began to churn. Why would
Khrushchev, an ambitious leader in pursuit of global power, foil his own
2
plans by launching an attack on the United States on the very day he was
visiting the country? Khrushchev would not launch such a strike, these
commanders reasoned: therefore, however odd the blips on the radar, and
however difficult communication with the Pentagon, something other than a
nuclear attack must explain the coincidence of problems.
As it turns out, the radar was malfunctioning—reflecting off the
moon, of all things—and communication systems with Washington just
happened to be malfunctioning that day. Although they did not know this,
quick logical thinking enabled them to determine that there was no nuclear
attack warranting retaliation. Because of this logical thinking, the base
officers successful averted World War III and a global nuclear catastrophe.
Careful, logical thinking is not only needed by those guarding against
unnecessary retaliation. Consider another example of a different radar
screen, some twenty years prior, on the morning of December 7, 1941. On
that morning, Lieutenant Colonel Kermit A. Tyler of the Army Air Corps at
Fort Shafter in Oahu, Hawaii, a military installation several miles to the east
of Pearl Harbor, was the senior officer responsible for monitoring reports
from nearby radar
stations.1 At about 7:15
AM that morning,
Lieutenant Tyler received
a call from the radar
station at Opana, on the
north side of the island,
reporting “a larger number
of planes than [the radar
operator] had seen before
on his scope.” Tyler says
he thought about this
report for a moment, and
replied, “Thanks for
Picture credit 2: http://commons.wikimedia.org/wiki/File:Pearl_Harbor_file2.JPG
calling in the report.” He is
reported later infamously to have told his station assistants, “Don’t worry
about it.”2 The blips seen on the radar at this time were, of course, planes in
the first wave of the Japanese attack on Pearl Harbor. About a half hour
1
For Lieutenant Tyler’s own account of the events that morning, see
http://www.ibiblio.org/pha/myths/radar/tyler_4.html.
2
See “Kermit Tyler, Player of a Fateful, if Minor, Role in Pearl Harbor Attack, dies at 96,” New York
Times, February 25, 2010, http://www.nytimes.com/2010/02/26/us/26tyler.html
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later, these planes would commence an attack on Hawaii that would kill over
2,400 Americans.
Even if Lieutenant Tyler had known to warn his superiors about the
impending attack, there is of course little difference this could have made in
the last 30 minutes leading up to the attack. Perhaps more planes could have
been mobilized to resist the attack, perhaps more ground personnel could
have prepared for the attack, perhaps the Navy could have sought out the
Japanese carrier group serving as the base for the attack. There is still much
debate about how much foreknowledge American military and intelligence
officials had about the Pearl Harbor attacks, and some even claim there was
a conspiracy to allow the attack and draw the U.S. into war with Axis
powers. Whatever the outcome of that debate, it is interesting to think about
what Lieutenant Tyler knew at this time, and whether he could have done
anything to give Hawaii an earlier warning.
What was Tyler thinking during the minute before he thanked the
radar operator for his report and proceeded to tell his assistants not to worry?
Apparently, some advice from a friend, who had told him that “any time the
radio stations were playing this Hawaiian music all night, I could be certain
that a flight of our bombers was coming over, and when I had gotten up at
4:00 a. m., to report for duty, I listened to this music all the way to the
station, so I was looking for a flight of B-17s.” Tyler reasoned that if he
heard the Hawaiian music on the radio, B-17 bombers would soon be
arriving, and when he heard the music, he inferred that these radar blips
were indeed friendly planes, not an enemy attack. As it happens, both Tyler
and his friends were correct: a group of B-17s was on route to Hawaii that
morning. But they would not arrive until later, during the middle of the
attack. The bombers were not the only flight arriving that morning.
Could Tyler have known that these radar blips were planes other than
the American B-17s? Recall that the radar operators in the arctic thought to
make contact with Washington to determine whether there were any
corroborating reports of a nuclear attack. But by Tyler’s own account, he did
not think to ask the radar operators of the number of planes on the radar, nor
to contact the Navy about whether the planes were part of a force departing
from an American carrier. He also did not think to pass along the report of
the unusual radar blips to any further authorities who could verify whether
the planes were American bombers. In response to the question, “did you
make any effort from any source to find out whether this flight was foreign,
or local?”, Tyler said that he did not–even though the radar operator had
reported such a large group of incoming planes.
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To be fair, Tyler as well as the radar operators were new on the job
and had not yet been trained to reliably identify or evaluate the blips they
saw on the radar. What’s more, Tyler claims that he had less reason than
usual to expect a Japanese attack that morning: while his station had been on
alert the earlier week, news of a diplomatic reconciliation between the U.S.
and Japan had been reported in recent newspapers and the alert had been
dropped. Still, he could not have missed the news over the years of Japan’s
unmistakable aggressive intentions in the Pacific, as they had invaded and
occupied Chinese Manchuria and French Indochina. If the radar operators in
the arctic in the 1960s could have thought to corroborate their judgment
about radar blips, it seems Tyler could have just as well. But he did not.
There was not much Tyler could have done at this late stage to
prevent the attack, even if he had known to ask the right questions and think
about the bigger picture. But his logical error was, in pattern, the same
mistake that his superiors made many years earlier when, receiving news of
a diplomatic reconciliation with Adolf Hitler in 1938, they decided that
Hitler could be appeased and would no longer pose a military threat to the
Allies. (We will examine this example in greater detail later in chapter 8.) In
both cases, failure to think logically inhibited the victims of looming
aggression from preparing to defend themselves.
In the arctic radar example from the 1960s, logical thinking stopped
unnecessary retaliation. In the Hawaiian radar example from the 1940s, a
failure to think logically inhibited necessary retaliation. In both cases,
thinking logically was a matter of life or death. The practical stakes of
thinking logically might not always be this high in
your daily life, but it is worth considering other,
less dramatic ways in which logic affects practical
everyday living.
When it comes to achieving practical
results, logic is not just about avoiding disasters. It
also helps us achieve positive, productive results.
The same technology that enables us to rain
destruction on our enemies also enables us to fly
to the moon and explore the depths of outer space.
Perhaps you think that a journey to the moon was
exciting, but can’t see how it has affected you
personally. But consider that IPhone in your
pocket. You can bring up a digital map that
pinpoints your exact location on Earth and
Picture credit 3:
http://commons.wikimedia.org/wiki/File:Apollo_6_launch.j
pg
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navigate your way to new places with very little prior planning—all by way
of a system of GPS satellites in orbit around the Earth. Without the space
program, we would have none of these. Nor would we have the weather
satellites which deliver to your pocket a real-time picture of the planet from
space, and by which you can plan what to wear and where to picnic. And it
was the logical thinking of generations of scientists that enabled the
achievements of the space program—and as a consequence, your IPhone.
We could go into details about the complicated logic of the software
programs running on your IPhone. We could talk about the logic involved in
constructing electrical circuits. We could talk about the logic by which
Newton discovered and justified his theory of universal gravitation, which
scientists use to this day to calculate the orbits of the satellites that make our
GPS devices tick, and which they use to calculate how much thrust it will
take a rocket to get those satellites into orbit. Later in this chapter, we’ll
consider in some detail just one of the crucial assumptions behind the marvel
of modern technology in general, and the space program in particular: the
knowledge that the Earth these satellites orbit is spherical, rather than flat. It
turns out that there is a definite logical process by which human beings first
came to understand this, well before they were able to look down on the
Earth from orbiting satellites above—indeed they needed to be able to do so
to get the satellites up in the first place.
But perhaps you are still unimpressed with the practical importance of
logical thinking. Not everyone is a military tactician or a scientist, and
perhaps while logic is an important tool in their profession, it is not in every
field. Consider, again, your IPhone. Scientists and programmers were not the
only logical thinkers who helped make it possible. Beyond the raw
technology of it, market researchers had to realize the consumer appeal of a
device that brought together so many functions in such an elegant package.
Accountants had to calculate how much Apple could afford to invest in
developing the technology given the expected revenues. And advertising
consultants had to conceive of how best to reach you, the targeted consumer,
and deliver information about how a device like this could improve your life.
At every level of the productive process, theoretical or applied, human
reasoning is the power that has brought us from subsisting in caves to
flourishing in a modern industrial civilization. It is the power that we need
not only to grow our civilization further, but to preserve it against
destruction, both physically and culturally. Logical thinking is at work not
only in the clearest of military strategy, but in the best political theory and
philosophy. Even artists, conventionally celebrated for their emotional
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sensitivity and “intuition,” must use a logical process to conceive and
execute their masterpieces.
But what exactly is a process of logical thinking? There is no way to
detail the many examples of logical thinking that contribute to our wellbeing. The purpose of this book is to illustrate the principles behind logic by
outlining the most important methods of logics and corresponding mistakes,
especially on matters of greatest relevance to many students.
Before we reveal the definition of “logic” that we intend to work with
in this book, it is worth noting some popular conceptions of what logic is,
and evaluations of its relevance.
Exercises
1. Think about an important time in your life when you had to make
a decision, and you think you made a logical decision. What do
you think was logical about it?
B. Why we need logic
If human beings really do stand to benefit from using this tool called logic,
there must be a reason for it. There must be something about who we are and
the nature of the universe that demands this particular tool.
Consider, for example, why tools are useful, in general. Shovels,
hammers, knives, ropes: they’re all useful to us because they extend the
reach and function of our appendages. We can, if we try, dig a hole in the
ground with our bare hands. We can even try to tear things apart by ripping
them with our fingernails. But shovels and knives improve our ability to do
this dramatically—though we still need our hands to use them, of course. So
we need tools because the “tools” we’re born with (or hands) have limited
abilities, which abilities can be expanded by the assistance of artificial
devices well-fitted to our hands.
What is the set of basic “tools” we
are born with, whose reach or
effectiveness logic helps extend? The
answer is our senses. We have a limited
number of senses which work in a limited
way. We perceive light and sound, for
instance. But we only perceive specific
frequencies of light and sound: we cannot
see ultraviolet and infrared light, nor hear
hypersonic dog whistles. Some things are
simply too big or too small or too
Picture credit 4:
http://commons.wikimedia.org/wiki/File:The_Earth_seen_fr
om_Apollo_17.png
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distant for us to perceive with our senses. We can perceive neither distant
galaxies nor atoms and other subatomic particles with the naked eye. We
cannot see the distant past or have clairvoyant visions about the future. Even
those things we can perceive with our senses, like the middle-sized ordinary
objects in our office, can only be seen from limited aspects. We can only see
one side of our desk at a time, not every angle simultaneously as some cubist
paintings like to pretend.
Of course a skill like logic does not literally extend the reach of the
senses. That is the task of a tool like a telescope or a microscope. But note
that even the construction of these tools presupposes a certain logical
process. To construct a telescope, an inventor needs to notice that glass has
interesting refractive properties and find a way to isolate them by grinding a
lens in a specific way. And once the telescope is built, to know that it really
does give us a picture of the way things which are far away look up-close,
one has to calibrate it. When Galileo turned his telescope to the craters of the
moon, how did he know that he was really seeing distant mountains and
craters, and not some optical illusion created by the telescope? He reasoned
that when he turned the same telescope to distant mountains on the earth,
they looked the way he already knew that mountains looked up-close, and so
he must be seeing something real even when he looked at objects not
previously viewed up close. So, even our interpretation of what we directly
perceive through a tool like a telescope is assisted by a kind of logical
inference.
More generally, all logical inferences assist us in “seeing” facts
distant from our perceptual awareness. Consider that presupposition of the
space program which I mentioned earlier: the belief that the Earth is
spherical rather than flat. How did scientists know this before they launched
satellites into outer space? Consider
that the only aspect of the Earth
human beings could see directly for
millennia was the flat stretch of the
land stretching out in front of them.
Had any men of millennia ago been
whisked into space by benevolent
aliens, they could have seen directly
the curvature of the Earth, or even the
Picture credit 5:
whole globe. But to be able to launch
http://www.flickr.com/photos/question_everything/398368315
9/
real astronauts into space today,
we’ve got to know already that the Earth is a sphere. There were, in fact,
logical arguments available even to the ancients which permitted them to
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draw the logical inference that the Earth was shaped like a sphere, even
though they could not see this directly. Like all informative inferences, it
was based on things that they could see directly.
The first reason we need logic, then, is that logic allows us to know
things about the unperceived on the basis of evidence we can perceive. In
this way, logic is like a telescope, but opens up a universe of facts that even
telescopes cannot reach. But why do we need something like logic to let us
do this?
Of course logic does not literally let us
see things we otherwise couldn’t see, as a
telescope does. The ancient Greeks knew that
the Earth was round, but they had no way of
imagining the blue-green wonder that we saw
when the Apollo astronauts first took a picture
of the whole of it. The Greeks could only
“see” with their mind, i.e., they possessed a
conceptual rather than a perceptual awareness
of this fact. They were able to form a higherlevel judgment that the Earth was round, even
Picture credit 6:
if they could not see its roundness. The fact
http://commons.wikimedia.org/wiki/File:Herefo
that we possess the faculty of judgment is a
rd_Mappa_Mundi_1300.jpg
great distinction that enables us to project the
unseen, but it is also dangerous in a way,
because we can use the same capacity to
project things that are unreal. The possibility
of error exists for any other judgment we
might make about the universe. We may see
the relatively flat Earth around us and
conclude that the Earth as a whole is flat. This
would be a projection beyond what we can
see, but in this case, a false one. Or we might
get the shape of the Earth right, as the ancient
Greeks did, but get its position in the universe
wrong, thinking that it is at the center of the
Picture credit 7:
http://commons.wikimedia.org/wiki/File:Armil universe, and that the planets, the sun, and all
lary_sphere.png
of the stars orbit around it. Our ability to
arrive at a multiplicity of conclusions about the unseen is great promise but
also has the potential for great peril.
Some philosophers have said that our senses, like our judgment, can
be deceived. The more you think about it, the less convincing this sounds:
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when you see a stick in water that looks bent, it is certainly an unusual way
of seeing a stick, but our senses are not “censoring” information from us. In
fact they are giving us important raw data: what we need to understand that
the stick is in a medium through which light travels at a different rate, for
instance. The error comes when we make a conceptual-level judgment that
the stick is bent, when we assent to that proposition using our mind. Then it
is we, not our senses, who are in error.
Here, then, is the second fact about human cognition that makes logic
necessary. Because the limited information we receive from our senses is
compatible with a great number of different judgments or beliefs, and
because sensory appearances can sometimes be misleading, we need logic
because we need a step-by-step method of piecing together this perceptual
information in the right way to see the bigger conceptual picture, the whole
truth. In this way, logic is a lot like a ladder which, if we climb carefully and
high enough, allows us to see further than we would by standing on the
ground.
It is worth considering briefly how the ancient Greeks were able to
piece together the evidence they could directly observe in order to come to a
conclusion about the shape of the Earth as a whole. You might wonder why
it’s worth asking the question about the Greeks. Well, how do we know that
the Earth is (roughly) a sphere? The fact that we have pictures from outer
space is pretty convincing, but we would not have these unless someone
knew enough about the Earth to venture into space in the first place. You
might say that before the space program, we had plenty of evidence
concerning the Earth’s shape based on the frequent circumnavigation of the
globe. Magellan was the first to do it between 1519 and 1522. But why was
he confident that he could sail around the world?
The answer turns out to be the same as what made
Columbus confident enough to venture into the
Western sea.
It is a longstanding historical myth that the
leaders of the Age of Exploration thought that they
might sail off the edge of the Earth, and that it was
only a bold “leap of faith” across the ocean that
proved otherwise. In fact Columbus knew that the
Earth was a sphere (even if his sailors did not), and
he is thought to have been bolstered in his
knowledge by reading the following paragraph in Picture credit 8:
http://commons.wikimedia.org/wiki/Fil
Aristotle’s treatise, De Caelo (On the Heavens)
e:Aristotle_Altemps_Inv8575.jpg
about how one could sail from the Atlantic (“the
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Pillars of Hercules”) to India:
Hence one should not be too sure of the incredibility of the view of those
who conceive that there is continuity between the parts about the pillars of
Hercules and the parts about India, and that in this way the ocean is one.
Columbus, like many of his contemporaries, was relying on ancient wisdom,
wisdom that had been abandoned earlier by many medieval scholars, who
instead took the Bible’s account of a flat earth on faith. But how did the
ancients know better?
The bulk of the ancient evidence is found right there in Aristotle’s
treatise. The first observation he refers to is not even an observation about
the Earth itself, but about the moon. What do we observe during an eclipse
of the moon? We see the circular
edge of the Earth’s shadow move
across the moon, engulf it entirely,
and then we see the opposite
circular edge of the shadow, until
the shadow disappears and the
moon is once again in the light of
the sun. Now this evidence could
be taken by itself to suggest that
the Earth is just a flat but circular
Picture credit 9:
disk. But then it would be next to
http://www.flickr.com/photos/aresauburnphotos/2280484803/
miraculous that every eclipse
looked the same way, and that we never see an eclipse involving flat-as-apancake shadows. Only a sphere produces a circular shadow under any
projection. Notice that the observation of the circular eclipse itself requires
step-by-step interpretation: the reasoner must consider all of the possible
shapes that could project such a shape, and rule out those that do not explain
what is seen consistently, until only one possibility is left.
Aristotle also reported that as we move from one latitude to another,
the patterns of the stars we observe change. Some stars seen in Egypt, he
says, cannot be seen further to the north at all. This is a familiar observation
today. Look at the flag of Australia: it has a constellation called the Southern
Cross, which can never be seen from the Northern hemisphere. This
observation is easily explained by the fact that the Earth is a sphere. Since
the edge of a sphere is curved, a star in the distance might be beneath the
viewer’s horizon at one latitude, but not at another. Using this simple
geometric fact, together with some more impressive trigonometry, the
11
ancient Greek astronomer
Eratosthenes was actually able to
calculate the size of the Earth to
an amazing degree of accuracy
(somewhere between 1% and
16% error, depending on how we
interpret his ancient units of
distance). Other Greeks used the
same observations and
calculations to calculate, again
with great accuracy, the size of
the moon, the distance to the
moon, and even the distance to
the sun. The Greeks may not
have been able to explore the
universe with space ships, but
using logic, they were able to
explore it with their minds. As
before, notice that a single
Picture credit 10:
observation or two will not
http://www.nasaimages.org/luna/servlet/detail/NVA2~4~4~6554~10708
0:Star-Trails-at-Dawn;
interpret itself: one has to
http://commons.wikimedia.org/wiki/File:Steve_Ryan_observe the sky from a series of _Stars_around_Polaris_-_Day_62_%28by-sa%29.jpg
different places, recall how the different observations vary continuously, and
conceptualize the geometry that would account for this variation.
A third piece of evidence not cited by Aristotle was nonetheless
available to early explorers like Columbus, especially those who would have
had access to telescopes. If the Earth were flat, only a tiny elevation above
its flattest regions would enable us to see to its furthest edges. But we cannot
do this. Instead we see ships disappearing over the horizon at sea. As before,
this observation does not
automatically give us knowledge
of the Earth’s shape. One might
account for the observation
because of atmospheric effects.
Perhaps it gets to hazy to see
very far at a certain distance.
But atmospheric effects would
not account for the curious
phenomenon of being able to see
Picture credit 11: http://commons.wikimedia.org/wiki/File:Shiphorp.jpg
the masts of the ships peak
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over the horizon before the rest of the ships follow. This observation can be
accounted for only by supposing that the surface of the Earth is curved.
There are a great many other examples we could use to illustrate the
power of a step-by-step method of gathering evidence to reveal to us the
wider workings or innermost secrets of the universe, but none are more
dramatic, at least to this author, than the way these relatively simple
observations literally opened up our world for exploration.
There is one more fact about the human mind, apart from the
limitations of the senses and the open-endedness of our judgments, which is
crucial to understanding why we need logic. Part of what makes human
beings distinctive is their cognitive freedom: we can choose to gather
evidence or not, and choose to use the evidence we gather or not. There are
many ways we can fail to integrate the needed evidence, and many different
motives for failing to do so. We might be mentally lazy, for instance. We
might see that the Earth looks flat around here, and literally not be interested
in what lies “beyond our horizons.” Or, we might be mentally evasive, and
seek to suppress our awareness of evidence beyond those horizons. This
second option is the only way to explain the temporary medieval European
abandonment of the Greek theory of a spherical Earth. Medieval Europeans
wanted to believe the picture of the world according to a literal Biblical
interpretation, which in various places implied that the Earth was a flat disk
with a dome of the heavens or “firmament” covering it overhead. They
believed this in spite of possessing the easily accessible evidence the Greeks
had summarized for them.
The third fact about human beings that explains our need for logic,
then, is that in an important sense, we operate our minds by choice. We can
choose to lower our level of awareness, for instance, by either drifting lazily
or actively seeking to rationalize our wishful thinking.3 Because of this fact
about us, we need the method of logic to guide our choices in favor of those
which respect our evidence. Logic is not just like an instrument that helps us
see farther, but like a compass that reminds us where to look. It is like a
“moral compass” for our mind.
There is one last but crucially important fact that underpins our need
for logic. So far I have presented three facts about human beings and their
minds: our senses our limited, our beliefs can conceptualize the universe in
different ways, and we can choose to use our minds well or poorly. But these
are just the facts about us. Also of importance are facts about the world, and
one crucial fact in particular. It is actually a fact that everyone recognizes,
3
For more on what it means to operate our minds by choice, see my essay with Greg Salmieri, “How We
Choose Our Beliefs,” <http://www.benbayer.com/how-we-choose-our-beliefs.pdf>.
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whether or not they always admit it: facts in the world are not contradictory.
No one would claim, for instance, that Earth is both a sphere and flat, or that
it is both a sphere and not a sphere. It is either one or the other, it cannot be
both. Commenting on this, the law of non-contradiction, Aristotle remarked
that anyone who denied this most basic of the laws of logic could not be said
to be thinking at all, and would be “no better than a vegetable.”
Now, most human beings have no problem avoiding contradictions
like “The earth is a sphere and it is not a sphere.” These contradictions are
too obvious for anyone to miss. But notice that for a long time, astronomers
believed these two propositions: “All planets are spherical,” and “The earth
is not a sphere.” The trouble is that it turns out that the Earth is a planet,
which makes these propositions contradictory. Only astronomers did not
realize that they were committing a contradiction by implication, because
they did not recognize that the Earth is a planet. Usually the contradictions
that bedevil our thinking are of this variety, contradictions that crop up by
implication, because we cannot see important links between items of our
knowledge.
It is for this reason that the science of logic not only counsels us to
pay attention to our evidence, but to work to actively integrate our evidence.
The fourth and final reason we need logic, then, is that we need a step-bystep method which guides us against a basic error: contradiction. In this
way, the tool of logic is like any other tool we use: it is fitted not only to the
nature of the tool user, but to the nature of the objects on which the tool
operates. A shovel must be rigid to scoop the earth; a knife must be sharp to
ply apart softer material. Likewise, logic must counsel us to avoid
contradictions in our thinking, if the object of our thinking is to know
reality—reality is not contradictory.
C. Logic defined
Having surveyed the facts about us and the world that give rise to our need
for logic, we now have a better idea of the purpose served by logic. We have
said that logic serves many practical purposes, but it does so in virtue of its
serving a special cognitive purpose. In order to achieve practical success
with logic, we need to know the world around us. And in order to know the
world around us, we need a method of cognition of the kind we have
described.
Knowing the purpose of logic, we are now in a better position to
formulate a preliminary definition of the concept. We often define the nature
of our tools by the nature of their purpose. We define a shovel as a tool for
digging, a knife as a tool for cutting, etc. Logic is a tool for knowing reality,
14
but a very special kind of tool for doing so. Our senses give us a kind of
basic, automatic knowledge of the world, but logic gives us more than that.
Logic is the science of the method of non-contradictory inference.
By now you should see how each of the reasons for which we need
logic play into this definition. The fact that our senses are limited means that
we need to use inference. The fact that we can form many different beliefs
about the same reality means we need a method for forming our beliefs. The
fact that we can use a method poorly means that we need guidance in its use.
And the fact that the world cannot be contradictory (but our beliefs can)
means that our method must counsel against forming contradictory beliefs.
Hopefully, this very brief sketch of what logic is and why we need it
should motivate you to carefully reconsider the stereotypes about logic we
are about to discuss. So far from being impractical in the affairs of the
world, the dedication to logic has been responsible for some of the greatest
glories of human civilization. We should all be able to appreciate the
emotional significance of that.
Exercises:
1. Think of an example of a logical inference made in a field that
interests you. Briefly state the kind of observable evidence it relies
upon, and the conclusion about the unobserved that it helps to
produce.
2. Think of an example in which different people (either at the same
time, or over time) developed competing views or theories about
the same topic. It would be especially interesting to state an
example in which having more evidence allowed for the
development of a different theory.
3. Give an example of a person you know (keep it anonymous to
protect their privacy!) formed a judgment in a mentally lazy or
evasive manner. What was the conclusion they came to? What
evidence were they ignoring?
D. Stereotypes about logic, and why they are misconceptions
What do you think of when you hear another person described as “logical”?
Some people think, “This person must be stuffy and not much fun”? Perhaps
some apparently logical people really are that way. Surely many of us have
known a least a few of these types. But are all logical people really this way?
Why think of logic as “stuffy”? Some think of logic as they do of
chess, as a technical game to be played, sometimes just to best another in
15
competition. There are some similarities between logic and chess. Both
involve careful thinking in accordance with rigorous rules. And chess is just
a game. Its rules are basically made up. There’s nothing about reality that
requires that things shaped like knights have to move in the pattern of an
“L.” Real knights probably moved in many other patterns. When someone
says that chess is “just a game,” they mean that the object of the game, and
the rules that describe how we are to obtain that object, don’t reflect
anything in real life. In real life, real knights don’t move in an “L” pattern,
and we aren’t real knights. We don’t do battle with kings and queens and
pawns. Chess is just a game, because the object of taking out the enemy king
is a pretend goal that we adopt in order to entertain ourselves.
Logic and chess do have some similarities. Does it follow that logic is
just a game? According to one stereotype, logic deals with strange symbols
and rules that stand in an arbitrary relationship to the world in the same way
that the knight in chess does.
Consider an example of a piece of apparent logic that looks like an
elaborate game. The philosopher Zeno once gave what looked like a logical
argument proving that we could
never move across the room. To get
across the room, we need to first
cross half the distance; to get half
the distance, we need to go half
that distance; and so on…the
process involves an infinity of
steps, and we can’t take an infinite
number of steps! But we all know
that we can move across a room, so
this argument looks like an
elaborate parlor trick. Presumably Picture credit 12:
commons.wikimedia.org/wiki/File:Rembrandt_Philosopher_in_Me
Zeno knew this as well, since he
ditation.jpg
thought he could move his stylus across the parchment to write out his
argument.
Perhaps it’s true that some arguments that look logical are like games.
But is everything that looks logical really logical? Learning logic helps us to
be on guard against logical fallacies—superficially plausible but ultimately
erroneous inferences that people commonly rely upon. Fallacies, in fact, are
part of what gives logic a bad name: when philosophers try to demonstrate
fantastic conclusions using what appears to be logic, you can bet that their
argument probably isn’t really logical. Just as a parlor trick performed by a
16
magician employs “sleight of hand,” normal physical movements so quick
that, to the eye, they appear to involve miraculous powers, arguments that
lead to paradoxical or absurd conclusions have to involve some kind of
subtle illogic. The illogical argument involves some erroneous assumption,
or moves from its assumptions to the conclusion in an erroneous way, or
ignores relevant additional facts which, if considered, would lead to a
different conclusion.
One of the most directly practical uses of logic is the detection of
fallacies in other peoples’ arguments. While we will, from time to time, look
at the results of famous scientific discoveries and experiments, we do not
need to study the most dramatic uses of logic to appreciate how even nonscientists can use logic to our benefit in everyday practical affairs. We don’t
need to be rocket scientists to use logic in intellectual self-defense against
those hucksters and demagogues who attempt to foist illogical arguments on
normally unsuspecting ears. We will spend a fair amount of time trying to
catalogue and understand logical fallacies like these in this text, but we will
always do so by first contrasting them with examples of solid reasoning. 4
One question for those who consider logic to be a game detached
from reality is: How could such a
game have so many practical
results, of the kind considered in
the first section? And how could
the discipline of logic be so
practical unless it had some
bearing on facts in the world?
Logic can be likened to a refined
version of “common sense.”
Nobody would consider common
sense to be unrealistic, and logic is
simply the norms and practices of Picture credit 13:
http://commons.wikimedia.org/wiki/File:Old_timer_structural_wor
ordinary reasoning, held up to a
ker2.jpg
critical light and examined in
4
The lesson to take away from learning about the fallacies is not that people are easily duped and that you
might use the fallacies to dupe them yourself! It is that logical arguments can be separated from illogical
ones, so logical ones are at least possible, and just as you would not want a shyster to use fallacies against
you, you yourself should aim to argue clearly and logically to others, as well.
17
closer detail, with an eye to improving it by making it more consistent.
Logicians study reasoning processes used by ordinary people, and why some
of these processes work, while others do not. 5
Another stereotype holds that logic is somehow alienated from human
nature, because it is somehow opposed to emotion. It’s thought that when
people think logically, they must act in a completely unemotional manner,
and that emotional people are thereby irrational. The ultimate representative
of this viewpoint is Spock from Star Trek. Mr. Spock is the ruthlessly
logical Vulcan who does not understand the motives of his human comrades,
or know how to relate them because of an
inability to empathize. Captain Kirk, by
contrast, is passionate—seducing many an
alien woman in many a space port—and he
cannot understand Spock’s obsession with
calculating the probabilities and risks
involved in important decisions. He adheres
to the “act first, think later” philosophy, and
often his gambles pay off. Many think that
if we were like Spock and simply crunched
numbers all day, not only would we never
get anything done, but we’d never be able
to relate to other people or be happy.
The view that logic and emotion are
opposed to each other is driven home by the
assumption that emotions are passions, that
is, that we are the passive recipients of these emotions, rather than active
causes of them. Emotions simply filter through us like wind through the
grass. And it’s thought that we can either bend with this wind, or stand
rigidly and risk breaking. It’s thought that too much logic will cause us to
repress our emotions, and bottling up a force like this will only lead to an
explosion later on. Psychologists have certainly learned much about why it’s
a bad idea to bottle up our emotions. But is it true that being logical
Picture credit 14:
http://www.flickr.com/photos/unforth/2821996848/
5
There is much debate among philosophers about just precisely how logic relates to the world. Does it do
so because it helps us discover real causal connections between facts, for instance, or does it help us simply
because it helps invest our decisions with a high degree of probability, by which we can make rational bets?
Does it deliver practical results because it accurately predicts the behavior of really existing unobservable
properties in the world, or does it merely serve the task of calculating the play of different experiences
before our minds? Whatever the answers to these questions and however it is that philosophers understand
the “reality” these questions concern, it is obvious, at least to this philosopher, that there is a world
independent of our minds which logic must have some way of latching onto.
18
necessarily involves bottling up our emotions? Is it true that to be logical, we
must all be like Spock?
Consider again the base commanders at the arctic nuclear missile
base. They are certainly frightened by the possibility of a nuclear war, and
desire to avoid it at just about any cost. They use logic to achieve this desire
and alleviate their fear. When they realized that their reasoning had paid off,
they also must have been elated. We might describe their decision making
process as a “passionate search for dispassionate truth,” as one philosopher
once described the practice of logic more generally. These base commanders
did not let their passions cloud their judgment. They did not become so
frightened of the possibility of a nuclear attack that they never stopped to
consider the other possibility, that none was occurring. And so when they
made the delicate connections of logic themselves, they did not allow their
emotions to sway their judgment. But the need to make this logical judgment
was still motivated by ordinary human concerns: to avoid the worst possible
outcome, the officers needed to know the truth of the situation. So there is a
straightforward way in which reason serves emotion—by providing it with
objective data needed to accomplish a desired end—and there is a way in
which emotion serves reason—by motivating it to inquire when it is needed
most.
But there is an even deeper affinity between reason and emotion that
we will explore in greater detail later in chapter 6. It is not simply that we
have various emotional motivations, and use reason to satisfy them. There
are ways we can use reason to evaluate those emotions themselves. This is a
point that is taken very seriously by
contemporary cognitive therapists. Since the
late 20th century, these therapists have
realized that many of our most chronic
psychological problems—depression,
anxiety, phobias—are the result of various
entrenched thinking problems. Though it is
no easy task to solve these entrenched
problems, asking enough questions about our
basic but often hidden premises about what is
good and bad, about what is important or not
in our lives can yield answers, and when we
are able to subject or hidden premises to the
light of day and evaluate them, we can at
least begin to change our overall psychology, Picture credit 15:
http://www.flickr.com/photos/jerry7171/17519669/
including the way we respond to life
19
emotionally. It seems that our emotions are relics of our older thinking, and
if there are emotions that bother us, it may be because our older thinking has
not been integrated well with our newer thinking. If this is true, then reason
not only cooperates with but molds our very emotions, enabling us to live
confidently and harmoniously with our emotions. It turns out that
understanding where emotions come from can help us understand why it is
improper to rely on an emotion as if it were a new source of thinking, which
some people (maybe even Captain Kirk) too often do.
A third, related stereotype is that logic is useless when it comes to
dealing with other people, because many people are irrational. We may have
the best argument in the world, but if another person doesn’t “listen to
reason,” we have no influence over their thinking and acting. Sometimes
logical people speak of having “knock-down” logical arguments for or
against various propositions. But we all know that no argument has ever
knocked anyone down.
Does logic need to force others to change their minds to be useful for
dealing with them? Of course some people allow themselves to believe
fallacies, rather than good logical arguments. But when you know the
difference between logic and illogic, at least some of the time you can point
this out to people, and explain why their beliefs do not hold together
sensibly. If they still don’t listen, you can at least work to understand where
their reasoning went wrong, what mistaken premises might be motivating
their emotionalistic reaction, and be on guard against similar reasoning of
your own. Logic may not give us a way of “knocking down” other people,
but it will at least help us stop them from knocking us down, and in a few
rare cases, it may help us gently nudge the other person to stop trying to
knock us down.
A final stereotype about logic holds that in addition to not helping us
deal constructively with other people, logic can assist us in manipulating or
exploiting them. This is the origin of the expression “criminal logic.” It’s
thought that the criminal who concocts the most devious scheme to dupe or
bilk his fellow men for their riches is acting in a perfectly rational way. His
arguments might not knock down the other person, but his scheming might
knock down the other person’s safe. Monty Burns from The Simpsons, Dr.
Strangelove from the film of the same name, even Henry Kissinger from
politics of the last century (in some people’s views)—each is thought to be
an “evil genius” with a grand scheme to plunder the masses, construct a
doomsday device, or rule the world. All are thought to follow the “logic” of
Machiavelli, the Renaissance political theorist who counseled the politicians
of his day to find the most practical scheme to maintain their power—
20
whether or not it involved the exploitation or
oppression of innocent citizens.
There is a sense in which one can be
“logical” in calculating the best means to an
end—regardless of what that end might be.
But does logic have nothing to say to us
about those ends themselves? And is it
logical to manipulate and exploit other
people to achieve one’s own ends? We have
just spoken briefly about how logic might be
used to evaluate a given person’s emotional
motivation. But consider also that one of the
most devious forms of manipulation of
others is the issue of illogical arguments. The huckster and demagogue rely
on fallacies, not scientific analysis, to sway the masses. We have already
emphasized how logic can be practical to one’s own life. By the same token,
we ought to encourage other people to use logic, too; when they are left free
from manipulation they produce rockets and satellites and GPS and IPhones,
which they can trade with us to mutual benefit. So if we can benefit from
others rationality in this way, why should we suppose that by duping other
people—by depending on their
irrationality—we will
somehow prosper in the long
run? Fly-by-night hucksters
and demagogues all too often
find that in the long run, you
can’t fool all of the people all
of the time. Dealing with other
people rationally, however,
allows us to benefit from the
best in other people, not hang
Picture credit 16: http://commons.wikimedia.org/wiki/File:Sonsbeck_perilously on their worst.
Picture credit 17:
http://www.flickr.com/photos/unforth/2821996848/
_Ferkelmarktbrunnen_03_ies.jpg
Exercises
1. Can you think of an example of a case where a logical argument
seems like a game? Or when it seems to be detached from reality?
2. Consider the example of Zeno’s argument for the impossibility of
motion. Do you think it is a good argument? If it isn’t one, how
would this effect your evaluation of logic?
21
3. Think about the contention that we can’t use logic to deal with
irrational people. Can you give an example of such a person? Is it
true that such a person would never listen to reason? What are the
kinds of things he’d be least likely to listen to reason about? The
most likely?
4. Suppose that Spock knew that if he sat around calculating risks all
day, he would run the risk of never accomplishing anything.
Would it be logical for him to keep calculating?
5. Can you give an example of an emotion that you think is
irrational? Why do you think it is irrational? Are there no
circumstances under which it might be a good thing to feel?
6. Can you think of an example in which you think you may have
been mislead by a salesman or a politician into believing
something that wasn’t true? What tricks of reasoning did he or she
use?
7. Do you agree that it is never good to encourage another person’s
irrationality? Why or why not? Can you think of an example in
which you have benefited from another’s sloppy thinking? Why do
you think it was really a benefit, as opposed to a short-term thrill?
22
§2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 2:
The basic requirements of good argument
Ben Bayer
Drafted January 24, 2010
Revised July 19, 2010
The science—and art—of logic, and its products
At the end of the last chapter, we defined logic as the science of the method
of non-contradictory inference. As we discussed, we need such a science
because we begin our cognitive lives with limited information—hence the
need to draw inferences from what we begin with. We can make mistakes
when we make inferences, so we need a method to guide us. We need to be
reminded to rely on this method, because we can fail to be completely
conscientious in the way we think. And we need to be conscientious,
because the world isn’t going to change itself to make up for our mistakes: it
is what it is, and not another thing.
The definition we have used so far treats logic as a kind of science,
but we can also think of it as an art. It is not an art in the sense that painting
and music are (it is not a fine art), but it is in the sense that we speak of “the
art of cooking”: it gives us a “recipe” for
producing a special kind of product, a product we
need to achieve important goals. In just the same
way that the art of cooking instructs us in the
production of soups, cakes, and soufflés, which
we need if we want to eat and enjoy ourselves, the
art of logic instructs us in the production of
conceptual knowledge, which we need if we want
to grasp reality and live successfully in it.
How does the logician decide on the recipe
needed to produce this knowledge? Of course
cookies can’t be made in just any way. A mixture
of tofu, Worcestershire sauce, and deer venison
wouldn’t do the job. A good cook observes which
ingredients actually go together to produce a tasty Picture credit 18:
http://commons.wikimedia.org/wiki/Fil
and nutritious meal. He may experiment, by
e:Crisco_Cookbook_1912.jpg
adding or subtracting ingredients to see which
best perfect the dish. The same is true of the art of logic. The logician
23
doesn’t just decide in advance which thinking processes are best, but
observes the actual methods of reasoning people use, and which ones of
them lead to real knowledge and practical success.
A model logician in this regard was one of the first: Aristotle. In his
treatise, the Prior Analytics, Aristotle surveyed every possible form of
deductive, syllogistic reasoning (which we will study in more detail in
chapter 18): he observed which forms yielded false conclusions when
supplied with known premises as inputs, and discarded these as invalid. The
rest that avoided contradiction were classified as valid.
Most logic textbooks will not focus on every ingredient of knowledge,
only on one of the most crucial, the argument. An argument is a connected
series of propositions (premises) intended to establish another proposition
(a conclusion) as known. Here is an example of an argument of the kind that
logicians study:
The Earth always casts a circular shadow on the moon during an
eclipse.
Circular shadows are cast by flat circles, cones, cylinders, and
spheres.
Flat circles, cones, and cylinders cast shadows other than circular
shadows from different perspectives.
Only a sphere always casts a circular shadow.
Therefore, the earth is spherical.
This argument should look familiar, because it’s one of the examples we
considered in the last chapter of evidence that needs to be assembled and
interpreted methodically to derive
even the most commonplace piece of
knowledge, such as that of the shape
of the planet on which we live. Notice
that this time, the evidence is
structured in a more formal way. The
premises are written neatly at the top,
like the separate addends in an
addition problem, while the
Picture credit 19:
conclusion is under a line drawn
http://commons.wikimedia.org/wiki/File:Lunar_eclipse.svg
beneath the premises, like the sum in
an addition problem. In this argument, we need each of these premises to
systematically consider all of the possible explanations for the shape of the
Earth’s shadow, and then rule out all of those that we have other evidence
24
against. By this methodical use of the “process of elimination,” logic helps
us see how premises “add up to” a conclusion.
At their best, logicians study the widest range of cognitive processes
over which people exercise control that is relevant to acquiring knowledge.
A good cook wouldn’t just pay attention to which combination of
ingredients adds up to the best soufflé. He’ll search the world for the best
ingredients. Not just any old cream, but the finest cream from the finest
dairy, for instance. A good logician will do the same. What makes for a good
argument is not just a matter of the way the premises add up to the
conclusion, but a matter of premises and the components of those premises.
In this chapter, we will spend at least a little time talking about what makes
for a good premise, i.e. what makes it contain knowledge which can add up
to more knowledge in the form of a conclusion. In other chapters, we will go
even further than that. A premise is only as good as the concepts which
make it up.
Sometimes philosophers speak as if we should take our concepts for
granted and leave it to psychologists to account for them. But concepts are
of philosophical and especially logical
interest if human beings have some control
over them: specifically, over their
formation and their definition.6 Consider
just one example from the argument above:
the concept of “eclipse.” Forming that
concept is a cognitive achievement: early
astronomers had to carefully distinguish the
surprising temporary darkness that appears Picture credit 20:
http://commons.wikimedia.org/wiki/File:Bcmom_over the moon on a single given evening
_Lunar_Eclipse_%28by%29.jpg
from the more regular darkness that waxes
and wanes across the moon over the course of the month, the kind that
accounts for the phases of the moon (new,
half, full, crescent, etc.). Astronomers also
had to notice the similarities between the
temporary blotting out of the moon and the
temporary blotting out of the sun, and realize
how both had a common cause: the
positioning of one heavenly body between
the sun and another, so as to blot out light.
6
Picture credit 21:
http://commons.wikimedia.org/wiki/File:Half_Mo
For more reasons on why this author considers this
on.jpg
approach to be a mistake, see “A Role for
Abstractionism in a Direct Realist Foundationalism,” Synthese, forthcoming, 2010, <
http://www.springerlink.com/content/l243927tjw6756k6/>.
25
Noticing these differences and similarities required effortful attention, and
the result of these choices—the concept of “eclipse”—adds something useful
to human thinking. Like the selection of ingredients of a soufflé, then, it is
something that can be done well or poorly, and
part of the subject matter of the art and science
of logic. Since the formation of a concept or
definition is not exactly an inference—it is
more like a condensation of many past
observations—the definition of logic is
actually broader than we originally suggested.
It is not only the science of the method of noncontradictory inference, but of any kind of
non-contradictory identification.
Picture credit 22:
http://commons.wikimedia.org/wiki/File:Tot
al_solar_eclipse_1999.jpg
Exercises
1. Above we compared the art of logic to the art of cooking. Can you
name some other practical activities that involve a kind of “art,”
and what products they produce?
2. Can you think of other parallels between the art of logic and the art
of cooking? Consider the argument concerning the earth’s shape. Is
it well-prepared or only half-baked? Is the conclusion something
that sustains us?
3. Can you identify other concepts in the argument about the earth
which could have been formed only by careful attention to various
differences and similarities?
The crucial ingredient of inferential knowledge: logical argument
We will devote a separate chapter (12) just to the logic of concepts
and their definitions. But the bulk of this book will follow the tradition and
deal with the logic of arguments, the formal statements that illustrate the
structure of inferential knowledge. For
this reason it is important to get really
clear on what arguments are and what
they are not. To begin with, an argument
in logic is not merely a “heated
exchange,” the kind of argument that
two lovers may have during a fight.
There’s a famous sketch from Monty
Python’s Flying Circus in which one
Picture credit 23:
http://commons.wikimedia.org/wiki/File:Steen_Argument_o
ver_a_Card_Game.jpg
26
character patronizes an “Argument Clinic,” looking for a good argument. He
first enters the wrong room, and is met with a torrent of expletives and
name-calling. It turns out that he has entered the room for abuse, not
argument. Too often people who engage in arguments, conventionally
understood, are just heaping abuse on one another, not engaging in any
intellectual process.
In the next room, the Python character says he’s looking for an
argument, and the attendant says no, he isn’t. The patron insists that he is,
and the attendant continues to deny it. They go back and forth affirming and
denying this proposition for a while, at which point it becomes obvious to
the patron that this is not an argument, but simply “contradiction.” “An
argument is a connected series of statements intended to establish a
proposition,” he says. “Argument is an intellectual process. Contradiction is
just the automatic gainsaying of any statement the other person makes.”
Even if this exchange is not as heated as what we found in the room for
“abuse,” it is still clear that there is no intellectual process here, just
mindless affirming and denying. (One is reminded of the old commercials
for Budweiser: one crowd yells “Tastes great!” The other responds, “Less
filling!” They go on and on.) Remember: the reason that we need logical
arguments is that they formalize the process of methodically collecting
evidence needed to draw inferential conclusions. Just saying that something
is or isn’t so is not a methodical collection of evidence.
The fact that logical arguments involve the methodical organization of
propositions does not mean that every methodical organization of
propositions is an argument. The purpose of assembling them is important,
too. There are at least two methodical ways of assembling propositions from
which arguments should be distinguished, because they involve a different
purpose.
One notable example is the explanation. Here’s an example of a good
explanation:
The earth is spherical in shape, because eons ago, nebulae
collapsed into disks of gas and dust, forming stars and clouds of
dust, which collected together due to gravitational attraction.
Eventually the collections become large enough that they
melted and formed globular structures.
27
You might look at this passage and think that it involves an argument,
because special prominence is given to an idea in the first sentence, “The
earth is spherical in shape…”—the same proposition that’s the conclusion of
the argument in our example above—and what follows the “because” is a
series of sentences that might be mistaken for premises that seem to support
this first sentence as if it were the conclusion of an argument. But if you
look at these sentences
that follow, you’ll
notice that they serve a
different purpose than
the premises that would
argue for the
conclusion that the
earth is spherical. The
fact that we see ships
disappear over the
Picture credit 24: http://commons.wikimedia.org/wiki/File:Protoplanetary-disk.jpg
horizon, or that star
patterns shift as we move north or south, are pieces of evidence that help us
come to know that the earth is a sphere. But the kinds of facts related to the
earth’s shape in this new passage do not help us come to know the shape of
the earth in the first place. Indeed, it is hard to imagine how we could ever
know about the history of the solar system or the theory of gravitational
attraction if we did not first know about the shape of the earth. Instead, what
these new facts do is help us to understand something we already know.
Supposing that we already know that the earth is a sphere, these facts about
the history of the solar system and the nature of gravitational attraction help
us understand why the earth is a sphere—they help us grasp the cause of the
earth’s being round. To summarize, arguments help establish what we know;
explanations help us understand it.
(One further note of clarification: The distinction between arguments
and explanations is complicated by the fact that arguments can be thought of
as one particular kind of explanation: they are an explanation of how we can
come to know something: they identify the premises which, if accepted and
processed in the right way, will cause us to know the conclusion. This is
probably why arguments use the same language as other explanations: they
are one form of explanation. Still, beware that not all explanations are
argumentative explanations. Many explanations identify the causes of facts
in the world apart from our knowledge of them.)
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A second example of a carefully organized set of propositions that is
also not an argument can be seen in the following example of a conditional
statement:
If the earth is a sphere, that is, if points on its surface are
roughly equidistant from its center, then it follows that volume
can be computed by measuring its radius and computing V= 4/3
πr^3.
Here again, the passage in question is divided into two separate claims: first,
that the earth is a sphere, and second, that it has a certain volume. This
ordered sequence of statements might
look like an argument in which the claim
about the earth’s shape is seen as a
premise, and the claim about the
calculation of its volume is seen as a
conclusion. But if you think about the
meaning of “if – then” statements, you’ll
realize that their function is not the same
as that of arguments. A statement that
talks about what is true if the earth is a
sphere is not committing itself to the
claim that the earth is a sphere. It is
Picture credit 25:
merely considering a possibility, and
http://en.wikipedia.org/wiki/File:Sphere_wireframe_10d
eg_6r.svg
what follows from it. The same is true of
the second part of the passage, concerning what follows. So this statement is
not committing itself to the claim that the Earth’s volume can be measured
according to the stated formula. It is merely claiming that if the earth is a
sphere, then that formula applies. Arguments, by contrast, are very much
about making a commitment! We advance arguments for claims that we
think are true, and on the basis of premises that we think are true. To
summarize: a conditional statement describes how the truth of one statement
or statements would affect the truth of another, but a full-fledged argument
actually takes the position that a set of statements (the premises) really is
true, and really does affect the truth of another (the conclusion).
(As before, there is a qualification here. Arguments can be used in a
noncommittal way. We can use “if – then” statements to describe arguments
in a neutral way: we can say, “if these premises are true, then this conclusion
must follow.” But this is a derivative use of argument, as it is no longer to
endorse the argument as an argument. If there were no practice of
29
committing oneself to arguments, there would be no need or possibility of
merely pretending to commit oneself to arguments, to see what follows,
hypothetically.)
There are a few other types of organized discourse that should be
distinguished from arguments, such as reports, statements of belief,
warnings, advice, or any set of loosely associated statements. We won’t go
into the details of how each differs from argument. The key is to understand
the function of argument: its primary purpose is to establish inferential
knowledge, whereas these other types of discourse either do not have this
function, or do not perform it in the same way.
Sometimes one can tell when another person is making an argument
by looking for the presence of special kinds of language. The use of special
“inference indicators” can help determine what the arguer intends to use as a
premise vs. as a conclusion. Here is a list of prominent inference indicators
which, when placed between a set of propositions, suggests that the
propositions listed first are premises, while those listed second are
conclusions;
thus
consequently
accordingly
implies that
therefore
so
entails that
hence
Here are some examples of how some of these different inference indicators
might be used to present the same argument:
I think, therefore I am.
I think, so I am.
I think, and for this reason we know I am.
There are, of course, other words or phrases that perform the same function.
The list above is not exhaustive (in fact there’s a new inference indicator in
the third example, just to show how many we have in our language).
But don’t think that arguments always have to be presented in premise
– conclusion order. It is just as easy to state a conclusion first, and then
present the premises we would use to argue for it. (One could even state a
premise, state a conclusion, and then state more premises—or vice versa.
There is no mandatory order here.) Here are some of the inference indicators
for the reverse order:
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since
because
for
in that
as
given that
seeing that
inasmuch as
Notice that “because” appears on this list—the same word we used up above
to state an explanation rather than an argument. So the presence of a word
from the list in someone’s discourse is not a guarantee that an argument is
actually being used. (It might be a non-argumentative explanation, for
instance.) These words are merely symptoms or signs of the presence of
argument.
To be able to tell if an argument is really present, and if so, which
statements are premises and conclusions, you’ll need to look to the role
played by various connected statements. Linguistic symptoms are not
enough. Are some statements presented as more obviously true or
uncontroversial than others? Then it’s likely that they’re premises. Is another
statement given prominent emphasis, as if other statements all lead up to it?
Is that statement itself not as obviously true or uncontroversial as the others?
Then it is likely a conclusion, rather than a premise.
Very often, arguments will be presented in ordinary discourse with no
inference indicators at all. People use arguments all of the time, but they
rarely state them formally (and there is not always reason for them to do so).
Consider this final example of an informally stated argument. Think about
how you would classify its component statements.
People need freedom to live. People need to think and produce in
order to live. But, to think and produce, they need to be left free.
Exercises
1. One of the differences between an argument and an explanation is
that an explanation explains a statement we already know, using
other information we already know. What kind of argument is
needed to establish knowledge about the history of the solar
system? About the theory of universal gravitation? Why might we
need to know that the earth is spherical in order to establish this
knowledge?
2. Consider the argument about human freedom above. What are the
premises? What is the conclusion? How can you tell? For instance,
which statements are more or less obvious? Which ones, if true,
would provide support for the others?
31
3. Having identified premises and conclusions for the argument about
human freedom, formalize it. Write the premises and then write a
line, to indicate the conclusion.
4. Having formalized the argument, figure out a way to present
premises and conclusion in a different order. Write it out using one
of the inference indicators needed to present the alternate order.
5. We have not yet discussed how to evaluate arguments. But how
would you evaluate the argument stated above?
The art of logic performed well: basic requirements of good argument
We have defined an argument as a connected series of propositions intended
to establish another proposition as known. But notice that an argument only
intends to establish some proposition as known, and not everything succeeds
in achieving its intention.
A cook may intend to bake a tasty soufflé, but fail. If he doesn’t
follow the recipe precisely—or if he pokes it or makes a loud noise at the
wrong time—the final product could be ruined. Just as the cook can fail to
back a tasty soufflé, a thinker can fail to establish a conclusion as known.
And just as the cook might fail by neglecting to follow a recipe or other
important principles of cooking, the thinker can fail by neglecting some
important principle of logic. Arguments fail in many ways, depending upon
the principle of logic they violate. They might be merely “half-baked,” or
collapse entirely. In what follows, we’ll survey the variety of ways in which
arguments can fail, in order to give you, the thinker, a better understanding
of what it takes to formulate genuine inferential knowledge.
There are many nuances involved in good reasoning, but most of them
are summarized by three basic principles:
1. The premises of the argument must be known and known better
than the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must be
likely to establish the conclusion as true)
3. The argument’s premises must contain all of the known
relevant evidence.
We need to say a little bit now about the meaning of each of these
requirements. In future chapters, we will expand on them dramatically. As
mentioned in the first chapter, much of this book will be concerned with the
study of logical fallacies, superficially plausible but erroneous inferences
upon which people commonly rely. As it turns out, just about every
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important fallacy can be categorized as a violation of one of these
requirements or another.
First: premises must be known, and known better than the conclusion.
The function of argument, as we have stressed, is to take something we
know very obviously and to organize it in a way that allows us to know
about something that is not as readily obvious to us. So it follows that what
we take as a given to form this new knowledge really must be knowledge in
the first place. So, for example, it is much more obvious to us that the earth
casts a rounded shadow on the moon during an eclipse than it is that the
earth as a whole is a sphere. We can directly see the whole of an eclipse, but
we cannot directly see the whole of the Earth (as long as we are standing on
it). It does take a little extra reasoning to know that it is the Earth’s shadow,
as opposed to some other body’s, but the data itself, the view we have of that
dark shape traveling over the face of that heavenly body is right there as data
for the senses.
Of course not everything we know that is worthy of being a premise
in an argument is known by direct perception. Suppose we establish that the
earth is a sphere. That knowledge now becomes available as a new premise
for new arguments. Once we know that the earth is a sphere, we can also
come to know (with the help of many other premises) that it is a planet like
Mars or Venus, that it orbits around the Sun, and that all of these planets are
held in this orbit by a force of gravity. So when we say that premises must
be known, this means that they must be obtained either from a direct form of
knowledge (like perception) or from something else that is itself obtained
from a direct form of knowledge. When we say they must be better known
than the conclusions, this means that they must be closer to direct
observation than the conclusion in need of proof. This is the most objective
meaning we can give to the idea that premises of an argument need to be
“more obviously true.”
Consider a simple example of an argument that fails to meet this first
requirement:
Everything made of rock is spherical.
The Earth is made of rock.
Therefore, the Earth is spherical.
Notice that this argument actually reaches
the right conclusion, a conclusion we
otherwise know to be true. The earth really
is spherical. But if this argument is a
33
person’s basis for believing that claim, the claim may be true but the arguer
won’t know that it’s true. The argument is bad, because one of the premises
is not something we know. “Everything made of rock is a sphere” is not a
part of our knowledge: in fact, we know that it’s false. There may be a few
rocks that are spherical (marbles, bowling balls, strange rock formations),
but mountains and mesas and even most pebbles are no where close to
spherical—and again, this is all easily available to observation.
A premise does not need to be obviously false to violate the first
requirement. Consider this example:
All planets are spherical.
The Earth is a planet.
Therefore, the Earth is spherical.
Suppose that you are making this argument in the year 500 B.C.E. At this
point, nobody had the knowledge that the Earth is a planet, and in fact most
thought explicitly that it was not. A planet, in their view, was one of the
observable heavenly bodies that moved in a different pattern than the stars.
(We still agree with this regarding the
planets we see in the sky, but think that the
Earth is a planet because it exhibits the
same motion which causes other planets to
be observed in this way.) If you do already
know that the Earth is a planet, and that
planets are spheres—say because you live
on a different planet, and only see the Earth
in a telescope as a tiny speck—this would
make for a good argument for the Earth’s
Picture credit 26:
shape. But for someone to whom that
http://commons.wikimedia.org/wiki/File:Apollo_10_eart
knowledge is not available, the argument’s
hrise.png
first premise would be entirely unknown,
and not the basis for a good argument. Even to someone living on Earth
today, the above is not a good argument for the conclusion. It does not help
show how we come to know that the Earth is a sphere, because we could not
know that the Earth is a planet without already knowing that it is a sphere.
This set of statements is better appreciated as an explanation for the fact of
the Earth’s sphericity, not as an argument for knowledge of that fact.
Next: The premises must be relevant to the conclusion (they must be
likely to establish the conclusion as true). The argument given in the
previous section about human freedom is a good example of how premises
34
can be relevant to a conclusion. Here is the argument formalized (in case
you were still wondering what was the premise and what the conclusion):
Human beings need freedom in order to think and produce.
Thinking and production are needed in order to live.
Therefore, human beings need freedom in order to live.
Whatever you think of the truth of these
premises—whether you think we know them
well enough or not—it is clear that they are
relevant to the conclusion. “Needing X in order
to Y” is the kind of relationship that
philosophers call “transitive”: if you need X for
Y, and you need Y for Z, then obviously you
need X for Z. With that assumption in the
background, the conclusion follows quite
clearly. Bringing that assumption to the
foreground, we have:
Human beings need freedom in order to Picture credit 27:
http://www.flickr.com/photos/ajagendorf25/401
think and produce.
2265423/
Thinking and production are needed in order to live.
If X is needed for Y, and Y is needed for Z, then X is needed for Z.
Therefore, human beings need freedom in order to live.
In fact, the kind of relevance here is what logicians call deductive
validity: if the stated premises are true, the conclusion has to be true. To say
otherwise would be like saying that Al is taller than Bob, and Bob is taller
than Charlie, but still Al is shorter than Charlie. Deductive validity, which
we will explore more in chapters 17 and 18, is not the only kind of logical
relevance, but it is the most clearly obvious kind and the best example to use
here. Sometimes a conclusion will not be necessitated by the listed premises
alone, and sometimes our evidence will only establish a conclusion to
varying degrees of probability. We will explore examples of these other
types of relevance in chapters 14 and 15.
Now consider a simple example that violates the relevance
requirement:
35
Napoleon lost the battle of Waterloo.
Therefore, human beings need to be free.
Hopefully you agree that this is also an example in which we know the
conclusion to be true. A little knowledge of history tells us that the premise
is, as well. But what does the premise have to do with the conclusion?
Absolutely nothing. The military failures of a long-dead general have little if
any relationship to the timeless truths of human politics.
Not every argument involves premises that are as obviously irrelevant
to their conclusion as the example above. Consider this argument:
Freedom feels good and many people desire it.
Therefore, human beings need to be free.
Probably you will also agree that the premise here is true. But what do the
two statements have to do with each other? The premise would be relevant
to the conclusion only if we also knew this:
All things that feel good and which
people desire are things human
beings need.
But it is at least very debatable that this is
true. There are some illicit drugs that
make people feel good, and that some
Picture Credit 28:
people desire, but are they needed?
http://www.flickr.com/photos/aarmono/393650532/
Needed for what? Certainly not needed
for living in the way that thinking and production are needed. Now perhaps,
even if not everything that feels good is good, feeling good gives us some
degree of confidence that the thing is good. So at best the argument’s
premises are of questionable relevance to its conclusion. Depending on how
you interpret the meaning of our feelings, it may not be relevant at all. We
will discuss the question of the evidential relevance in greater detail in
chapters 4 and 6.
In the previous section logic was compared to a telescope and to a
ladder. In this section, the art of logic was compared to the art of cooking.
The first comparisons were to types of tools, the second to types of
activities. These aren’t unrelated comparisons, because some activities
concern themselves with the use and production of tools. Logic is both a tool
itself and an activity engaged in the use of tools. Think of it as a kind of
36
carpentry that uses a whole tool kit for
assembling and evaluating arguments.
Aristotle’s work on logic, not by coincidence,
was called the Organon, which in Greek meant
“tool.”
There’s another way to combine all of
the metaphors for logic into a single image: to
think of logic as a form of architecture, and its
products as
buildings. With
that comparison
in mind, we can
think of the ways
Picture Credit 29:
good and bad
http://commons.wikimedia.org/wiki/File:Olson
arguments are
_Observation_Tower.jpg
constructed along the lines of the architecture
metaphor. A good argument is a like a sturdy
building constructed on solid ground. Having
well-evidenced premises is like having the
solid foundation. Having premises that are
relevant to the conclusion is like having a
Picture credit 30:
building skeleton of sturdy construction. By
http://commons.wikimedia.org/wiki/File:Laputa
_-_Grandville.jpg
contrast, an argument without known premises
is like a building that tries to hang itself from “sky hooks”—something
which is of course impossible, however well constructed the building might
be. And an argument with irrelevant premises is like a building with shoddy
construction that might collapse at any moment—however solid the ground
beneath it might be.
There is one last, important
requirement of a good argument which is
not quite captured by the first two
requirements, and which we will focus on
exclusively in chapters 7 and 8: The
argument’s premises must contain all of
the known relevant evidence. It’s often said Picture credit 31:
http://commons.wikimedia.org/wiki/File:House_for_S
that there are only two certainties in life:
ale,_damaged.JPG
death and taxes. Whatever you may think
about the second, the first is as certain as anything could be. Why is it
certain if anything is? Because everything we know points to the same
conclusion: we’re all going to die some day. It is hard to enumerate all of the
37
evidence we have for this conclusion, but here is an attempt to list some of
the major categories of evidence:
Many people have died in the past.
No one alive today is older than 114.
All people fall along a continuum of states of growth and decay.
Human bodies are delicate mechanisms in which much can go wrong.
Therefore, all human beings are mortal.
Here is an example for a slightly different conclusion which clearly
does not look for all of the relevant evidence:
Every person in this classroom is alive.
Therefore, all human beings are
immortal.
We ought to know that there are places to look
outside of the classroom—and outside of the
immediate moment—for cases of human beings
who have died. If we’ve entered the classroom,
we know there’s an outside. And if we
remember what happened before we entered it,
we should know that there is a past. To make
Picture Credit 32:
this argument in spite of what we know would
http://www.flickr.com/photos/firepile/384292
1467/
be to ignore very relevant evidence.
Not every case of ignoring relevant evidence is as obviously
ridiculous as the example above. What if we argued for what we in fact hold
to be true about human mortality, but instead came to it this way?:
Many people have died in the past.
Therefore, all human beings are mortal.
Even though this argument relies on one of the premises in the earlier, better
argument, it does not rely on enough. We know that not all people have
exactly the same characteristics. Some are different sizes and different
shapes. If we only count many deaths in the past, we would know of nothing
in the nature of human beings that would account for their necessary
mortality. Perhaps these people who died in the past were simply unlucky, or
victims of a poor state of technological development. Merely building up a
lot of examples of mortality would not take into account all of the relevant
38
evidence. Here, the most important evidence we know we should look for is
evidence of the cause which would bring about the effect of death. Only
knowing that would give us any certainty of death’s necessity.
There is no easy way to make the requirement that an argument must
use all of the known relevant evidence fit the metaphor of a well-constructed
building, unless we stretch it to think about the way in which one building
can support another. When two buildings are constructed next to each other,
for instance, each provides mutual support to the other. Now imagine a
whole cluster of such buildings with a network of interacting supports. Such
a structure would clearly be superior to an individual building standing all
by itself. In the same way, the certainty of our knowledge is bolstered when
interconnects with more and more pieces of other knowledge.
The science and art of logic is like the discipline of architecture for
our knowledge. Just as there are principles of cooking and architecture, there
are principles of acquiring knowledge. We would not want our soufflés or
our buildings to collapse, so why would we not govern our thinking by
similarly strict standards—especially when we need this thinking to cook, to
build, and to engage in any other practical activity in life?
Exercises
1. Determine which if any of the basic requirements of good
argument is violated by these examples. Explain your answer.
Creating tools, building shelter, planting crops, and finding medicines
require special prayers to the Greek gods.
Creating tools, building shelter, planting crops, and finding medicines
are basic acts of human survival.
Therefore, the basic acts of human survival require special prayers to
the Greek gods.
The earth is good
All spheres are good.
Therefore, the earth is a sphere.
2. Take the example of an inference from a field of knowledge of
interest to you (from the last chapter) and state how much direct
observational knowledge it involves. Is its evidence directly
observable, or does it require argument of its own?
39
3. Think of an example of conclusion that could look plausible until
new evidence emerges to contradict it.
40
§2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 3:
Better known premises and the fallacy of begging the question
Ben Bayer
Drafted January 26, 2010
Revised July 19, 2010
The better known premise requirement
In the last chapter, we briefly discussed three basic requirements of good
reasoning:
1. The premises of the argument must be known and known
better than the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must be
likely to establish the conclusion as true)
3. The argument’s premises must contain all of the known
relevant evidence.
In this chapter we will focus on the first requirement in particular, but
mostly from a negative perspective. That is, in order to give a better picture
of what it is to rely on good evidence in our reasoning, we will examine one
of the major ways in which one can depart from this requirement. Sadly
there are more ways to depart from it than we can hope to cover, but one of
the major violations, the fallacy of “begging the question,” is all too
common and worth analyzing by itself.
What is it to have premises that are known and better known than
their conclusion? In the last chapter, I urged that this means that a premise
must be obtained either from a direct form of knowledge like sensory
perception or from some further argument whose premises ultimately derive
from a direct form of knowledge. Consider the following example:
Clouds are formed by the condensation of water vapor.
The condensation of water vapor releases heat.
Therefore, the formation of clouds releases heat.
It is difficult to measure the release of heat in clouds in the upper
atmosphere, so an argument like this allows us to make a prediction about
what we might discover there on the basis of two premises that are easier to
41
know. But how do we know them? Thankfully, these premises are easier to
know because we can make observations and experiments closer to solid
ground supporting them. But notice that they’re not themselves direct
observations. They each require a further argument from further premises
closer to direct observation.
Consider just the first premise, whose justification is easier to offer,
such that it was known as far back as Ancient Greece, whereas the second
was not proven until the 18th century. How would we know that clouds are
formed by the condensation of water vapor? Consider how we come to know
about such a thing as water vapor in the first place. Perhaps we are boiling
water over a fire, and we see steam rising from the pot. Something is coming
from the water. How do we know it is water vapor, and not just some
additional byproduct of the boiling process? Of course if we boil the water
long enough, and produce enough steam, the water itself eventually
disappears. Further, we can place our hands in the steam and notice that our
hand gets wet—we taste it and it is water. This experiment shows with a fair
degree of certainty that water evaporates into a gaseous form, but it doesn’t
yet show that clouds are a condensed form of water vapor—small droplets
hanging in the sky.
To know that clouds are formed
from evaporated water, we have to think
about all of the water sources that are
subject to evaporation during the day—
rivers, lakes, oceans—and consider the
heat source that must be causing them to
evaporate—the sun. All of that water
vapor must wind up somewhere in the
sky, and that’s where the clouds are.
Figure 1:
What else do we know about clouds that
http://www.flickr.com/photos/typicalnaloboy/4150265051/
confirm this? Of course we know that
rain comes from clouds. But unless we have an airplane, can we know that
clouds are water vapor? One way of knowing is from low-hanging clouds,
which we might come into direct contact with if we’re on a mountain—or if
we simply run into a bank of fog. It’s easy to see how dew forms on solid
objects in a fog bank. If we understand that these are clouds, we come to
know that the clouds higher up in the sky are also made of condensed water
vapor.
So really, to represent the argument for how we know that the
condensation of clouds must release heat, we would have to list many more
premises than in the argument listed above. Just to list a few more of these,
42
without even trying to list the premises behind the idea that water
condensation releases heat:
Heating water creates steam.
Creating enough steam causes liquid water to
disappear.
Steam condenses into water on surfaces.
Therefore,
Heating water transforms it into a gas.
Gaseous water travels into the atmosphere.
Large bodies of water are heated by the sun.
Therefore,
There must be much gaseous water in the Earth’s
atmosphere.
Clouds are in the Earth’s atmosphere.
Rain comes from clouds.
Low-hanging clouds condense into water on
surfaces.
Therefore,
Clouds are formed from the gaseous water in the Earth’s
atmosphere.
Therefore,
Clouds are formed by the condensation of water vapor.
The condensation of water vapor releases heat.
Therefore,
The formation of clouds releases heat.
In the above, we have indented and bracketed premises representing some of
the evidence needed to reach intermediate conclusions to the left, which are
needed, in turn, to establish that clouds are formed by the condensation of
water vapor, which is in turn a premise in the argument for the final
conclusion. We would need a whole series of other premises to establish the
second big premise, that the condensation of water vapor releases heat. We
would need to know about how heat is required to evaporate water in the
first place, and other experiments showing that molecules entering less solid
states of matter absorb heat. 7
7
http://www.meteohistory.org/2004polling_preprints/docs/abstracts/emeis_abstract.pdf
43
The point of the above is to impress upon you what it is to find better
known premises to support conclusions that are harder to know. We do not
typically have direct evidence that clouds are formed from condensed
water—let alone that their condensation releases heat. We are not typically
close enough to clouds in the sky to verify this directly, and we are certainly
never in the position to directly observe the process of heat transfer. So we
need to find evidence closer to earth and easier to observe that helps us come
to these conclusions. Sometimes we need an entire chain of reasoning, a
body of evidence that leads to a conclusion, which is in turn evidence for
further conclusions, to get to our ultimate conclusion.
Exercises
1. Think of an example of another ordinary belief (like the claim that
clouds are made of condensed water vapor) that requires a long
chain of reasoning to establish. Can you offer any of the needed
premises?
The illusion of good argumentation in the absence of better known premises
The fact that reasoning can work in chains like the one described
above is what allows us to come to conclusions about facts that are
extremely distant from the senses. But it can also cause various confusions
in the way we reason. Sometimes the fact that a solid chain of statements has
been presented can make it look like a good argument has been presented—
even if the premises of the argument are not better known. And sometimes
the length of the chain can cause the reasoner to forget that earlier links in
the chain simply repeat the conclusion that is supposed to come later.
An oar in water has a strange appearance: it looks bent, even though
you know it is straight. It is an optical
illusion. But there are also illusions of the
mind, arguments that have a veneer of
plausibility even though they do not deliver
knowledge. They appear to fulfill the
requirements of good reasoning, but they do
not really. Presently, we’re interested in the
requirement that arguments have premises
better known than their conclusion. Some
arguments can have features that distract
from the absence of better known premises.
Picture credit 33:
For instance, an argument’s premises can be http://www.flickr.com/photos/lisa_pedrosa/3045445
strongly relevant to the conclusion—its chain 88/
44
of reasoning can be strong—and this can lead reasoners to neglect what it is
that the chain leads back to.
Here’s a fairly simple example in which the presence of a strong chain
of reasoning could distract from the fact that its premises are not better
known than the conclusion. Suppose that one day you are flipping through a
chemistry textbook—chemistry being a subject you might not know a great
deal about—and you happen upon the following argument:
Cloud particles are made of two parts hydrogen and one part oxygen.
Two parts hydrogen and one part oxygen is water.
Therefore, cloud particles are made of water.
Both of these premises are, in fact, true. You may have even heard snatches
of science before that suggest to you that they are true. But are they any
better known to you than the conclusion? Could you even know them if you
didn’t already know the conclusion?
How, in particular, could you know that clouds are made of hydrogen
and oxygen without already knowing that they are made of water? It is hard
enough to know that water on ground level
is made of hydrogen and oxygen. Atomic
elements are not visible to the naked eye,
not even under an optical microscope. The
development of the atomic theory required
decades if not centuries of development,
beginning by distinguishing between pure
substances that have invariant physical
properties and those mixed substances that
do not. Scientists had to be able to
independently identify hydrogen and
oxygen as separate pure substances,
Figure 2:
http://commons.wikimedia.org/wiki/File:Electrolysis.svg
working with them first in their gaseous
form. Only after this could scientists run an electrical current through water
and learn how it produced these separately identifiable gases. To know that
the proportion of hydrogen to oxygen was 2:1 required even more advanced
discoveries.
Perhaps one does not need to know specifically that clouds are made
of water in order to know these facts about the composition of water. (Still it
would help: knowing that substances can exist in both liquid and gaseous
forms is important for being able to know that a liquid like water can be
composed of substances which themselves are better known as gases.) The
45
main point is that one could hardly avoid knowing that clouds are so
composed well in advance of knowing what water is composed of. This is a
symptom of the fact that the premises in the argument above are not better
known than the conclusion: this conclusion is already much closer to
observation than its premises, so these premises would not help us come to
know the conclusion. Perhaps if we were subatomic beings who had direct
awareness of hydrogen and oxygen atoms, we would know this chemical
composition of clouds and of water more easily than we could know that
clouds are made of water. But we are not these beings.
But notice that there is something appealing about this argument. If
we knew that clouds particles are made of two parts hydrogen and one part
water, and if we knew that this is the chemical formula of water, then we
would know that clouds are made of water. These premises are certainly
relevant to the conclusion. If you mistakenly believed that this was a good
argument, it might be because you were seduced by the relevance of the
premises without realizing that the premises were not themselves well
known. This happens especially easily when people have prejudices to
which the premises in question conform. Someone who thinks he already
knows what clouds and water are made of even when he doesn’t will think
that the above is a pretty good argument.
There are other prominent cases in which the relevance of the premise
to the conclusion will distract from the fact that the premise is not better
known than the conclusion, and hence create the illusion of a good
argument. In the rest of this chapter we will focus on a special fallacy that
draws its plausibility from a related kind of illusion of the understanding.
Consider this example:
Capital punishment is a form of unjustified homicide.
Therefore, capital punishment is murder.
This is the first example we’ve encountered in the book of an argument
involving value judgments. For the moment, put aside questions about what
it is for an act to be justified or unjustified—we will return to some of these
questions later in chapter 4. For the time being, simply note that the premise
here is one that at least some people agree with. And notice how premise
looks different, linguistically, from the conclusion. This is as we would
hope: for a premise to be better known than a conclusion, it needs to be
distinctly known. At the same time, the premise seems to be closely related
to the conclusion, for some reason. So while it seems to be distinct from the
46
conclusion, it is also relevant to it. So far, neither of the first two
requirements seem to be violated.
But like the argument above for
the claim clouds are made of water, the
present example offers only an illusion
of logic. If we look closely enough at
its premises and determine whether
they are really any different in meaning
than the conclusion, we’ll see that they
aren’t. In this case we have a very
special kind of logical illusion. At least
in the argument about the composition Picture credit 34:
of clouds above, the premises really do http://www.flickr.com/photos/joshstaiger/273593601/
state distinct facts from the conclusion—they’re just stated in the wrong
order (we could not know the premises before the conclusion). But the
illusion of the understanding in the second argument is more like the illusion
in a hall of mirrors: we see an endless set of windows converging at infinity,
but really it’s just the same scene repeating itself to infinity. It turns out that
the premise in this argument is not really different from the conclusion, and
so does not provide new evidence for it. We shall see why, and why there is
a “trick of light” involved in this argument, as we begin to examine the
fallacy of begging the question, of which it is a simple example.
Exercises
1. Look again at the argument for the composition of clouds from
premises about hydrogen and oxygen. What argument from
chapter 2 does it remind you of? What are the similarities in the
mistake being committed?
2. If you were a subatomic being with more or less direct awareness
of oxygen and hydrogen, would you still be able to defend the truth
of premises 1 and 2 of the problematic cloud argument?
3. Look at the argument about capital punishment. We have not yet
analyzed what is wrong with it. Can you guess?
Three simple versions of the fallacy of begging the question
In previous chapters, we’ve described a fallacy as a superficially
plausible but erroneous inference upon which people commonly rely.
Another author describes a fallacy as “a defect in argument arising from
47
some source other than merely false premises.”8 This is perhaps a more
precise definition, and we can appreciate why by reference to the present
fallacy of begging the question. As in the examples discussed in the previous
section, begging the question involves a premise that may in fact be true—
the problem is that the reasoner does not know it is true. As we shall shortly
see, this is because the reasoner is presupposing the very conclusion in need
of proof as a premise.
When trying to understand a type of fallacy, it is best to begin with
limiting cases: examples that are so simple and pure that they lay bare the
error that makes it an example of the fallacy that it is. Of course when the
error can be seen so clearly, one might wonder why anyone would be
deceived by the error or rely on it commonly. But the simple examples that
lay bare the error are not the arguments people rely on; they rely on
arguments in which the same error is subtle. That is why it is useful to
identify the nature of the error using the simpler examples first: so that we
can more easily recognize it when we get to the trickier cases later.
So, consider: nobody would ever be deceived by arguments like the
following:
We know the Earth is round because it is
round.
People should be free because they should
be free
I say so because I say so.
It’s wrong to lie because . . . it’s just wrong.
These are examples of simple repetition. Simply restating the claim that the
earth is round doesn’t bring us any closer to finding out how we know this.
The fact that the conclusion is exactly the same as the premise deprives us of
just about any illusion that some new evidence is being pointed to. Even
young children are able to see through the third statement when uncreative
parents assert it in defense of demands for obedience. It is really only the last
example that some grown-ups might still resort to, because many have
trouble thinking about what kinds of reasons would ever justify claims about
morality. But even here, the fact that we don’t know the reason for a claim
8
Patrick Hurley, A Concise Introduction to Logic.
48
doesn’t relieve us of the responsibility of finding one! (We will discuss in
more detail the kind of evidence we might give for value judgments in
chapter 4.)
While no one would find these “arguments” convincing, only a slight
change is needed to raise the level of deceptiveness. Consider these
examples, the last of which we previewed briefly in our previous section:
People deserve their liberty.
Therefore, human beings should be free.
The Earth is a three dimensional body with a surface equidistant from
a single point.
Therefore, the Earth is spherical.
Capital punishment is a form of unjustified homicide.
Therefore, executing convicted criminals is murder.
Each of these arguments involves the same error seen in the examples of
mere restatement, but the error is obscured by the fact that the premise and
the conclusion are different linguistically. Again, it looks like the evidence is
pointing to a new conclusion.
But a difference in language does not always imply a difference in
real meaning. We can see this most easily in the first example. “People” and
“human beings” are different words, but they are synonymous: they refer to
the same things with the same characteristics. “Deserve” and “should be”
may have subtly different shades of meaning, but for the most part in this
case they come to the same thing: the endorsement of some moral claim.
Finally, “liberty” and “freedom” are nearly identical in meaning as well.
This argument is a far cry from the one we presented in the last chapter for
human freedom, concerning its relationship to thinking, production, and
living. Those are facts that really are distinct from freedom itself, and facts
we know a good deal about.
The second and third examples are a little trickier because any
synonymy here is not just term-by-term. Instead of one term like “liberty”
matching up with another single term like “freedom,” in the second example
we have one term “sphere,” matching up with a complex of terms, “a surface
equidistant from a single point.” That is the definition of “sphere.” But the
effect is the same as in the first example. The premise makes the same claim
as the conclusion, and so doesn’t give us any new evidence that it is true.
49
(We now know what evidence is needed for this conclusion, and clearly it’s
not being given.)
The same issue is at stake in the third example, only this time the
definition in question—the definition of “murder”—is one that people are
sometimes not clear about. Sometimes people use the word “murder” to
mean just the same as “killing.” But at least according to prominent ethical
theories as well as common sense, there is a difference between justifiable
and unjustifiable killing. Justifiable killing
would include killing in self-defense, or
killing aggressors in order to defend their
innocent victims. We need the concept
“murder” to denote killing that doesn’t fall
under either category, and which is further
distinguished from the accidental killing of
innocents (which is called “manslaughter”
or “negligent homicide”). Murder is
intentional killing with no justification. For this reason, you can see that the
third example is also a case of restatement through synonymy, where the
synonymy is summarized by a definition.
Our third set of examples of the present fallacy, the last we need
before giving its definition, follows shortly. In these examples, unlike
previous examples, we begin with our conclusion rather than our premises,
and list a series of premises that must be taken in a specific order to make a
plausible case:
I know I am good, because:
People love me, which I know because:
They must, because I’m a good person.
People should be free, because:
People need dignity, because:
Dignity is the attitude proper to free people.
I know Al is trustworthy, because:
Bob says I can trust Al, and I trust bob because:
Charlie trusts Bob, and Charlie’s word is good because
Al vouches for Charlie.
50
As usual, the first example is the simplest example. Someone is trying
to convince himself that he is a good person. Suppose that other people did
love him. This might count as evidence that he is a good person, if we
suppose that the other people in question themselves have good character
and are apt to recognize it in persons other
than themselves. But how do we know
that these other people love the first? We
could imagine the kind of evidence that
would provide independent justification
for believing that some people love
another: perhaps they pay attention to
Picture Credit 35:
him, lavish gifts on him, embrace him,
http://www.flickr.com/photos/pheezy/480374623
etc. But our first example doesn’t present
this independent evidence. It just goes back to the original conclusion. It
might be true that if someone really is a good person, others will recognize it
and love him for it. But the problem here is that whether the reasoner does
know that he’s good is the very question at issue. So it can’t be relied upon
to prove itself! This is circular reasoning.
The other two examples rely on forms of circular reasoning, with a
few added twists. The second example also circles back to relying on the
very conclusion in need of proof, but it does it in an indirect way. The final
stated premise is “dignity is the attitude proper to free people.” The
conclusion to be proved was “people should be free.” These statements are
not exactly the same, but clearly if we applaud something (dignity) because
it is the attitude free people would adopt, this must be because it’s good for
people to be free. And that is the same as the conclusion in need of proof.
In the final example of circular reasoning, it is very clear how the
conclusion to be proved and the finally
stated premise are identical: the first is
the claim that Al is trustworthy, and the
second clearly depends on that claim. The
example here is included for its length:
there is some distance between the
statement of the original conclusion in
need of proof, and its restatement in a
premise later offered as part of the proof. The longer the distance to the
restatement, the harder it is to remember what one was trying to prove, and
the more likely that one will forget that a given premise is identical to the
conclusion being proved. Probably you won’t actually forget in the present
case—especially since you were already on the lookout for the restatement
51
of the conclusion. But circular reasoning can really gain its force from the
distance between premises and conclusion, as for instance in the distance
between intervening chapters in a book, or in the distance of years between a
philosopher’s authorship of one book, and another in which conclusion
works its way into the statement of one of his premises.
Suppose, for example, that you wanted to prove that the sun will rise
tomorrow. What justifies your belief in this claim? You might say: the fact
that you saw it rise yesterday, and the day before, etc. You believe the sun
will rise tomorrow because you trust your past experience, and assume that
the future will resemble the past. Very well, but why assume that the future
will resemble the past, and rely on your experience in this way? You might
be tempted to say in response that experience has been a reliable guide in the
past: often when you’ve relied on your stored knowledge in years past, it’s
turned out to be a fruitful indicator of the future. Your argument now looks
like this:
Past reliance on experience of the past has successfully
predicted past futures.
Therefore:
The future will resemble the past.
The sun has risen in the past every morning.
Therefore,
The sun will rise tomorrow morning.
Notice that the argument has now become somewhat complicated. The chain
of reasoning has been lengthened, since the premise “the future will
resemble the past” is in need of support itself. But why does the premise
listed at the top support “The future will resemble the past”? To appeal to
what we have relied on in the past is already to presuppose that the future
will resemble the past, the very claim in need of support. The circularity in
this argument was first pointed out famously by the philosopher David
Hume, who offered it as an example of the difficulty of demonstrating the
validity of what we now call inductive reasoning, reasoning from observed
particulars to the unobserved in the form of generalizations. We might still
think that induction is basically rational while accepting that this attempt to
demonstrate its rationality is hopeless.
Exercises
52
1. Evaluate the following argument. Does it commit one of the
fallacies described in the previous section?
We know God exists, because
The Bible says that God exists, and we trust the Bible because:
The bible is the Word of God.
“Begging the question” defined
We are now in a better position to give a definition of the fallacy
we’ve been discussing: the fallacy of begging the question. Begging the
question is the fallacy of taking as known the very conclusion in need of
argument. When calling it “begging the question,” we say that reliance on
the very conclusion in need of proof is “begging” the very question at issue.
The origin of the phrase “begging the question” is obscure,9 but you can
think of the somewhat odd use of the word “begging” in the same way that
we see people on the street begging: they ask for and rely on unearned gifts.
In logic, we “earn” our conclusions by proving them, but when we beg the
question, we refuse to earn our conclusions and instead rely on them as if we
could use them to prove themselves. In fact begging the question is even
worse than asking for and relying on the unearned. It is comparable to taking
unearned money from someone in order to repay a debt—to the very same
person.
One last point before we break to discuss subtler (and more deceptive)
forms of question-begging. Sometimes people—especially journalists who
are trying to sound like critical thinkers—will use the phrase “begs the
question” to mean “raises the question.” Here’s an example from a recent
college newspaper article:
With the Iranian resistance becoming more and more stubborn
and an Iranian government just as stalwart and unwilling to
compromise as ever, something must give way in the coming
year. . . This begs the question obvious to proactive
Americans: “What can we do?’”
--The Daily Nebraskan, January 12, 2010
It’s clear enough what the author has in mind here. The problem is just that as
more and more journalists use “begs the question” to mean “raises the
question,” more of them forget what the fallacy is. Too many times, then,
9
http://languagelog.ldc.upenn.edu/nll/?p=2290
53
there is little left to stop them from committing the fallacy. Interestingly, there
may be a genuine example of the fallacy in this very article. Think for
yourself about what assumptions the author is relying upon in this paragraph:
The religious overlords and their approved government have
always been strict, but dodged criticism as guardians of piety.
When they violently suppress their citizens who are marching
in the name of a religious man, on a religious day, they come
off as merely interested in power. Ideology, the government’s
greatest strength, seems to no longer be in play now that Iran
has its gloves off.
After our last two sections dealing with subtle versions of the fallacy of
begging the question, you may be able to return to this example and spot a
subtle version here, too.
As for journalists who misuse the phrase “begs the question,” you
may be interested to know that there is a recourse:
Suppressing controversial premises: begging the question through silence
Probably one of the most insidious forms of question-begging—insidious
because it is hard to notice when it is occurring, and therefore, hard to
combat—happens without anything even remotely like repetition of a
conclusion in the form of a premise. So far is this version of the fallacy from
merely repeating the conclusion as a premise, that the question being begged
54
does not even appear as premise or as conclusion in the course of an entire
argument. And that is precisely the problem.
Considering the two following political arguments, one more likely to
be made by members of the political right, the other, of the left:
Most people are offended by flag-burning.
Therefore, we should outlaw it.
Raising doubts about global warming stops us from cutting carbon
emissions.
Therefore, people who raise doubts about global warming are
dangerous.
The first thing to observe about these arguments is that the premises
stated are both fairly easy to know on their own. Most Americans probably
do find the idea of burning the flag to be offensive, and there are easy ways
(like polls) to verify this. Likewise, premise of the second argument is also
easy to make sense of: when “climate skeptics” raise challenges to the idea
that the Earth is warming because of man-made carbon emissions, and when
the public listens to them, it becomes more difficult to adopt public policies
aimed at reducing those emissions in order to solve the alleged problem. It’s
hard to motivate people to solve a problem which they don’t think exists. So
both arguments involve fairly well known premises, but begging the
question is supposed to be a problem involving whether the premises are
known or better known than the conclusion. So what is the problem with
these arguments?
The second observation about these arguments is that, at least on the
face of it, the premises are not directly relevant to their conclusions. If
people happen to be against a particular kind of protest demonstration, what
does this have to do with whether or not the law should ban it? And raising
doubts about a theory happens to make a policy difficult to implement. What
does that have to do with whether or not those people are dangerous? If
these premises are not directly relevant to the conclusion, why then is it that
we are classifying them as forms of question-begging, which is not supposed
to be a problem of relevance (the second big requirement of good
reasoning), but a problem concerning the evidence for one’s premises (the
first requirement)?
The answer to both of these questions is that there is at poorlyevidenced premise or at least a premise that is more in need of support than
the conclusion itself that is at work in this argument. The trouble is that it is
55
a suppressed premise, not seen explicitly in either argument. This is also the
reason that this is not primarily a problem of relevance. Given the type of
argument being made and what we know about the people who usually make
these arguments, it is reasonable to infer that they are counting on these
suppressed premises, and would probably affirm them if given the chance.
So even though the first premise is not directly relevant to the conclusion, it
is indirectly relevant once that suppressed premise is brought to light. The
reason this counts as a form of question-begging is that the suppressed
premise is the one most in need of proof, since it is likely the most
controversial idea at issue, and yet it is being relied upon as if one already
knows it is true. Let’s look at the suppressed premise that must be behind
each of these arguments in turn, and see why each is engaged in a kind of
question-begging.
The way to unearth the missing premise in each case is to think about
what kind of premise you would need in order to make the first premise
relevant to the conclusion. In our first example, it is something like the
premise we are now putting in parentheses:
Most people are offended by flag-burning.
(Anything people are offended by should be outlawed.)
Therefore, we should outlaw it.
So what is the problem with this suppressed premise? Of course, the
conclusion that we should outlaw flag-burning
is already fairly controversial. But it is possible
to hold it for reasons less controversial than this
one. Some might think it should be outlawed
because it has the potential to disturb the peace
or incite people to riots. Still others may think
that it is a kind of intellectual property of the
state, which has the right to protect it. Each of
these is a nuanced reason that would make the
first premise relevant, but not as controversial
as “Anything people are offended by should be
outlawed.” To see why this is so controversial,
try to imagine all of the other things we would
Figure 3:
have to ban in addition to flag-burning. We
http://commons.wikimedia.org/wiki/File:US_fl
would have to burn countless kinds of free
ag_burning.jpg
political speech, pornography, and various religious practices. If someone
eats a diet composed of meat and potatoes, and vegetarians found this
56
offensive, we would have to ban it. But if a meat-eater found a vegetarian’s
diet senseless and offensive, we would have to ban it, too! There is nothing
in a pluralistic society that somebody doesn’t find offensive, and by the logic
of this premise, just about everything would have to be banned. Now
perhaps the person advancing this argument could try to tame the
implications of his premise by saying it is only what offends most people
that should be banned. But that would still have fairly significant
implications. It would suggest that any political or religious minority should
be outlawed, because the majority opinion goes against it (by definition).
Anarchists and atheists would simply be forbidden to profess their beliefs.
And in a society where the majority happens to harbor prejudices towards
racial minorities, who knows what kinds of restrictions could be passed
against them. So you see, whatever it is to prove an ethical or political
premise—and there is much philosophical debate about how this might
occur—the burden of proof for a suppressed premise such as this would be
heavy, indeed. And unless we have reason to think that the reasoner
advancing this argument is assuming one of the more nuanced suppressed
premises, the only alternative is that he is assuming uncritically the
controversial premise. In that case, he is relying on the very claim that is
most in need of proof in this conversation. This makes it an example of
begging the question.
Now let’s look at the second argument, this time one that is more
likely to be made by people on the opposite end of the political spectrum as
those who would advance the argument above. As before we need to start by
identifying the suppressed premise:
Raising doubts about global warming stops us from cutting carbon
emissions.
(Cutting carbon emissions will stop dangerous global warming.)
People who raise doubts about global warming are dangerous.
Clearly if someone is concerned that
raising doubts about the existence of a
problem and stopping the implementation
of a policy is dangerous, they must think
that the problem really exists and that
failing to implement that policy intended
to solve it is dangerous. But notice that in
this case, the suppressed premise that
makes the first premise relevant to the
Figure 4:
http://www.flickr.com/photos/rizzato/2671575856/
57
conclusion is what amounts to a statement of the theory of anthropogenic
(man-made) global warming. But whether or not we should adopt this theory
is precisely what is at issue between the climate skeptics and the proponents
of the global warming hypothesis. I hasten to add that if the person making
this argument does have good independent reason to think that global
warming is happening, and that there are good independent reasons to think
that the doubts raised by skeptics are unscientific, then there is no problem
relying Figure 5on a premise like this. The trouble is that very often critics of
global warming skeptics make arguments like this with the suppressed
premise suppressed, as if it is already supposed to be self-evident to
everybody that global warming really is caused by human activity and
clearly dangerous. But it is not self-evident—it takes proof—and if the
disputants do not actually discuss that proof, but instead rely on
conventional wisdom to blame the skeptics for being “dangerous,” then
those advancing this argument are begging the very question at issue,
because the skeptics are claiming to question whether there is adequate proof
for the hypothesis. Perhaps they are wrong and there is adequate proof, but
then that needs to be established, not just dismissed.
Why do people who advance arguments on controversial matters
leave the most controversial premise—the belief most in need of proof in the
overall discussion—suppressed? Usually this is because the person is
wearing “ideological blinders.” Sometimes people can be so immersed in a
particular political ideology, for instance—sometimes they can be so
accustomed to having their friends or family agree with them on these
matters—that they lose sight of the fact that there can be differences of
opinion on these matters. They end
up taking for granted that what they
are offended by, for instance, should
be the standard of public policy, or
that their particular worldview about
the destructiveness of industrial
capitalism is so obviously true that all
known science simply must recognize
it. The trouble is that religious or
ethical or political ideologies are not
Figure 6: http://www.flickr.com/photos/virtualsugar/357908606/ self-evident to everyone concerned.
They may seem that way when they are reinforced by an agreeable peer
group, but this is often the accident of not associating with enough people
outside of our peer group. As mentioned above, there is much philosophical
debate about how or even whether controversies about basic core premises
58
in religion, ethics, and politics could ever be settled by logical
argumentation. But the fact that it is a difficult question to answer does not
mean there is no way to answer, or that we should just give up and go with
our prejudices. Instead we should think carefully and philosophically about
these core premises, and see what kinds of reasons we might be able to give
to defend them. This is one of the reasons it can be so beneficial to study
philosophy.
Exercises
1. Consider the following exchange between skeptical humorist
Woody Allen and renowned evangelical preacher Billy Graham.
Do you see any instances of begging the question? If so, why?
Allen: Do you remember the worst sin you ever committed?
Graham: . . . If you wanted to find out which sin is the greatest, I
would choose, if I were forced to choose, I would say idolatry,
breaking the first commandment, “Thou shalt have no other gods
before me.
Allan: . . . And that doesn’t seem as, say, an egomaniacal position?
Graham: . . . Oh no, God is perfect.
Begging the question through the arbitrary redefinition of terms
A final form of question-begging is similar to the one we have just
described, especially insofar as it relies on a suppressed assumption to allow
a desired conclusion to follow from the evidence. Only in this case, it is a
very specific kind of suppressed assumption that is at stake: an assumption
about the definition of a term.
Consider these examples:
Professor Lindzen isn’t a real scientist because he doubts the
manmade global warming hypothesis.
Therefore, all scientists believe in the man made global warming
hypothesis and we can trust that it exists.
Even Woody Allen is beautiful in God’s eyes.
Therefore, everyone is beautiful and God is a perfect creator.
59
The first of these arguments we can imagine being advanced by a
defender of the manmade global warming hypothesis. The premise of the
argument is needed to prove the conclusion (among other premises), because
some might cite Professor Lindzen, a prominent meteorologist at M.I.T., as a
counterexample to the claim that all real scientists believe in global
warming. The arguer, however, claims that Lindzen is not a real scientist.
After all, he does not accept a popular scientific theory.
Clearly the definition in question here is that of “scientist.” Normally,
we would define a scientist as a practitioner of science, the intellectual
discipline devoted to uncovering explanations of natural phenomena. Here,
however, the arguer is relying on a suppressed definition of “scientist” that
would have to differ from the ordinary definition:
(A real scientist is, among other things, someone who does not doubt
the manmade global warming hypothesis.)
Professor Lindzen isn’t a real scientist because he doubts the
manmade global warming hypothesis.
Therefore, all scientists believe in the manmade global warming
hypothesis and we can trust that it exists.
Not only is the first premise here an example of a suppressed controversial
premise, but it is also a suppressed controversial premise that, for the most
part, takes for granted that the conclusion has already been proved. The fact
that it at least as controversial as the conclusion to be proved is bad enough,
however: the ordinary definition of a scientist as a seeker of explanations of
natural phenomena seems to leave open whether or not one regards any
theory about the cause of global warming as the best. And defining a
scientist’s work by the method involved in the work, rather than by any
particular outcome of that method, seems a far more fundamental and
relevant way to define it.
Later in chapter 13, we will discuss various rules of definition that
would support this assessment of the definition. For the time being, it is
enough to note that the definition is clearly being adopted because it is the
one that makes the conclusion come out as desired, which makes it arbitrary
and not better known than the conclusion. This particular example of
begging the question through arbitrary redefinition of a term seems to be
akin to a famous example once described by the philosophy Antony Flew, an
example that later inspired logicians to call this the “No true Scotsman”
fallacy:
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Imagine Hamish McDonald, a Scotsman, sitting down with his
Glasgow Morning Herald and seeing an article about how the
“Brighton Sex Maniac Strikes Again.” Hamish is shocked and
declares that “No Scotsman would do such a thing.” The next
day he sits down to read his Glasgow Morning Herald again
and this time finds an article about an Aberdeen man [Aberdeen
is a city in Scotland] whose brutal actions make the Brighton
sex maniac seem almost gentlemanly [Brighton is a city in
England]. This fact shows that Hamish was wrong in his
opinion but is he going to admit this? Not likely. This time he
says, “No true Scotsman would do such a thing.” 10
The second of these arguments was actually advanced by Billy
Graham in an exchange that followed the quoted exchange in the previous
exercise. Graham advanced this argument because Allen had challenged the
idea that God was perfect, by challenging the idea that everything God
created is perfect. As evidence, Allen cited the way he looked in the mirror
in the morning. Graham countered this claim by arguing that really everyone
is beautiful, because even homely Woody Allen is beautiful, beautiful “in
God’s eyes,” that is.
What is suspicious about this argument? The trouble is that Allen’s
objection to Graham depends on an ordinary concept of “beauty.” Because
Allen doesn’t think he is beautiful in the ordinary sense, he thinks a creator
God must have produced an imperfect product. But Graham redefines beauty
to mean “beautiful in God’s eyes.” It’s not clear what this is supposed to
mean, and if it were a valid standard of beauty, then of course everything
could be made to be understood as beautiful, even sin and death. One also
wonders why one should be impressed by the perfection this argument is
supposed to attribute to God, since it would also have to be “perfection” in
an unusual sense, the kind of “perfection” that creates “beauty” in an
unusual sense. Graham’s definition is arbitrary because it is appealed to
mainly so that his argument can reach his desired outcome: to demonstrate
that, contrary to any objections, God really is perfect after all. The overall
problem is that Graham’s definition, rather than being derived from the
observable difference between Woody Allen and Brad Pitt—that is, from
actual evidence—is made to order just to reach a desired conclusion. In that
way it is much like circular reasoning and begging the question through the
10
Antony Flew, Thinking about Thinking, 1975.
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suppression of controversial premises. The arbitrary definition serves the
same role as a conclusion that is relied on as a premise, or the suppressed
controversial premise that does the work of an inference behind the scenes.
In each case, something crucial is being taken for granted, when in fact one
should have evidence for the assumption.
Exercises
1. Does the following argument involve begging the question through
arbitrary redefinition? If so, what term is being arbitrarily
redefined? What is the proper definition of the term, and why is the
assumed definition arbitrary?
Even Mother Theresa is selfish, because she wants to help the
poor.
Therefore, everyone is selfish.
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§2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 4:
Relevance and the fallacy of subjectivism
Ben Bayer
Drafted January 30, 2010
Revised July 23, 2010
The relevance requirement
In our chapter 2, we first listed three basic requirements of good reasoning.
1. The premises of the argument must be known and known better
than the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must
be likely to establish the conclusion as true)
3. The argument’s premises must contain all of the known
relevant evidence.
As before, in the present chapter we will examine one of these requirements
in particular, especially looking closely at how it is violated flagrantly by
one type of fallacy, what we will call the fallacy of “subjectivism.”
What is it for a premise to be relevant to a conclusion? In chapter 2,
we began by giving an example with premises that were strongly relevant to
the conclusion.
Human beings need freedom in order to think and produce.
Thinking and production are needed in order to live.
Therefore, human beings need freedom in order to live.
With the addition of the premise that if X is needed for Y, and Y needed for
Z, then X is needed for Z, this argument became deductively valid: if the
premises were true, the conclusion would have to be true. This form of
relevance is of the strongest kind, when the truth of the stated premises
forces the truth of the conclusion.
Not every form of relevance is as strong as deductive relevance. We
also mentioned that some premises might lend only degrees of probability to
a conclusion. Consider, for instance, this argument for the same conclusion,
whose premises are seemingly relevant but not as strongly relevant:
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In unfree countries, human beings are less likely to be prosperous and
happy than in free countries.
Therefore, (probably) human beings need freedom in order to live.
Here we can assume that the premise is supported by information easy for
journalists to access, data from countries like North Korea, Iran, Myanmar,
Zimbabwe, etc. Why
are the premises not
as strongly relevant to
this conclusion?
People in unfree
countries may be less
prosperous and less
happy but a) they may
not be this way
because they are
unfree, and b) even if
Picture credit 36:
http://commons.wikimedia.org/wiki/File:2009_Freedom_House_world_map.svg
they need freedom
for happiness and
prosperity, they may not need them to live. This is why we’ve prefixed a
“probably” to the conclusion here. Maybe it is an accident of geography or
climate that they have the economic and psychological status that they do.
Maybe people in freer parts of the world can afford to be free because they
are already more properous. It would take further evidence than what is
stated in the first premise to rule out these reasonable possibilities that are
inconsistent with the conclusion.
Nevertheless it seems that the data in this single premise does provide
at least some preliminary evidence for how people need freedom to live. We
have background knowledge that when an entire country differs in standard
of living from another country, countrywide factors such as differences in
politics can help explain the difference. This helps us take seriously the
possibility that the correlation between the political system and the standard
of living is not an accident. What’s more, we also have the background
knowledge that political freedom and standard of living are not unrelated to
the ability to survive. A government with the power to restrict individual
liberty on a grand scale also has the power to undertake and hide the use of
deadly force. Further, material prosperity is not without connection to
material survival. The more material wealth a country has, the further its
inhabitants are from starvation and disease. Even the psychological state of
happiness has some effect on a person’s motivation to keep living.
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Notice the important role of background knowledge in our
assessments of the relevance of the premises in the argument above. We
decided that the
premises were
somewhat relevant,
but not strongly
relevant to the
conclusion,
because we possess
some general
knowledge
pointing to the
Picture credit 37:
possibility of a
http://commons.wikimedia.org/wiki/File:GDP_nominal_per_capita_world_map_IMF_2008.png
connection
between the premise and conclusion, but other background knowledge
suggesting that there may be no connection. So, for instance, we have
general background knowledge about geopolitics that suggests that
government policies can and do affect a nation’s entire population, and
knowledge from economics, biology and psychology that a nation’s material
condition can bear on the ability of its people to survive. But we also have
general knowledge from other fields, such as geography and climatology,
that other factors besides politics can influence a people’s well-being. We
may also think that our knowledge from economics, biology and psychology
about the connection between material condition, freedom, and survival is
not conclusive, and we may believe that we know of places where people
without high degrees of freedom or material prosperity have nonetheless
lived long lives.
How do we decide which of our background knowledge is most
relevant to the question at hand of the vital importance of freedom? How do
we decide, for instance, that factors such as geography and climate are
negligible, and that political freedom is preeminent? That is a hard question
for political philosophers, but notice that if the premises of the original
argument about freedom were known to be true, they would indirectly
highlight which background knowledge is the most relevant, which is part of
why the argument from these premises is much stronger:
Human beings need freedom in order to think and produce.
Thinking and production are needed in order to live.
Therefore, human beings need freedom in order to live.
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If we really knew, for example, that thinking and production were not only
necessary for human life, but in the long run, some of the most important
tools of human survival, and we really knew that political freedom is an
important necessary condition for the exercise of thought and production, we
would be able to decide that geographical and climatological factors were
less fundamentally important. After all, the way human beings cope in the
face of inclement climate or landscape is by using their minds to devise new
tools and new technologies to make life easier. If the restriction of their
freedom makes it harder to innovate in this way, then we could reasonably
infer that whatever the physical circumstances of a country, its degree of
political freedom is the most important variable determining the ability of its
people to survive and flourish. Of course this is a great many “ifs”: it is the
job of the political philosopher to think about whether these two premises
about the importance of freedom, thinking and production are really true.
The philosopher would need to bring to bear a large amount of still further
background knowledge in order to determine their truth: knowledge about
human nature and the good life, and ultimately principles from the broadest
questions of philosophy.
The examination of the role of background knowledge in the
assessment of relevance will be something of a subtheme in many of the
chapters that follow. Occasionally, we will even return to the role of
philosophic judgment in organizing our background knowledge in the way
we’ve suggested it might in the example above. The point of the previous
discussion is to show that our background knowledge helps determine how
strongly relevant premises can be to a given conclusion. As we shall see in
the next section, this point must be kept in mind when assessing arguments
in which the premises bear no relevance at all to their conclusions.
The illusion of good argumentation via the illusion of relevance
Even if the weakly relevant premise in the previous example is only
weakly relevant, it still is relevant. We know from examples in the chapter 2
that there can be arguments in which the premises are not at all relevant to
the conclusion in any obvious way, for example:
Napoleon lost the battle of Waterloo.
Therefore, human beings need to be free.
But if examples like these were the only ones in which premises could fail to
be relevant to the conclusion, the task of logicians would be very simple,
indeed—because no one is convinced by such an argument!
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Why is it so obvious that there is no relation between the premise and
conclusion? It is not that there is only one premise. In the previous section
we considered a single premise (concerning standards of living in unfree
countries) that did appear to bear relevance to a conclusion (about the
importance of freedom). In that case, though it was not explicitly stated as a
premise, we had background knowledge suggesting a connection between
facts about freedom, standard of living, and life. The problem with the
Napoleon argument is not only that we have no background connection
linking the outcome of a single historical battle and a timeless question in
philosophy, but that we have background knowledge suggesting that there
could be no connection. We think that the general facts of human nature
which determine our needs are independent of individual historical events.
Unless we have reason to think there is a mechanism by which Napoleon’s
loss could have some effect on human nature in general, we do not think
there can be any relevance between this premise and conclusion.
The logician’s job is made harder by the fact that some arguments can
involve an illusion of relevance, just like the arguments we examined in the
last chapter involved an illusion of having evidence or better known
premises. Consider this specimen:
This ball is heavier than this paper clip.
Therefore, this ball will fall faster than this paper clip.
In the first argument, the premise seems relevant to the conclusion, so much
so that for hundreds of years, many people—including philosophers and
scientists—accepted arguments like this as quite convincing. They took the
premise to be relevant to the conclusion
because they assumed as a suppressed
premise that heavier objects fell to the
earth faster than lighter ones. Careful
experiments, conducted most prominently
by Galileo, showed this to be false. (The
reason that people suspect otherwise is
because some lighter objects, like
feathers, may also exhibit air resistance
that makes them float to the earth rather
Picture credit 38:
than plummet. The illusion of relevance,
http://commons.wikimedia.org/wiki/File:Pisa_experiment.
png
then, came from the failure to distinguish
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between weight and the role of air resistance. Only with experimentally
devised bodies of identical shape and different weight (and later,
experiments in vacuum chambers) could this distinction be made clearly.
Consider another argument involving illusory relevance:
All communists are atheists.
Therefore, all atheists are communists.
In this argument, the premise appears to be relevant to the conclusion
because of a linguistic similarity between premise and conclusion, in much
the same way that linguistic difference created an illusion of evidence in
examples of question-begging. Both premise and conclusion mention
atheism and communism. And this similarity leads some people to fall for
arguments like this. The reason the argument fails is that “All communists
are atheists” at best shows that communists are a subcategory of atheists, not
that they are identical with the category of atheists. Especially since religion
and political philosophy are nominally separable issues in a person’s belief
system, there may be other subcategories of atheists apart from communists.
There might be godless capitalists, for example, in spite of the fact that
secular people in America are predominantly on the political left.
In cases like these, the illusion of relevance created either by mistaken
background beliefs or linguistic similarity has the same effect as the famous
Penrose staircase optical illusion, immortalized by the drawings of M.C.
Escher. Following the path of the
stairway with our eyes, we seem to
keep ascending forever as we go
around and around in circles. But we
know that when we reach the same
landing over and over again, we could
not have gotten any higher. In the
same way, an argument with premises
that have only illusory relevance to a
conclusion seems to carry us from
some evidence, “higher up” to a new
Picture credit 39:
conclusion. To invoke the metaphor of http://en.wikipedia.org/wiki/File:Impossible_staircase.svg
the tower we used in the second chapter, this seems to take us higher and
“see” further. But, like the Penrose illusion, we know that this argument
can’t really be helping us to see new things, it is just an illusion that results
from tricks of argumentative “geometry.”
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The kind of illusion of relevance we will focus on in the rest of this
chapter is similar to the argument for the claim that “All mortals are men”
insofar as can rely on a kind of linguistic similarity to create the illusion of
relevance, though this is not the only source of the illusion. Consider the
following example:
I share the feeling of many that all people ought to be free.
Therefore, therefore all people ought to be free.
As in the “All mortals are men” argument, in this one there is a significant
similarity between the lone premise and the conclusion. At least as it is
written on paper, the premise involves much of the same language as the
conclusion. However the argument is to be presented, what’s clear is that
both the premise and the conclusion have the same content. The question is
whether the status of their content is the same.
Is having a feeling that something is true really evidence that it is true?
Generally speaking, most people would agree that a feeling is not the same
thing as evidence. Feeling that the Earth is flat is not the same as having
actual evidence that it is flat. But there are some topics, especially questions
concerning value judgments, for which people are more likely to see
subjective feelings as the only possible source of judgment. Whether or not
they are correct to think that some topics are the exclusive province of
subjective opinion is a question we cannot answer at the moment, but we
will return to it towards the end of the chapter. For the time being, it is
important to note that there is at least a difference between evidence and
feeling in principle, and we must on guard against conflating the two, even
when they have the same content.
If a feeling is not evidence of truth, then the argumentative illusion
created by arguments like the above may
be similar to the optical illusion created
by looking at distant stars: we perceive
their light in the moment, but because the
light has traveled so far, the stars which
produced it may have gone supernova
and long ago ceased to exist. We are left
with what a real star would look like,
from afar, but the star is no longer there.
As we will begin to see both in this
chapter and in chapter 6, our feelings at
most “echo” the content of our past
Picture credit 40:
http://commons.wikimedia.org/wiki/File:SN1994D.jpg
69
thinking—past thinking which is not even necessarily correct—and this has
significance for whether they should count as evidence, even on matters that
are often regarded as the domain of “opinion.” All of this will give us reason
to be on guard against the fallacy of subjectivism, examples of which we are
about to examine.
Three simple versions of subjectivism
As in chapter 3, we begin here with the simplest versions of the fallacy to be
analyzed, and gradually build up more and more complex (and persuasive)
versions of the same.
Here, I think, are examples of the present fallacy which few if any
would find very persuasive:
I strongly believe the earth is flat.
Therefore the earth is flat.
I feel it would be healthy to jump out this window and fly.
Therefore it will be healthy to jump out this window and fly.
I want people to be my slave.
Therefore people should be my slave.
In each case, I assume that most of us agree that the conclusions are false.
But notice that each of the premises contain statements that could easily be
true and in many cases were true of some people at various times in history.
People really have believed that the earth is flat. Pentecostal religions like
the Christian Catholic Apostolic Church led by John Alexander Dowie
championed the flatearth doctrine well
into the early 20th
century, and an
organization called Picture credit 41: http://theflatearthsociety.org
the Flat Earth society was active into the 1950s and 1960s. Likewise, people
who have partaken of the wrong kind of “recreational” drug can many
strange feelings and feel that jumping out the window and flying is a safe
thing to do. And surely the desire to have others as one’s slave was part of
the motivation of historical slave-holders.
So if we know these premises about what people believe, feel and
desire can be true, but that the conclusions are false, it must be that these
premises are simply not relevant to establishing the truth of their
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conclusions. What do these premises all have in common? What do belief,
feeling, and desire all have in common with each other? How does a belief
that the earth is flat differ from the earth’s being flat, for instance? The
answer is that whereas a belief is a state of mind, the earth’s shape is
something out there in the world, not in the mind. Likewise, feelings and
desires are also mental states, as distinct from facts about health and about
the rights of other human beings (if we assume that there are facts of human
nature grounding moral claims about individual rights).
Seeing the difference between the mind and the world helps us
understand why premises of this kind are not obviously relevant to the
conclusions. These premises are linguistically similar to the conclusions, but
the difference between a mental state and a non-mental state is quite
significant, significant enough that there is no clear reason to think that
possessing one (e.g., the belief that X) is relevant to concluding the other
(e.g., the fact that X). The fact that someone believes or feels or wants X to
be true does not mean it is true. Beliefs can be false, feelings can be inapt or
unhealthy, and it is possible to desire what is wrong or even evil. By the
same token, our beliefs can’t create the facts in the world that they purport
to be about, to guarantee that they come out right. We will expand on each
of these points later in the chapter.
Let’s now examine examples of the same kind of argument which
people have taken more seriously historically, or continue to take seriously
even today. We divide each of these types by a specific kind of motivation
experienced by the arguer. Sometimes there can be elements of each of these
two motivations in a given argument, so the line between them is not always
crisp. Indeed the previous examples probably involve elements of each. But
at least in this next set of arguments, the motivation is especially clear:
I have always felt that I am doomed to failure.
Therefore, I am doomed to failure.
I’ve long believed that human beings will never fly.
Therefore, human beings will never fly.
It’s hard to imagine how species could have evolved over millions of
years.
Therefore species could not have evolved over millions of years.
I grew up thinking it was okay to steal.
Therefore it is okay to steal.
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What unites each of these arguments? As in the previous set of examples, we
have an appeal to some state of mind as a form of evidence. So these all
involve the same mistake as before, but
in spite of this they can be more
persuasive. Why? What else do they
have in common? What is the particular
attitude each arguer takes toward his
mental states? It’s not just that mental
states are regarded as a source of
evidence. In each case, the arguer
assumes that he could never have a
reason to change his mind. Each of
these arguments is one that would be
Picture credit 42:
made from a position of mental laziness
http://www.flickr.com/photos/oddsock/267206444/
or lethargy or inertia. The arguer knows
that there is effort involved in thinking, in checking whether one’s
conclusions are well-supported by evidence, but doesn’t want to expend that
effort. These are the arguments of an intellectual couch potato.
For example, many people will observe that they have failed in many
exploits in life. Who among us cannot observe this? But the mentally lazy
way to deal with this fact is to assume that there must be some inherent
limitation on our abilities, some kind of “fate” that hangs over us and dooms
us to eternal failure. If the world is simply out to get us, why bother trying to
fight it? We do each have limitations in what we can do, but if we find we
lack skills in one area, we may find we can develop them in another.
Nobody is completely without talent. The active-minded approach to
evidence of past failure is not to welcome more failure, but to find out what
kinds of errors we may have made in estimating our skills in the past, try to
find where our real skills are, and find out the best way to make the most of
them.
The next two examples involve the same kind of mental lethargy. In
particular they each betray a lack of imagination. Of course it took
geniuses—the Wright brothers and their predecessors—to find the precise
way to make heavier-than-air flight possible for human beings. But an
active-minded person should probably not have ruled out the existence of
this possibility in advance of their innovations. Birds, for example, are
surely heavier than air, and still can manage to fly. They also do so by a
demonstrable mechanism (their wings), and so there should at least have
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been some reason to think human beings could grasp this mechanism and
replicate it on a different scale.
Understanding how one species can evolve from another, in the
manner described by Darwin’s theory of evolution by natural selection, is
certainly a great deal more difficult than understanding how to build planes.
It took Darwin’s collection of a great deal of evidence from incredibly
diverse fields of knowledge to understand how gradual change over millions
and millions of years could account for seemingly radical changes in the
fossil record. Perhaps one would be justified in ruling out the possibility of
this radical change if one did not know about the evidence from geology that
showed how many millions of years the earth has existed. But all one really
needs to at least accept the possibility of such change is evidence of the
success of dog-breeders: how they have been able to select their dogs’ mates
and, merely in the course of hundreds of years, produce surprising diversity
among the ranks of man’s best friend. Once we know how much time nature
may have had to produce the same diversity, evolution by natural selection is
at least quite conceivable, if not yet proved.
What about the last example, concerning stealing? People can be very
entrenched in their beliefs about values, whether moral or political. Our
values are even part of what makes us who we are, and abandoning them can
be painful—especially if we change our value beliefs in a way that implies a
negative estimate of ourselves, even if only of our past selves. Only
courageous people are willing to exert the effort needed to change these
beliefs and bear the temporary pain associated with doing so. But beliefs
about values—for instance, about whether it is right or wrong to steal—are
still just beliefs, mental states that are separate from the rest of the world.
Part of the reason that many have difficulty understanding why there
may be reason to change their value judgments is that they may not be able
to imagine the kinds of facts these beliefs might be answerable to. They may
even have the background belief that moral values are relative to one’s
personality or culture, and therefore that we have no way of reconciling
disagreement about morality. But relativism is not self-evidently true. If it is
true, it will take an argument to establish, to dismiss various facts of our
experience which tell against it. We will return to this question later in the
next section, so for now we can only urge that students not passively assume
that relativism is true: this assumption might itself suffer for a lack of
imagination!
A final set of arguments (if they can really be called that), suffer from
the same basic error, but can be especially forceful:
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It would be terrible if this lipstick on his collar was evidence of an
affair.
Therefore, this lipstick on his collar is not evidence of an affair.
I really need to win this next round of poker.
Therefore I will win this next round of poker.
I want to think my spouse will stop abusing me and can be forgiven.
Therefore, my spouse will stop abusing me and can be forgiven.
I like to think that I’m not stealing this car, but borrowing it!
Therefore, I’m not stealing this car, I’m borrowing it!
Some of these arguments may involve explicit
reference to mental states in their premises,
while some involve only indirect reference.
Some of them may even be advanced through
the same kind of laziness witnessed in the
previous set of examples. But there is an
additional motivation that would have to be
present in each case, because in each case, the
arguer is not just failing to look for evidence
or imagine possibilities, but actively
suppressing evidence in front of his nose.
What motivates the arguer to suppress this
evidence? There is something that the
evidence reveals which the arguer does not
Picture credit 43:
want to accept. These are arguments adopted
http://www.flickr.com/photos/36791303@N00/23
5648648
out of wishful thinking—that is, pretending
that the evidence doesn’t show what it does show, as a result of elevating
one’s wish above the facts.
The lipstick on the collar argument is a textbook example. Learning
that a lover is cheating is a terrible discovery. Some people would rather live
with a cheating mate and receive the benefits of a deceptive relationship than
risk ending it by bringing the infidelity to light. But even this is not wishful
thinking: at least these people are willing to recognize for themselves that
their mate is cheating, and learn to live with it. While the merits of this
decision are debatable, it is infinitely superior to deluding oneself into
believing that really one’s mate isn’t even cheating in the first place. Here
the victim of infidelity pretends that he or she can make the fact of the
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infidelity go away by refusing to acknowledge it. Sadly, as too many have
learned, this cannot be done. Similar analysis applies to the rest of these
examples, including the qualification about value judgments from the
previous set in regards to the last example. The error here is the same; it is
only worth pointing out that the motivation for the error differs. Because the
motivation here is a powerful wish, rather than laziness, the error here can be
even more misleading.
Exercises
1. Is there mental laziness or wishful thinking in these examples?
Why or why not?
These others from this foreign land look totally different from me
and make funny noises. They must not be human beings, but some
kind of subhuman creature.
If there is no afterlife, that means we are just food for worms. Then
life would be pointless and death horrible. So there must be an
afterlife!
I share the feeling of many that all people ought to be free.
Therefore, therefore all people ought to be free.
“Subjectivism” defined
Having surveyed these three sets of examples, we can step back, observe
what they have in common, and define the fallacy they each commit. The
fallacy is subjectivism, which is the fallacy of inferring the truth of some
idea from mere belief in that idea, or from some other mental attitude
toward it (desire, hope, feeling). We call this fallacy “subjectivism” because
the person using this style of argument proceeds as if our mental states, i.e.,
our subjective states, could somehow create reality.
Why is subjectivism an error? The answer has been implicit all along,
but it is worth expanding upon here. First, what is true is determined by the
impersonal universe; it is not up to us and our minds. Reality is “out there,”
independent of our minds, which means that we can be incorrect in our
assessment of it. We are fallible. As you may recall, this was one of the main
reasons we needed logic in the first place: we needed a method of guiding
75
our thinking to arrive at the truth. Simply going with our first belief or
feeling is not a method.
Second, our beliefs, feelings, and desires do not affect the world in a
way guaranteeing that we are right. We can bring new things into existence
by making certain decisions, as when we decide to flip a switch and turn the
lights on. But this is not because we believe in advance that the lights are on.
We can even use our imagination to invent whole new types of things (like
airplanes), but we can only do this by drawing on our preexisting knowledge
of what is possible to certain elements in the world (for example, birds), and
then create new effects by recombining them in a new way. We do not
invent the airplane by believing that has already been invented!
The issue here is not that facts about our states of mind cannot be
evidence for anything. We surely can know facts about our state of mind, the
knowing of which can be relevant to establishing other truths. But the truths
that would be so established are fundamentally truths about ourselves.
Suppose someone knows that it would be terribly painful if the above
mentioned lipstick on the collar turned out to be a sign of an affair. This is
surely evidence that one cares about one’s relationship and detests lying.
From this evidence, one might also infer that one believes strong moral
character to be an important character trait of a mate. One might then be
motivated to find out whether or not one’s mate really lives up to these
values, rather than defaulting on them by lying to oneself. Notice, however,
that in drawing these inferences from evidence about what one believes, one
is not committing the fallacy of subjectivism and inferring from one’s fear of
infidelity that infidelity is not occurring.
So far we have characterized subjectivism as the appeal to mere belief
in some idea as evidence that the idea is true. But once many students learn
about the existence of this fallacy, they start to think they see it
everywhere—even many places where it probably isn’t. The problem with
subjectivism is appealing to mental states alone as evidence—that is, mental
states in the absence of any other real evidence, the kind that comes
primarily from sensory observation. But there is nothing wrong with
expressing what one thinks if one has evidence for thinking it. Sometimes
students assume that the mere fact of thinking something renders it
catastrophically subjective, as if there is some problem with not being able
to get out of our heads to be the truth without having to think it. But this is
nonsense! We have already seen examples of arguments that involve good
logic, and there can hardly be arguments with good logic unless there are
thinkers to think them. For this reason there is nothing logically wrong with
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the use of the language of “thought” or “belief” when one is expressing
thoughts like the following:
I see the shadow of the earth on the moon, ships disappearing over the
horizon, and different constellations as I move north to south.
Therefore, I think (with good reason) that the earth is spherical.
There is no problem in expressing a thought which is the conclusion
resulting from consideration of evidence. And there is likewise no logical
problem with expressing desires which result from similarly justified
thought processes:
Eating high-protein food is an excellent source of nutrition.
This is high-protein food.
Therefore, I want to eat this, and will!
This means, among other things, that saying “That’s what you think!” is not
a “universal philosophical refutation”! The fact that someone thinks
something doesn’t mean we shouldn’t pay attention to them. If they have
good reason or evidence for what they think, they may be on to something,
and this is all the reason we can have to pay attention.
A philosopher once had the following dream.
First Aristotle appeared, and the philosopher said to him, "Could you give me a fifteen-minute capsule
sketch of your entire philosophy?" To the philosopher's surprise, Aristotle gave him an excellent exposition
in which he compressed an enormous amount of material into a mere fifteen minutes. But then the
philosopher raised a certain objection which Aristotle couldn't answer. Confounded, Aristotle disappeared.
Then Plato appeared. The same thing happened again, and the philosophers' objection to Plato was the
same as his objection to Aristotle. Plato also couldn't answer it and disappeared.
Then all the famous philosophers of history appeared one-by-one and our philosopher refuted every one
with the same objection.
After the last philosopher vanished, our philosopher said to himself, "I know I'm asleep and dreaming all
this. Yet I've found a universal refutation for all philosophical systems! Tomorrow when I wake up, I will
probably have forgotten it, and the world will really miss something!" With an iron effort, the philosopher
forced himself to wake up, rush over to his desk, and write down his universal refutation. Then he jumped
back into bed with a sigh of relief.
The next morning when he awoke, he went over to the desk to see what he had written. It was, "That's what
you say.“
--From Raymond Smullyan, 5000 B.C. and Other Philosophical Fantasies. St. Martin's Press,
1983.
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As mentioned earlier, one place where students have a tendency to see
subjectivism everywhere is in matters concerning values. It’s thought that
matters of right and wrong are no different than matters of taste in food. Of
the latter, we often say, “there’s no accounting for taste,” which means,
there’s no way to explain or rationally justify what we like and what we
don’t. And there surely is a component of our taste in food that is this way.
If you don’t like broccoli, for example, it may be because you are simply
born with a greater number of “super-tasting” taste buds (called “fungiform
papillae”).11 You can’t say what it is about broccoli that makes it inherently
unworthy of eating, apart from the fact that it just tastes terrible.
But “there’s no accounting for taste” isn’t even true of choices about
what to eat. We know that there are nutritional facts about what is good and
bad for us, regardless of whether we like it. It may be good for us to eat it
even if it tastes bad. An important question, then, is whether values—
especially moral values—are more like taste, or nutrition? There are
philosophers who argue in favor of each side here, and since this is not a text
on moral philosophy, we cannot hope to resolve the question here.
But we should make some observations about the debate about the
factual basis of value judgments. One is that to enter the debate, you’ve
already got to have an argument. Famous subjectivists about values like the
Scottish philosopher David Hume gave philosophical arguments to establish
that moral values are ultimately derived from our sentiments. It is not
obviously true. In fact there is much that seems to count against value
subjectivism, and arguments are needed to show that moral objectivity is an
illusion, if it is. For example: people often debate about moral values, but
they do not debate about taste in food. If you think that you can disagree
with someone about the morality of abortion, you think that both you and
your opponent can’t be right: either one of you is right and the other is
wrong, or both are wrong. If you disagree with a Nazi about his view that it
is okay to persecute and kill the Jews, don’t you actually think you’re right
about this? If either of you can be wrong, there must be some fact against
which the view counts as wrong. Or at least, so it seems. To show that this
ordinary aspect of our thinking about morality is an illusion requires a
philosophical argument, not just an assertion.
Second, even the value subjectivists like David Hume didn’t think that
just any feeling is the basis of moral judgment. Hume thought that moral
sentiments were very special kind of feeling, and that a subject needed to
11
“Hate Broccoli? Spinach? Blame your genes.” The Los Angeles Times, February 19, 2007.
<http://articles.latimes.com/2007/feb/19/health/he-eat19>. Accessed January 31, 2010.
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enter into a special disinterested state of mind to experience the morally
relevant feeling. According to Hume, when we think something is immoral,
it’s not just because we get a sense of annoyance or inconvenience about it.
It’s because when we dispassionately leave aside our narrow interests, we
still feel a sense of more weighty disapproval. So even value subjectivists in
philosophy think that reason has a role to play in thinking about values—
insofar as it is involved in isolating the relevant sentiment— and they would
never endorse the raw, personal subjectivism in the arguments we have
examined so far.
And it is especially important to note that not all philosophers are
value subjectivists. Every philosopher will grant that values are not the kind
of thing we can directly see, taste, or feel. So how could we ever gather
evidence about them to formulate in easy to know premises? That is a
difficult question, but so is the same question about atoms. Atoms cannot be
seen, but we know they exist. How? On the basis of other things that we can
see. We can see atoms tracing a path under the influence of a magnetic field
in a “cloud chamber,” for instance. More indirectly, we can collect evidence
about how various chemicals combine in definite proportions, suggesting
that they have small parts that come in discrete amounts. So if we can know
things about invisible atoms, what about values? Of course nobody thinks
there are “value” particles. Maybe values are just things we see around us
every day, but understood in an especially abstract way. The philosophers
Aristotle and Ayn Rand, just to name a few examples, both thought that
what is good for a living organism is for it to live its life well, to function in
a biologically flourishing way. The nature and needs of a living organism are
not matters of anybody’s subjective tastes. If there are rules of action that are
the basis of human flourishing, maybe they are objective, after all.
But this is a debate not to be settled in these pages. The important
point, as we have urged, is that subjectivism should not be viewed as a
“default” position. If you think it’s true, you should give evidence for it and
explain away the aspects of our ordinary experience which suggest that some
acts really are right, and others wrong. It would be mentally lazy to assume
that just because subjectivism is trendy, it must be right.
Exercises
1. Think about when you first heard the idea that values were simply
a matter of opinion, not fact. Were you given any facts to back up
this claim? Or was it merely presented as an opinion?
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2. In the section above, reference was made to some philosophers
who think there are facts about the nature of living organisms that
determine what is good or bad for their lives. Is this view missing
the point? Is there a difference between good/bad and right/wrong?
3. Look at the story of the “universal philosophical refutation.” Why
is the refutation not really a refutation?
Social subjectivism
Now that the meaning of the subjectivist fallacy is clearer, there is one last
example of the fallacy that warrants examination. It merits our attention in
particular because it is so powerful and pervasive, in large part because it
doesn’t look like the other forms of subjectivism we have so far examined.
Here are some examples:
My parents say Santa Claus exists.
Therefore, Santa Claus must exist.
Sarah Palin says Barack Obama associates with terrorists.
Therefore, Barack Obama associates with terrorists.
Barack Obama says that the health care bill will bring down costs.
Therefore, the health care bill will bring down costs.
My minister says atheists will burn in hell.
Therefore, atheists will burn in hell.
You might wonder what these examples have in common with the previous
examples of subjectivism. After all, none of the premises make any overt
reference to one’s own mental states. Indeed none of the premises in these
arguments make any reference to one’s own person at all. What could
possibly be subjective about them?
The answer is forthcoming once we think about why we care what
other people say. We care about it because it expresses what they think. We
wouldn’t take seriously the advice of a tape recorder, unless we knew who it
was who had recorded the message. And in each of these cases, somebody
important—like a parent, a politician, or a religious leader—has spoken the
message which the arguer takes seriously. So the subjectivism here is not
direct. We are not thinking, “I lazily accept, or wishfully think Santa Claus
should exist, therefore he must.” But we may be thinking, “I lazily accept or
wishfully think that my parents are right about everything, therefore Santa
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Claus must exist.” This then involves subjectivism on two levels, rather than
just one: first there is subjectivism in lazily or dogmatically believing
something, and then there is subjectivism in the assumption that the mental
states of our parents (or our minister, or Sarah Palin, or Barack Obama) must
always be correct. But they are no different than us in this regard: they can
be wrong as their beliefs don’t affect reality in a way to guarantee that they
are correct.
Does this mean that we can never logically rely on the words of
another, or that if we do rely on them, it’s just a matter of faith? It seems we
have to do it all the time. Just to know our own birth date we have to rely on
our parents to tell us. To know about the past, we have to rely on our
teachers and our history books—likewise to know about foreign geography.
To know about the events of the world we rely on newspapers. And even to
make the simplest health decisions we rely on the advice of a doctor. Is all of
this illogical faith? This is a question we will examine in greater detail in
chapter 5, but we should make some preliminary remarks about it here.
Let’s consider just the example of our parents’ testimony about our
birthday, versus their testimony about Santa Claus. Here is the crucial
question: do we, the knower, have
reason to think that they, the
testifier, have the knowledge in
question? Knowing about the
birthday of your own children is
not something that is hard to
know. It’s an important day in
their life when parents observe
the birth of their children, and
they are likely to remember it.
And even little children can know
that their parents are capable of
observing and remembering things. They need only hear their parents tell
them not to touch the hot stove, and then touch it for themselves to find out
if their parents have the power of learning from experience.
But what about Santa Claus? He is supposed to be some kind of
immortal figure who visits millions of children in a single night, residing at
the North Pole the rest of the year. Does the child have reason to think that
his parents been there? Is it even easy to get there? If the child asks these
questions and gets answers in the negative, he should be suspicious. “How
does this man fit down our very tiny chimney?”, he might ask. Or if we
don’t have a chimney, how does he get in the house? Not hearing simple
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explanations, the rational child will conclude that this is not the subject on
which our parents are well-versed to know anything. Just a little knowledge
about geography and simple common sense physics should eventually be
enough for anybody to realize that their parents aren’t right about everything
if they go around talking about Santa Claus.
The rest of the examples can be settled on the same basis. There are
some issues about which people are authorities. We have ways of telling
whether or not someone has specialized knowledge, whether or not they are
an expert. We will discuss some of these ways in chapter 5. For the time
being, though, we will take for granted that doctors are relevant authorities
on medicine, auto mechanics are relevant authorities on the operation of our
cars, and newspaper reporters are relevant authorities on distant, timely
events. The subjectivist fallacy we are examining here is the fallacy of
appealing to irrelevant authority, of assuming that an important person’s
mere belief in some matter is sufficient evidence for its truth.
What would count as expertise on terrorism, health care, or hell?
Surely there are experts on international terrorism and on health care
economics. They can display their degrees and publications and research. Of
course even these experts disagree with each other on a great number of
matters, so even taking their word on
matters related to their expertise is not
to be done without care. But it should
also be obvious that Sarah Palin and
Barack Obama do not possess the
relevant kind of expertise, no matter
how spunky, intelligent, or otherwise
important they happen to be. Obama
may know a lot about constitutional
law and Illinois politics, and Palin may
know a lot about, well, Alaska, but
neither is an expert on the subjects in
question here. Perhaps both of them
can give further evidence for the claims
they make on these matters—and
political candidates usually do have a
cadre of expert advisors just for this
purpose. But we should not believe
them just on their say so. Politicians
Picture credit 44:
http://commons.wikimedia.org/wiki/File:1839-meth.jpg
especially are notorious for lying and
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breaking promises. Palin and Obama should not be treated any differently
than other politicians or other people, in general.
The last example (“My minister says atheists will burn in hell,
therefore they will”) is a little tricky. There is only a hell if there is life after
death. Presumably if anybody is an authority on this, a minister is a good
candidate. But is anybody? If we are being logical, we would expect that
ministers and theologians and philosophers could give arguments for the
existence of an afterlife before deciding if there is anything for them to
possess expertise about. There are indeed some religious thinkers who
attempt to give these arguments, but whether or not they succeed is a matter
of much debate. Indeed there are probably more religious thinkers who insist
that giving arguments destroys the faith in religious doctrines, and should
not be countenanced. But by rejecting the importance of demonstrating the
existence of something to be an expert about, these figures abdicate own
status as experts We see the results of good doctoring all the time. But we
don’t easily see the results of any religious expertise.
There is one final category of subjectivist fallacy which is closely
related to the appeal to irrelevant authority. From one perspective, at least, it
is just another example of irrelevant authority, but an irrelevant authority of
an especially influential kind: the majority of public opinion, or the majority
of our friends’ opinion. Here are some simple examples:
Most people believe the earth is flat.
Therefore, the earth is flat.
90% of people on earth believe in God.
Therefore, there must be a God.
Every industrialized country in the world has socialized medicine.
Therefore, the U.S. should have socialized medicine.
At one point in time, it really was true
that most people believed that the earth
was flat. But we know they were wrong.
The majority of people can be mistaken
or self-deluded. What they believe in the
absence of evidence is no better evidence
than what we as individuals or irrelevant
authorities believe in the absence of
evidence.
Picture credit 45: From Extraordinary Popular Delusions and
the Madness of Crowds, by Charles Mackay, 1841.
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Why, then, do many people still regard the last two arguments as
especially compelling? We can sometimes get a good idea of the truth on
various simple matters by taking a poll of our friends or peers. Wikipedia
entries—written by anonymous internet “peers”—are very good at getting
mundane trivia about the third season of Seinfeld correct, because the facts
about Seinfeld are so easy to find: you just watch it on TV or get the DVD.
So the masses can be said to be “experts” on some simple matters.
But are masses or nations of people experts on theology or health care
economics? Many people do believe in God, but many people can be
mistaken, especially if there is no field of expertise here, per above. And we
can come to understand why so many
people might be believe something
mistaken if they are pressured by their
parents, peers, and governments in the
right kind of way. Surely there are
better arguments for the existence of
God than this, such as arguments that
purport to find his “intelligent design”
in the universe he is thought to have
created. The same can be said about the
Picture credit 46: From Extraordinary Popular
socialized medicine argument, even
Delusions and the Madness of Crowds, by Charles
though it is usually made by a different Mackay, 1841.
camp of thinkers than the argument about God. Many countries may have
adopted a mistaken public policy. Surely there are better arguments for
socialized medicine than this, for example arguments that point to facts
about the improved health care outcomes that countries with socialized
medicine are said to experience. In both cases, of course, these arguments
are also debatable, but they are many times logically better than the appeal
to majority opinion, which is nothing but appeal to the opinion of the masses
of humanity or a mob of other nations. Thinking logically should not involve
getting on the bandwagon or giving into peer pressure, or whichever
metaphor you prefer.
Whether it is the appeal to important single individuals on matters
about which they are not experts, or the appeal to large quantities of
individuals on similar matters, the fallacy here is social subjectivism, the
fallacy of inferring the truth of some idea from its endorsement by some
other person or persons. Unless we have special reason to think that these
other persons know what they are talking about, this subjectivism is no
better—and in a way, even worse—than the personal kind surveyed in the
previous section.
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People rely on social subjectivism only because they know that we
often have to rely on experts for certain kinds of knowledge—the problem is
that they don’t realize that the subjects in their social subjectivism are not
experts. In the next chapter, we will examine the standards we can rely on to
determine when we do have experts, and therefore, when it is logical to rely
on relevant authority.
Exercises
1. Give an example in which people you know have relied on the
social subjectivist fallacy. The example could include the reliance
on some irrelevant authority, or on majority opinion.
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§2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 5:
Reliable and Unreliable Testimony
Ben Bayer
Drafted February 2, 2010
Revised July 25, 2010
The importance of testimonial knowledge
Chapter 4 focused on the especially flagrant violation of the second
requirement of good reasoning committed by subjectivist fallacies:
1. The premises of the argument must be known and known better
than the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must
be likely to establish the conclusion as true)
3. The argument’s premises must contain all of the known
relevant evidence.
We discovered if we believe or desire something strongly enough, this can
create the illusion that we have relevant evidence that what we believe or
desire is actually true. “I share the feeling of many that all people ought to
be free, therefore they ought to be free” is not a good argument, because our
feeling about an important principle of politics can be misleading or
mistaken. And the same moral applies to the feelings and thoughts of other
people: other people can be wrong, and so it is a fallacy to appeal to nothing
more than their beliefs to establish the truth of one’s own. Unless what we
are trying to establish is a truth about people’s beliefs (rather than about the
world), we need our evidence to consist of facts in the world that are
independent of people’s beliefs.
But we also briefly mentioned in the last chapter that there is a
distinction between the appeal to relevant and irrelevant authority, which
implies that sometimes it is quite logical to appeal to the views of another
person in order to justify a belief. Indeed, there does seem to be a difference
between these two arguments:
My doctor is an important authority, and says the earth is flat.
Therefore, the earth must be flat
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My doctor is an important authority in medicine, and she says I
have a heart condition.
Therefore, (probably) I have a heart condition.
Most of us would not appeal to the authority of our
doctor to decide the shape of the Earth (and would
probably consider a doctor who made this claim to
be a “quack”), but we would consult a qualified
doctor for medical advice. Indeed we have little
other recourse to seek medical advice from others
unless we have been to medical school ourselves
(even if accepting a single doctor’s advice only
gives us a judgment that is only probably true).
What makes for the difference between these two
Picture credit 47:
forms of relying on authority, and how can there be
http://www.flickr.com/photos/seattlemu
nicipalarchives/4058808950/sizes/m/
a difference? If another person can still sometimes
be wrong—even if she’s an expert—how can it ever be logical to appeal to
her belief as a source of evidence? How can another person’s belief be
relevant evidence ever count as relevant evidence?
It is very important to settle this question. We acquire a vast amount
of knowledge from other people, and we probably could not obtain most of
it on our own. Consider for a moment everything you know about our past.
You know that Washington was the first president, that there were 13
original colonies, that Columbus sailed the ocean blue in 1492. But how do
you know these facts? Probably you first heard them from your teacher.
Why trust your teacher? Of course many other people have probably
corroborated your teacher’s claims since you first learned them. But how are
they in a position to know them? Nobody alive today was alive in 1789,
1776, or 1492. Presumably they know about the facts of history by reading
history textbooks. But the same problem arises for the authors of those
textbooks. We would hope that a decent history textbook is written by a
historian who has consulted primary sources written by people who lived in
the time the events of history occurred. But why should we believe those
people? They could misreport the events occurring in their own day just as
much as reporters living in our own day can. And don’t forget that historical
documents can be forged, a matter we’ll address separately from the
question of the reliability of sincere sources.
The same problem arises in many other branches of our knowledge,
not just history. We need the words of others to know not only about the
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distant past, but also the distant reaches of the earth and the universe. If we
live in the United States, we need geographers and travelers to tell us that
there is such a place as China. We need news
reporters to report the news from foreign
lands or even from our own state capital. And
we need scientists to teach us about facts that
take specialized methods to uncover, which
we might not be able to uncover for ourselves.
All of these forms of knowledge are forms of
testimony.
When we hear the word “testimony,”
we often think of eyewitness testimony in a
courtroom. A witness will testify that he saw
Picture credit 48:
http://www.flickr.com/photos/cofrin_library/4093
some suspect commit some crime, or that he
447467/
saw him near the scene of the crime, etc. But
“testimony” is a broader concept than the courtroom kind. It is any form of
knowledge involving a report by someone claiming to be in a position to
observe or infer some fact, to someone who does not or cannot claim to be in
that position.
So a significant amount of our knowledge depends on the words of
others. Does this mean that it isn’t really knowledge at all, but faith? If we
must rely on the words (and therefore, the beliefs) of other people, does that
mean that we are condemned by the limitations of our place and time of
birth to rely on beliefs that we cannot justify logically? In previous chapters
we have criticized the reliance on the mere say-so or beliefs of other people,
but if we cannot avoid this reliance to live, how can it be criticized?
While reliance on testimony is unavoidable, it amounts to faith only if
it requires that we rely on the mere words or beliefs of others—that is, only
on their words, not on anything else. But if there can be reasons to regard
someone’s words as reliable, we can trust their words without trusting their
words alone. True, we are not always in a position to know facts about
history, geography, current events and science on our own. But we are often
in a position to know that other people in a position to know these kinds of
facts. If we can find evidence that they are good at knowing facts of a certain
subject matter, we can have good reason to believe their words at least on
that subject matter.
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Exercises
1. Consider the following items of your knowledge. How do you
know them, and to what extent does your knowledge involve
reliance on testimony?
Your date of birth.
Directions to a location in a town you’ve never visited.
The latest gossip about who is dating whom at your school.
2. We usually associate the idea of “faith” with religion. Why do you
suppose that some people see this connection? In what way does
religious belief sometime rely on testimony?
The relevance of basic testimony
The knowledge we acquire by the testimony of others follows the same
pattern as our knowledge in general. The ancient Greeks had a good estimate
of the distance to the sun which depended on their estimate of the distance
between the earth and the moon. That knowledge in turn depended on their
knowledge of the size of the moon, which in turn depended on their
knowledge of the size of the earth, which further depended in part on their
knowledge that the earth was round. At the bottom of this structure of
knowledge were basic observations, observations of ships and stars and
shadows on the moon. In the same way, there are basic forms of testimony,
on which further testimonial
knowledge can be built. If we want
to understand the overall structure
of testimonial knowledge, we need
to be clear about what these basic
forms of testimony look like.
A good way to think about
what basic testimony involves is to
think about the very first instances
of testimony we accept as children.
Picture credit 49:
http://www.flickr.com/photos/shelltyler/3903394184/
Children don’t know very much
yet, so if we think about what they are able to know by testimony with their
very limited resources, we should be able to figure out how they rely on
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testimony without yet having any other testimonial knowledge on which to
rely.12
Why do we believe our parents with any justification when they tell us
about our date of birth? We were certainly not self-aware enough to know
the date when we were born on our own. Perhaps our parents could show us
our birth certificates, but at an early age we wouldn’t know how to read
them, and at this age, we have even less reason to believe a piece of paper
than a real live human being. So why do we think we know from such an
early age when we were born, or how old we are?
Suppose (to take make an oversimplified hypothesis) that one of the
first things our parents tell us when we learn to understand language is our
age and date of birth. If we could understand them, would this be enough to
give us knowledge of this information? Is it enough to know our birthday
just to hear some voice telling us? Is it even enough simply to believe it with
good but inconclusive evidence? If you think it is enough, think for a
moment about what would happen if we walked up to a park bench one day,
and saw a tape recorder there, playing the message on a repeating loop,
“You are made of cheese, and your mother is a cow!” Most of us would
simply laugh this off, and probably most children would as well. Yet if we
only understand the language without knowing anything more about its
speakers (in this case, our parents), our position would be no better than that
with respect to the tape recorder.
What makes the difference between our parents and a tape recorder?
There are at least two important differences. The first is that in the usual
case, we have spent some time living with our parents well before they tell
us about our birthday, and have experienced them testifying in the past on
other matters. This is not true of the tape recorder!
Just as we would not trust that tape recorder, we
would also not trust our parents’ first message to
us. If it really were the first message, and we could
understand it, we would have no way to assess their
track record of delivering previous messages
accurately.13 So part of our reason for eventually
Picture credit 50:
relying on the words of our parents is that we have http://commons.wikimedia.org/wiki/File:
Descartes_De_homine.png
experienced their reliability in the past. The classic
example is the mother who tells her child not to touch the hot stove. The
12
Young children’s cognitive resources for evaluating the testimony of their parents are not as limited as is believed by some
philosophers who claim that reliance on testimony does bottom out in faith. See Jennifer Lackey, Learning from Words (Oxford
University Press, 2008), pp. 216-220 for an account of the evidence from developmental psychology on this matter.
13
It is a little strange to think that we could understand our parents first message without having any degree of trust in them, because
we probably learn language in the first place only by acquiring a kind of prelinguistic trust in those who teach us language. But this is
a complication we do not need to dwell on here.
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child touches the hot stove and learns that his mother was right. In this case,
the child is able to directly verify the accuracy of the mother’s words. Once
he has done enough of the same kind of thing, he comes to acquire a general
trust in her ability to observe facts about the world, remember them, and
relay them to others.
But this general trust is a trust in a specific ability, and this helps us
see the other big difference between our parents and the tape recorder.
Imagine that we also had a history with the tape recorder, and that it would
periodically state things that turned out to be true about our lives. We would
probably be very surprised by this fact and be intrigued about how it could
know so much about us. But we would probably still not be satisfied: we
would want to know who or what was making these recordings, so that we
could discover the identity of the person who had been spying on us so
closely. Track record is not a good enough reason
for trusting something; we also want to know how
they know what they know. In the case of our
parents, this is readily event. We see that our
parents are creatures like us: they have eyes and
ears attached to a head, and a voice for reporting
what is inside their head. We know that we receive
information from the world through our senses and
are able to remember it well enough to report later.
Picture credit 51:
http://commons.wikimedia.org/wiki/File When we realize that our parents come with the
:Descartes-reflex.JPG
same equipment, it is reasonable to conclude by
analogy that they can use it to the same end. So even at this age, we know
something about how they are able to reliably testify, not just that they have
a good track record of doing it. But we do not know the same about the tape
recorder: to us as children, it is simply a “black box,” with no apparent
access to the facts it speaks so well about.
These two ways in which our parents differ from the tape recorder are
the chief facts about them that give us reason to rely on their words. It is not
blind faith, because we have observed for ourselves, firsthand, their track
record and the sensory equipment they use to achieve this track record. Once
we come to rely on them, and begin to see that other people share the same
features as our parents, we begin to acquire an attitude of reliance on
people’s words in general, to the point where our reliance becomes
automatized, and we do not have to think much about why other people can
deliver us information about what we have not seen. It even becomes one of
the facts about people that define them as people in contrast to animals (and
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tape recorders). Of course we do not and should not trust other people on
everything, but more about this in the next section.
In the past we have drawn analogies between logic and various tools,
like telescopes, which extend the range of our senses. There is another good
application of the telescope analogy to be made
here, except this time we can think of a person’s
testimony specifically by analogy to the telescope.
There are also two important facts about
telescopes that allow us to trust that what we see
through the eyepiece is something real. Consider
Galileo, who was one of the first to use the
telescope to make careful observations of the
heavens. Looking carefully at the moon, Galileo
Picture credit 52:
noticed something that no one had ever appreciated http://commons.wikimedia.org/wiki/File:G
alileo_moon_phases.jpg
the significance of before: tiny ridges revealed by
the edge of the sun’s illumination of the moon, where the light ended and the
darkness began. Galileo knew, thanks to the Greeks, that the moon was very
far away, and given this knowledge, these ridges had to be the size of
mountains, which they resembled. This was a momentous discovery,
because previously it had been assumed that all heavenly bodies were
completely perfect spheres, as smooth as anything that could be imagined.
Galileo was discovering that the moon was really much more like the earth
than had been previously believed. And if the heavenly bodies were like the
earth, the earth might also be like the heavenly bodies. Galileo had
discovered important evidence that would help him prove that the earth was
a planet, not the center of the universe.
In what way is testimony like Galileo’s telescope? The telescope, of
course, does not speak to us or give us messages that are already encoded in
verbal or conceptual form (the phrase “the testimony of the senses” to the
contrary, notwithstanding). But in the same way that testimony helps us
know about things that we cannot verify for ourselves, the telescope also
helps us see things we cannot see with the naked eye. And it does so with
some assistance from our own reasoning: we do not take the telescope “on
faith.” After all, how did Galileo know that the ridges he was seeing through
the telescope were not some distortion of the lenses, making the telescope
more like a kaleidoscope than like a serious scientific tool? He had a way of
knowing. After all, there were also distant things on earth that he could point
his telescope towards, objects of which he knew the telescope would deliver
the proper magnified image. Suppose that Galileo had been on a journey
north, to the Italian Alps. He pointed his telescope at distant blips on the
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horizon, and saw mountains. After some hours of travel, he arrived at the
foothills, and was able to see the mountains with his naked eye, seeing the
same picture he had seen hours before only through his telescope. This is
how a scientific instrument is calibrated: we test it against some data for
which we already know the accurate result, and if it yields what we expect,
we begin to trust it in cases where it delivers new data. In the same way that
Galileo calibrated his telescope, we “calibrate” our parents when we learn
that they can accurately predict that the stove will burn us. Thereafter we use
their words to learn new things for ourselves.
There is one more point in
the telescope’s favor: the fact that
the telescope lets us see things at a
distance was not a mystery to
Galileo. He knew that it had
internal components, a series of
lenses, an understanding of the
Picture credit 53:
optics of which explained how
http://commons.wikimedia.org/wiki/File:Kepschem.png
this magnification was possible.
In the same way that his basic knowledge of the rules of optics let him trust
the mechanism of his telescope, our basic knowledge of the inner workings
of other people—reached by an analogy we draw between them and our own
inner cognitive works—helps us understand how they can know and testify
about what they know.
It is useful to summarize the reasons that go into relying on the
testimony of others through the following box diagram:
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The darker boxes represent the explicit premise and conclusion that we
usually reason with on a question like this. The lighter boxes represent
implicit background knowledge that help explain why our mother’s words
are relevant to the conclusion, why they count as a form of relevant
authority. You’ll notice that there are two major points needed to account for
our mother’s reliability: our knowledge of her track record, and our
knowledge of her equipment for knowing, which is itself a product of an
analogy we draw between her and us. You may recognize this kind of
background structure as similar to the structure we discussed when
identifying how suppressed controversial premises could be responsible for
special forms of question-begging. It is similar, but in this case, what is
suppressed is not controversial as in the examples of question-begging: it is
well-founded in evidence, and thus a legitimate source of relevance.
Of course the fact that we can rely our parents on some matters (for
instance, on basic facts about our life history or
basic facts about home safety) does not imply
that we should rely on them on any matter. The
same goes for other people: we may be able to
rely on them on relatively simple facts on the
same order as life history and basic safety, but
our trust should not necessarily extend further.
We might be able to trust strangers for directions
or to learn the time of day. But neither strangers
nor our parents are necessarily qualified to know
anything about distant history or geography, the
details of current events, or matters of complex
science. We go to a doctor for medical advice,
not to a snake oil salesman. The interesting
question is how we know how to tell the
difference.
Picture credit 54:
http://commons.wikimedia.org/wiki/File:Snakeoil.png
Exercises
1. Some philosophers think that children don’t have the cognitive
resources to verify the reliability of their parents’ testimony. Some
famous historical philosophers like Thomas Reid even thought that
children are naturally gullible and believe whatever their parents
tell them. Can you think of examples of your own gullibility as a
child? Did you ever doubt your parents’ testimony on any matters?
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2. Philosophers sometimes object to the idea that we come to be
aware of the minds of other people by the kind of analogy
suggested above. Can you think of any reasons to doubt the power
of the analogy?
Determining relevant authority
Of course our trust often does extend further than it should. Young
children can be gullible. Once they come to trust people on some matters,
they will often trust them on just about anything. This is likely an innocent
mistake on the part of children, for reasons we will shortly see. They have to
learn how to draw the boundaries between what most people can be relied
upon to know, and what they cannot. Some adults still need to learn the
same thing. How many of us have received emails from parents or relatives
forwarding amazing news from anonymous sources that turn out to be
ridiculously false? How many of us have ourselves been taken in by “snake
oil salesmen,” and purchased goods from late night infomercials promising
an easy way of losing weight, a new way of making money through a
multilevel marketing scheme, or the secrets to ongoing happiness, all at the
low, low price of $19.95?
Part of the reason young children can be gullible is that they do not
yet have the kind of self-knowledge that they need in order to know when
they need to rely on experts. Before a
child can fully appreciate that other
people are relevant authorities on
some matters, but not on others, he
needs to know that he himself is not
an authority on every matter.
Children first need to discover that
they are fallible, that they can make
mistakes, and only if they use certain
methods of thinking can they arrive
at the truth. In short, children need to
Picture credit 55:
http://commons.wikimedia.org/wiki/File:Gnothi_seauton.j self-consciously discover the
pg
rudiments of logical method.
The other reason that children can be gullible is that there is a further
stage of learning they are yet to go through, the stage in which they discover
that knowledge falls into a variety of branches, and that for each area of
knowledge there is specialized knowledge that only specialists know much
about. Usually we only begin to appreciate this fact after we have started
learning a specialized field of knowledge for ourselves, like in math or
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science. Last of all, we need to know enough about the content of various
fields of specialized knowledge to know that certain kinds of questions are
dealt with by certain fields: that questions about biology are distinct from
questions about astronomy, which are distinct from questions about
morality, from questions about economics, etc.
Once we realize that unanswered questions fall into specialized
branches of knowledge in which we are not specialized, we can start to spot
cases where we should be wary of relying on irrelevant authorities. Here are
a few examples:
A professor thinks that 7 World Trade Center could not have
collapsed without a bomb.
Therefore 7 World Trade Center could not have collapsed without a
bomb.
A long time storm chaser thinks that a statistical model about climate
change is flawed.
Therefore a statistical model about climate change is flawed.
My parents think a career in medicine would be best for me.
Therefore a career in medicine would be best for me.
In each of these cases, a source is appealed to who may have some
legitimate authority on some matters, but not necessarily the matters in
question. The first example is modeled after a real-life conspiracy theorist
about the September 11th attacks, David Ray Griffin. His book, A New Pearl
Harbor (which we will refer to briefly in chapter 10, on conspiracy
theories), argues among other points that one of the buildings that collapsed
on September 11th, 2001 could not have collapsed because of the damage
resulting from two jetliners crashing into the two main towers. Griffin
refuses to believe the official government story—and the overwhelming
consensus of qualified mechanical engineers—that the structural integrity of
the building could have been weakened by debris from collapse of the first
two towers, and cites fringe mechanical engineers who side with his story.
But Griffin is no mechanical engineer. He is, in fact, a professor of theology.
He hardly seems qualified to make judgments about the structural integrity
of buildings, or even to select which among the many mechanical engineers
can be trusted and which cannot.
The second example illustrates how even two fields closely related to
each other may not be closely related enough that one can deliver relevant
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authority for assessing the other. Both storm chasers and statistical
climatologists deal with weather, but storm chasers focus on taking pictures
of tornados and other extreme weather events. Some of them probably even
have specialized knowledge of the inner workings of tornados, but this is a
very different kind of specialized knowledge than what is involved in
climatology’s statistical modeling. This does not mean that there can’t be
storm chasers with adequate knowledge of statistics to discover flaws in
climate science models, or that climate scientists always engage in the most
reliable statistical methods, but the mere fact that a storm chaser has doubts
about the climatology gives us laymen little reason to doubt the findings of
the science.
The last example is especially tricky. We already know that our
parents are not experts on everything. But might they know us well enough
to be as close to an expert on knowing the best career for us as anybody
could? Perhaps they’re the closest anyone could come outside of ourselves,
but that doesn’t mean they come close enough. As much as parents may
have good advice to offer us on matters of career choice, and as much
experience they may have from their own life choices, an individual’s own
interests and skills and ambitions are really best known only by that
individual. When it comes to important decisions about our own lives, we as
individuals may be the only experts!
It is one thing to realize that we need to rely on experts to answer
certain kinds of questions; it is quite another to know who these experts are.
It’s such another thing that there is a real problem about whether it is even
possible to identify experts if we are not already experts ourselves. Can we
simply ask someone if he’s an expert on a subject matter? We can, but can’t
trust his assessment of the matter unless we are already convinced that he is
an expert—and this would be circular reasoning. By the same token, we
can’t simply ask other experts in the field with the first expert is an expert,
because then we would already know how to identify an expert—and this
would be circular reasoning again! We need to find a way to break into the
circle of expert testimony without using circular reasoning.
The solution to this problem is to think about the same kinds of
strategies we used to break rely on testimony at all in the first place. To
begin with, if we know someone who happens to be an expert (even if we
don’t know that they are yet), we can observe their success in making
predictions and solving problems on that basis. If we know a doctor, for
instance, we can notice that her diagnosis of our symptoms regularly yields a
cure. We may not know just how much of an expert she is in comparison
with other doctors, but we know at least that she must have some degree of
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expertise to deliver the kind of results she does. By their fruits we shall
judge them.
Of course, we would never have enough time personally to “calibrate”
every expert we relied upon in this way, by trying out their services before
declaring them an expert. Furthermore, we would also probably suffer from
the maltreatment of many non-experts before we hit upon the experts. So it
is useful that we can also rely on the testimony of other non-experts who
have worked with the experts to tell us who they are. In this day and age in
particular, there are numerous ways for non-experts to relay their experience
of experts to others, especially through the internet. Web sites like Angie’s
List that specialize in collecting and publicizing reports about service
professionals like mechanics, plumbers, and yes, even doctors. These can be
very useful for anyone seeking to break into the circle of expert authority.
To do so, we need rely on nothing more than our general trust in any
person’s ability to report on simple facts, such as those about whether or not
a doctor’s course of treatment has been successful. So because people can
assess the strengths of an expert first hand (our previous paragraph), other
people can “bootstrap” on their assessment through their testimony about it.
Both of these ways of breaking into the circle of experts are still only
“track record” arguments, ways of “calibrating” our experts (either directly
or indirectly). But we would hope that we could also understand something
of the internal mechanism of the expert, something about how his or her
“parts” work to deliver this expert knowledge. Of course we cannot
understand this completely unless we are experts ourselves, but there are
tests we can run to get a glimmer of how expertise works. Before taking
their word on some advice, we can ask the prospective expert questions to
see how well they can explain themselves. We can look for inconsistencies
in their stories. We can see how they deal with criticism, whether it is
defensively or sincerely. An excellent example of how a layman can probe
the expertise of a witness in a court proceeding was once portrayed in a
scene from the movie My Cousin Vinnie. In it, the district attorney crossexamines a witness (played delightfully by Marisa Tomei) to see if she
really is an expert on automobiles. The scene that follows is as entertaining
as it is logical:
D.A. Jim Trotter: Now, Ms. Vito, being an expert on general
automotive knowledge, can you tell me... what would the correct
ignition timing be on a 1955 Bel Air Chevrolet, with a 327 cubic-inch
engine and a four-barrel carburetor?
Mona Lisa Vito: That's a bullshit question.
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D.A. Jim Trotter : Does that mean that you can't answer it?
Mona Lisa Vito : It's a bullshit question, it's impossible to answer.
D.A. Jim Trotter : Impossible because you don't know the answer!
Mona Lisa Vito : Nobody could answer that question!
D.A. Jim Trotter : Your Honor, I move to disqualify Ms. Vito as an
expert witness!
Judge Chamberlain Haller: Can you answer the question?
Mona Lisa Vito : No, it is a trick question!
Judge Chamberlain Haller: Why is it a trick question?
Vinny Gambini: Watch this.
Mona Lisa Vito : 'Cause Chevy didn't make a 327 in '55, the 327
didn't come out till '63. And it wasn't offered in the Bel Air with a
four-barrel carb till '64. However, in 1964, the correct ignition timing
would be four degrees before top-dead-center.
D.A. Jim Trotter: Well... uh... she's acceptable, Your Honor.
Exercises
1. Decide whether or not each of the following argument relies on a
relevant authority to reach his conclusion.
My mother says it is dangerous to cross the street without looking
both ways.
Therefore it is dangerous to cross the street without looking both
ways.
An economist says that our tax policy is immoral
Therefore our tax policy is immoral.
This witness says he saw Mr. X in the moonlight commit a murder
Therefore Mr. X committed a murder.
The Wikipedia says that Episode 7 of Season 6 of Buffy the Vampire
Slayer first aired on November 6, 2001.
Therefore, this episode did first air on November 6, 2001.
Unreliable testimony: hearsay
In previous sections we’ve tried to draw a line between the topics on which
most people can be reliable reporters, and those requiring specialized
knowledge. Ordinary people are good at observing the obvious properties of
observable objects. They can tell the obvious difference between danger and
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safety, man and beast, chocolate and vanilla. Most people, however, unless
they are specially trained, cannot tell the difference between which
mushrooms are safe to eat vs. which are dangerous, between drugs that will
interact safely with others and which will not, between different species of
ant, or between artificial and real vanilla. These are discriminations that need
to be made by experts, whether specialists in botany, pharmacy, biology, or
cooking.
However, even the testimony of ordinary people on ordinary matters
can fail to be completely reliable. Spoken testimony, in particular, has the
power to create the illusion of knowledge where there is none. When a
testifier describes some circumstance he or she claims to know about, we
begin to paint our own picture of the circumstance in our minds. Because the
testifier speaks so sincerely, and the picture gradually acquires details in our
minds, it become harder and harder to remember that what the person tells
us might not correspond to reality. This happens especially under conditions
where the person describes a fact that we justifiably believe that they could
have observed for themselves without need of specialization. But the fact
that we can imagine their description being true does not of course imply
that it is.
What are sources of unreliability are there apart from the lack of
expertise? Consider the following argument based on testimony received
from one Ms. Reporter:
Ms. Reporter says that Billy Bob committed the robbery.
Therefore, (probably) Billy Bob committed the robbery.
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Something interesting about an example like this is that even though Ms.
Reporter may be in a good position to know (or believe with good
justification) that Billy Bob committed the robbery, she may not be in a
good position to transmit her knowledge or justification to the person
listening to her and making this argument. How could this be?
Imagine further that the reason Ms. Reporter knows about Billy Bob
is because she heard about it from her friend Ms. Eyewitness, who witnessed
it directly. So the following argument would give a more accurate statement
of the evidence:
Ms. Reporter says that Ms. Eyewitness says that Billy Bob committed
the robbery.
Therefore, Billy Bob committed the robbery?
Supposing that Ms. Eyewitness knew who Billy Bob is and that he was not
wearing a mask, we can suppose that Ms. Eyewitness would be in a good
position to know that Billy Bob is the robber, because identifying a person
one recognizes is not a matter of any specialized knowledge. Further, Ms.
Eyewitness should be in a position to reliably report this fact to Ms.
Reporter, in which case Ms. Reporter could also come to know it, or at least
to believe it with high probability.
But what about the person who is only listening to Ms. Reporter’s
report about what Ms. Eyewitness said? In other words, what about those of
us who are simply reading about what Reporter says Eyewitness says, and
drawing conclusions on the basis of it? Are we in the same position to know
what Ms. Reporter knows? If we ourselves know Ms. Reporter, and
especially since we know that it is not a matter of expertise to know,
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remember and report the words of another person, we can reasonably take
ourselves to know or believe with probability that Ms. Eyewitness really did
say that Bill Bob committed the robbery. But it is one thing to know that Ms.
Reporter is a reliable reporter of the words spoken by a third person; it is
quite another to think that this makes her a reliable reporter of the truth of
those words. With this in mind, the argument from Ms. Reporter’s testimony
is better represented in one of two ways:
Ms. Reporter says that Ms. Eyewitness says that Billy Bob committed
the robbery.
Therefore, (probably) Ms. Eyewitness says that Billy Bob committed
the robbery.
or
Ms. Reporter says that Ms. Eyewitness says that Billy Bob committed
the robbery.
Therefore, (probably) it is probable that Billy Bob committed
the robbery.
In the first argument, we’re able to conclude with the same amount of
probability that we would for any other testimonial argument, but the
conclusion is not one about what Billy Bob really did, only about what Ms.
Eyewitness says he did. In the second argument, the conclusion is about
what Billy Bob really did, but its degree of probability has been highly
qualified. Instead of saying he probably did it, we’re now saying that it’s
probable that it’s probable that he did it, which is no longer straight
probability: it’s equivalent to downright uncertainty.
The difference between Ms. Reporter’s ability to transmit knowledge
about Ms. Eyewitness’ words, and her ability to transmit knowledge about
the truth of those words is what has led logicians and legal theorists to
formulate the concept of hearsay. Hearsay is a concept that has been
carefully defined for courtroom purposes, but it is a useful concept to
employ in our everyday dealings with testimony. The United States Federal
Rules of Evidence defines it as follows: hearsay is a “statement, other than
one made by the declarant while testifying…offered in evidence to prove the
truth of the matter asserted.”14 Hearsay, in other words, is a form of second14
Rule 801(c).
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hand testimony: it’s testimony about the testimony of another person offered
as evidence for the truth of the original testimony. Hearsay is given special
attention because it is unreliable.
Why is hearsay so unreliable? There are several reasons. While it is
true that the giver of hearsay may be a completely reliable testifier on
matters that he or she has observed directly, and while we may be able to
acquire knowledge from this testifier accordingly, the only knowledge we
can so acquire is knowledge about what this testifier has directly observed.
In a case of hearsay, all that the testifier has observed is the additional
testimony of another. So we may be justified in believing that this other
testimony was in fact witnessed, but as indicated above, it is another matter
to decide if that testimony is true. Perhaps Ms. Reporter is in a good position
to know the reliability of the original testifier, Ms. Eyewitness. But we are
not in that position. We may never have met Ms. Eyewitness, and perhaps
we never can or will meet her. Perhaps she is dead (maybe she was
murdered by Billy Bob). In any of these cases, our lack of access to Ms.
Eyewitness prevents us from knowing, for example, about whether or not
she is an honest person or reliable under the circumstances in which she
claimed to be a witness to the crime.
But let us suppose that because Ms. Reporter knows Ms. Eyewitness
well, we could also accept Ms. Reporter’s testimony about Ms. Eyewitness’
honesty and general reliability when it comes to identifying criminals. Even
still, there is a problem with hearsay. At most, we could know reliably that
Ms. Reporter is accurately reporting the words of Ms. Eyewitness about
Billy Bob. But what is the meaning of those words? Perhaps Eyewitness
was talking about some other Billy Bob that neither we nor Reporter knows
about. Perhaps Eyewitness had a slip of the tongue and meant to say Bill
Rae, another suspect entirely. Perhaps Eyewitness was only joking, and
wanted to blame a good friend of hers on the crime who would be the last
person in the world to commit it. If Eyewitness were available for crossexamination, we could ask questions to clarify the meaning of her words.
We could ask her “Billy Bob Who?” Or “Do you mean Billy Rae?” Or
simply, “Are you serious?” But since Ms. Eyewitness is not present, we have
to rely on Ms. Reporter to report those words, and Reporter may not be able
to answer the same questions we would like to answer.
There is nothing wrong with following chains of evidence to infer
facts we cannot directly observe by ourselves. The detective in this case, for
example, might find footprints at the scene of the crime, footprints that
match only one kind of shoe. And she may discover that Billy Bob Jones is
the only on who owns shoes like that that in the whole county. So she is
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following a trail of clues from the scene of the crime to the criminal. But at
no point in this chain does she encounter a clue that she can’t learn more
about through her own investigation. She can hold a magnifying lens up to
the footprints to examine them closer, to get more detailed information about
the treads. She can do a more careful search of Billy Bob’s apartment, either
to look for the pair of telltale shoes, or to look for evidence that he once
possessed them (perhaps, scuff marks). But following a chain of evidence
like this is very different from following a chain of hearsay to its source.
Because it’s hearsay, we can’t examine more closely the meaning of Ms.
Eyewitness’ original words. They’re not in front of us to be examined, nor is
Eyewitness there to be queried about them. Of course, if we were able to
track down Eyewitness herself, perhaps after getting directions from Ms.
Reporter, this would be another matter. We really could ask her to repeat her
story and inquire into its meaning. We could find out more about her
reliability on matters such as this. But then it would no longer be hearsay:
we would be getting direct testimony about Billy Bob directly from the
eyewitness to his crime.
There is no better analogy for describing the unreliability of testimony
than the child’s game of “telephone,” which most of us have had the chance
to play. It is enjoyable because the message at the end of the chain of
telephone talkers is usually so very different from the message that the
game-players began with. Usually the message changes neither because of
our inability to check the reliability of the original source, nor because of
any misinterpretation of the words. Usually it just stems from mishearing
the words. That is not what is usually at fault in ordinary cases of hearsay,
but the analogy to “telephone” illustrates the point that the greater the
number of degrees of separation between us and the source, the greater the
chance that something could go wrong. But while we’re considering it, we
might as well include the possibility of mishearing as yet another one of the
reasons that hearsay can be unreliable.
Lawyers and jurists have spent a great deal of time carefully defining
inadmissible hearsay and distinguishing it from exceptional cases where the
words of a testifier about the words of another testimony can be admitted as
evidence. It is instructive to mention at least one of these exceptions,
because they help us to grasp the principle behind why hearsay generally is
not reliable. One exceptional case is the “excited utterance.” Suppose that
Ms. Reporter tells us that Ms. Eyewitness screamed “Billy Bob is a burglar!”
This may not be a reliable way of knowing if Billy Bob is guilty, but it is, at
the very least, a reliable way by which Reporter can let us know that
Eyewitness was upset. Perhaps we needed to know this because Eyewitness
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is missing, and we need to find her. If we know that Eyewitness was afraid
that someone she knew was a criminal, this is at least evidence of her state
of mind, evidence that she could have chosen to skip town to avoid the
person she believed to be a criminal. We might be able to find Eyewitness
somewhere out of town if we use this evidence—even if it turns out that she
was mistaken and Billy Bob was no burglar.
It is important to be wary of hearsay, not only for the sake of
determining truth in judicial proceedings, but also to be careful not to spread
irresponsible or malicious rumors. The spread of these rumors is especially
prevalent in times of crisis and confusion, when there is no time or way to
check on the reliability of sources and when everyone is expecting the worst.
Examples can be drawn from two of the major disasters of the last decade.
Immediately after the attacks of September 11th, 2001, rumors of further
terrorist attacks spread like wildfire. Bombs were said to be found under
major bridges, and various government buildings were said to be under
attack. Major news outlets reported some of these stories. The Washington
Post noted in a story on September 16, 2001 that they had heard these
reports, but that all of them had been proved bogus within days of the
attack.15 Likewise during the Hurricane Katrina disaster of 2005, there were
reports of roving gangs attacking people, of rapes and murders occurring at
the Superdome where many citizens had taken shelter—even reports of
sharks swimming in the city streets. According to the Los Angeles Times, all
of these rumors turned out to be baseless.16
You might think that you would be smarter than the rumor-mongers
during these times of crisis. But how many urban legends have you believed
without having reliable sources? Have you ever believed any of the
following claims, for example?
Men think about sex every seven seconds.
We use only 10% of our brains.
The average person swallows eight spiders a year.
A munchkin can be seen hanging himself during a scene of The
Wizard of Oz.
15
Ted Gup, “We Want to Hear it All, Even if it Isn’t All True,” The Washington Post, September 16, 2001.
<http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A35113-2001Sep15>
16
Susannah Rosenblatt and James Rainey, “Katrina Takes a Toll on the Truth, News Accuracy,” The Los Angeles Times, September
27, 2005.
105
The first two are often passed off as quirky conventional wisdom. We’re told
that men think about sex this often, because after all, they’re men, and
wouldn’t we expect them to be this distracted and prurient? And the figure
about using only 10% of our brain, this would help to explain why people
make so many stupid decisions, and motivate the search for a way to use the
remaining 90%, perhaps as part of some self-help program we can purchase
for $19.95 from a late-night infomercial. Believing these claims confirms
certain prejudices of ours, and testimony is often uncritically accepted when
it feeds our tendency to engage in wishful thinking. But it turns out that both
of these claims, along with the rest on the list, are baseless if not known
outright to be false. 17
Exercises
1. Consider the following passage from Lee Strobel’s book, The Case
for Christ: A Journalist’s Personal Investigation of the Evidence.
Do you think the professor being interviewed relies on hearsay?
Why or why not?
"Let's go back to Mark, Matthew, and Luke," I said.
"What specific evidence do you have that they are the authors
of the gospels?" Blomberg leaned forward."Again, the oldest
and probably most significant testimony comes from Papias,
who in about A.D. 125 specifically affirmed that Mark had
carefully and accurately recorded Peter's eyewitness
observations. In fact, he said Mark 'made no mistake' and did
not include 'any false statement.' And Papias said Matthew had
preserved the teachings of Jesus as well.
"Then Irenaeus, writing about A.D. 180, confirmed the
traditional authorship. In fact, here-," he said, reaching for a
book. He flipped it open and read Irenaeus' words.
Matthew published his own Gospel among the Hebrews
in their own tongue, when Peter and Paul were preaching the
Gospel in Rome and founding the church there. After their
17
According to the Kinsey Institute, the best statistics show that “54% of men think about sex everyday or several times a day, 43% a
few times per month or a few times per week, and 4% less than once a month.” <http://www.kinseyinstitute.org/resources/FAQ.html>.
According to the Committee for Skeptical Inquiry, brain scientist Barry Beyerstein has conclusively shown using magnetic resonance
imagining that there is no basis for the claim about how much of our brain we use. <http://www.csicop.org/si/show/the_tenpercent_myth>. Snopes.com explains that the spider rumor was actually started, ironically, by an author who wanted to give an
example of the crazy things people would believe after reading them on the internet.
<http://www.snopes.com/science/stats/spiders.asp>. The Wizard of Oz urban legend has also been contradicted by numerous
munchkins on the set of the film, and is most easily explained as resulting from misidentifying a bird flapping its wings as the
swinging victim of a hanging suicide. <http://www.straightdope.com/columns/read/1063/can-a-munchkin-be-seen-committingsuicide-in-em-the-wizard-of-oz-em>.
106
departure, Mark, the disciple and interpreter of Peter, himself
handed down to us in writing the substance of Peter's preaching.
Luke, the follower of Paul, set down in a book the Gospel
preached by his teacher. Then John, the disciple of the Lord,
who also leaned on his breast, himself produced his Gospel
while he was living at Ephesus in Asia.
Unreliable testimony: dishonesty
The examples of unreliable testimony we have considered so far—testimony
about matters on which one is not a relevant authority, or testimony about
the unverifiable testimony of others—
are both types that could be spread
through innocent error. Sometimes
testifiers simply don’t know that they’re
not relevant authorities on a certain
matter. Ignorance is dangerous because
the ignorant are usually ignorant of their
ignorance! Likewise, rumors can spread
easily by hearsay when testifiers repeat
the words of others and unintentionally
change the wording in subtle ways
Picture credit 56:
which, when repeated enough, can
http://commons.wikimedia.org/wiki/File:JanusVatican.JPG
eventually change their meaning. But
not every example of unreliable testimony is unreliable for reasons as
innocent as these.
We also know that people can be dishonest. Dishonesty can manifest
itself in myriad ways. It can come in subtle forms, as in the case of mere
bias: testifiers can have an agenda they want to push, and they can slant the
information they present in a way that puts better light on their favored
conclusion. This is dishonest, since the testifier could well know that he is
slanting, that there is information he is leaving out that others might want to
consider, and that the additional information could lead them to different
conclusions. But at least bias is not outright lying.
Unfortunately, dishonest testimony is not as easy to spot as honest
forms of unreliable testimony. A dishonest testifier may be biased or lie
about some matter that is fully within his or her area of expertise, and so we
may not be able to disqualify this testimony as a matter of irrelevant
authority. But this does not mean it is impossible to be on guard against.
There are obvious principles we can use to be on the look out for the
107
dissemblers and liars in our midst, even if it is not always easy to apply these
principles in every case.
One of the reasons we come to trust our parents’ testimony in the first
place is their track record of success. By the same token, a track record of
dishonesty can be relevant to determining whether or not a person should be
suspected of lying or exhibiting bias. We all know of news agencies which
slant their reporting to one side of the political spectrum or another. We
know that when some questions are “too close to call,” their bias can lean
toward the side they usually favor, rather than the other. Some people are
surprisingly deaf even to a record of outright dishonesty. How many people
believe that if they cheat with a married man or woman, the married cheater
really loves them and not their spouse? But if the cheater is lying to his or
her spouse, what reason does the lover have to believe that the cheater won’t
cheat on the lover in the future? All too often cheaters cheat on everyone,
which is to be expected, because part of being a cheater is having a record of
dishonesty.
Dishonesty, whether in the form of bias or outright lying, is like a
crime that we have to detect. Just as detectives look for evidence of means,
motive and opportunity to identify their suspects, we should look for
evidence of the same when we seek to identify a liar. The means and
opportunity of lying are obvious: we lie with our words, and we lie in
circumstances when we know the other person can be duped by our words,
as when, for example, we have some expertise on a matter that would
normally qualify us as relevant authorities. What can be especially
revealing, then, is evidence of motive. There is an old Latin phrase that
raises the important question here: “Cui bono?” This means: “Who
benefits?” Finding who would benefit from a lie is part of finding evidence
for who the liar is.
Note, however, that the benefits spoken of in “Cui bono?” can come
in many forms. Note these two examples:
A researcher paid by the oil industry says that global warming is
nothing to worry about.
Therefore, global warming is nothing to worry about.
A professor who’s received a government grant says that global
warming is an imminent danger.
Therefore, global warming is an imminent danger.
108
Usually we are taught to believe that anyone who is paid by corporate
interests to research policy questions that affect those same interests is
necessarily biased by the money they receive, presumably because this
money encourages them to find results favorable to their benefactors.
Sometimes this is surely true. But is it always? Suppose that there is a
scientist who is honestly skeptical about the manmade global warming
hypothesis. Finding that the ordinary academic research establishments do
not favor this line of inquiry, he can only find work through a corporatefunded think tank. If he reached his conclusions before and independently of
receiving corporate money, would you say that he is biased? Or is he simply
committed honestly to an unpopular idea? But it is surely important to be on
guard against research that is biased by its funding source. The concerted
effort of the tobacco industry late in the 20th century to distort research about
the health effects of cigarettes is a prominent example here.
By the same token, it is surely possible that a researcher who receives
government money rather than corporate interest could be unbiased and
more reliable than some corporate researchers. But does government money
free one completely of the potential for bias? Not necessarily. Government
money is given out by politicians, and politicians usually have a political
agenda. Researchers know this, and may also know that if their research
leads to conclusions at odds with politicians’ agendas, the money might not
continue to flow. Bias concerning government money can be even more
subtle than this. Even if money does not come with a political agenda
attached to it, there can still be special kinds of results that garner more
attention than others: claims about imminent climate catastrophe or about
the latest health risks of various diets make the headlines. Researchers who
know that more sensationalistic conclusions can make them famous can also
be biased to find these conclusions—and all without being influenced by any
corporate money. And let’s not forget that ideological blinders can motivate
and corrupt research even when it is entirely uninfluenced by money.
Unreliable testimony: anonymous sources
There is one overwhelming lesson to be derived from the previous three
sections: when it comes to determining the reliability of our testimony, the
source of the testimony really matters. It matters whether a testifier is an
expert or a layman, whether we know the testifier directly or it is a matter of
hearsay, and whether or not the testifier has a track record of honesty. So we
need to know who the source is before we can determine whether or not they
are a good source.
109
It follows from this that testimony whose source is unknown is of the
lowest order of reliability. Journalists will sometimes rely on unnamed
sources to blow the whistle about matters of controversy in government or
business. A famous example was Woodward and Bernstein’s reliance on
“Deep Throat” in their exposé of the Watergate scandal. (We now know
that Deep Throat was William Mark Felt, Sr.) If the journalist knows the
whistle blower and reports his words, we may assume that the journalist has
acquired knowledge from a reliable testifier. But since we do not know the
testifier, and are not even permitted to know the same testifier, news reports
that rely on these unnamed sources are still no better than hearsay to us.
An especially fascinating example of unsourced testimony is
Wikipedia, the online encyclopedia that anyone can edit. Of course the
Wikipedia is an extraordinarily useful internet tool. In the course of a
decade, it has amassed and organized a wealth of knowledge that had
previously been available only on scattered web sites, if online at all. And
Wikipedia is not
completely without
checkable sources. The
better articles will invoke
long lists of footnotes,
including references to
books, magazines, and
other more specialized web
sites. In spite of the wonder
of all of this, Wikipedia is Picture credit 57: http://en.wikipedia.org/wiki/Main_Page
still just an online encyclopedia that anyone can edit. The editors of
Wikipedia have taken steps in recent years to close controversial articles to
random editing, and have begun introducing more and more layers of
editorial control. But still the vast majority of these articles can be edited by
anyone—not to repeat ourselves—but that means anyone, regardless of their
level of expertise, regardless of their degree of honesty.
A telling example of the lengths to which Wikipedia’s unreliable
anonymity can extend occurred recently when a 22-year old Irish
undergraduate student decided to run a test to see how many journalists
would appeal to Wikipedia as their main source of information. When a
famous composer named Maurice Jarre died on March 28, 2009, Shane
Fitzgerald decided that he would update Jarre’s Wikipedia entry with a
completely fabricated quotation from the composer. Within days, obituary
authors all over the world were using Fitzgerald’s quotation in their
published pieces. Fitzgerald revealed after some weeks that he had
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fabricated the quotations, and these journalists were humiliated. Clearly
Wikipedia may the first word on internet research, but by no means should it
be the final word.18
The ultimate defense against unreliability: corroboration
Even if we don’t know when a testifier is an expert or a liar, there is always
one recourse by which to test its reliability: the reality check.
As knowers we are privileged to have a great number of background
beliefs about the world, beliefs according to which some claims of testifiers
will look highly improbable if not downright impossible. Of course our
background beliefs are not always right—not all background beliefs are
actually background knowledge. So sometimes the information we receive
from testifiers may contradict our background beliefs for the better. Surely
when Western explorers first visited the tropics and informed the natives
about the presence of lakes of frozen ice and snow in the north, the tropical
natives were understandably skeptical. All of their experience suggested that
water was always liquid, never frozen. In this case, their experience had led
them to formulate background beliefs about water which turned out to be
false. The same was also probably true of the Western explorers in regards
to testimony they had received about strange creatures living in the tropics.
But here it is important to remember that to rely on any testimony, we
have to rely on our background beliefs. So in the second section of this
chapter, we discussed various simple beliefs, about the track records of
testifiers, and about the equipment testifiers must have in order to observe,
remember and report their knowledge, which made the testimony of others
relevant, and not the simple appeal to subjectivism. If we have to rely on
some background beliefs to believe any testimony at all, then it’s possible
that we may sometimes encounter testimony whose very content is
undermined by the background beliefs we depend on to trust any testimony.
Here is a simple example: Suppose a stranger tells us that he has seen
with his very own eyes a man walk through a wall. Presumably even a
stranger we don’t know is in a position to observe things like men, and
things like walls, and we have some sense of what it would look like for a
man to walk through a wall. But we also know that if men could walk
through walls, their bodies and the laws of physics in general would be very
different from what we have been led to believe. Huge swaths of our
18
Genevieve Carberry, “Student’s Wikipedia Hoax quote used worldwide in newspaper obituaries,” The Irish Times, May 6, 2009. <
http://www.irishtimes.com/newspaper/ireland/2009/0506/1224245992919.html>
111
background beliefs about the properties of solid objects would have to be
thrown out.
As we have seen, sometimes the reports of testifiers can justify
throwing out our conventionally-held beliefs. But would they do that in this
case? If even our most basic beliefs about men’s bodies and the properties of
solid objects have to be thrown out, what is our reason for relying on
testimony from other men? Part of the reason we trust anybody’s testimony
is because we assume that other people are stable, predictable entities with
definite equipment that allows them to get in causal contact with the world,
know things about it, and be able to report it to us. This belief in an orderly
cause-and-effect universe is crucial to relying on the testimony of others.
But if we are now to believe that men can unpredictably walk through walls,
the universe begins to look much less orderly and causal. If it is not orderly
and causal, however, what is our reason for relying on the testimony of
others? The reason begins to disappear. It is as if this testimony about a
man’s walking through a wall cuts the off branch on which it is standing. It
must therefore fall.
The lesson here is that testimony, like any other belief, can be
corroborated by reference to facts of reality. Some facts are much better
known than the presuppositions of the reliability of testimony itself. So
when we hear reports of miraculous events, it is more likely, as far as we are
concerned, that something has gone wrong with the testimony, than that
what the testimony claims is actually true. (This is an important point made
by the philosopher David Hume in his treatise, Enquiry concerning Human
Understanding.) Since we only rely on testimony because of a belief in a
causal, orderly universe, if the content of the testimony calls this into
question, we will rightly think that it is more likely that the testifier was
hallucinating when he saw this, or that he is lying to us, or at least that he
honestly misinterpreted what he saw. It is more likely that this would
happen, than that cause and effect would break down—which would mean
we could no longer believe anything on the basis of testimony, anyway.
It is especially important to remember lessons like these when we
encounter rumors and reports that are wildly at odds with what we already
know. The pitfalls here range from the forwarded emails we receive from
our relatives, to reports of miracles in ancient texts.
Exercises
1. If you received this email today, forwarded by a friend who to
whom it was forwarded from someone else, how well would its
claims corroborate with what you know?
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Greetings To All of My Friends and Family
In just 4 days from today all U. S. cell phone numbers will be
released to telemarketing companies and you will begin to receive
sales calls. You will be charged for these calls! Even if you do not
answer, the telemarketer will end up in your voice mail and you
will be charged for all of the minutes the incoming (usually
recorded) message takes to complete. You will then also be
charged when you call your voice mail to retrieve your messages.
To prevent this, call 888-382-1222 from your cell phone. This is
the national DO NOT CALL list; it takes only a minute to register
your cell phone number and it blocks most telemarketers calls for
five years.
In case you have friends other than me, pass this on to them.
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§2: SOME BASIC FORMS OF GOOD REASONING, AND THEIR FALLACIOUS
COUNTERPARTS
Chapter 6:
Reason, emotion, and emotionalism
Ben Bayer
Drafted February 2, 2010
August 8, 2010
Popular views about emotions
In chapter 4 when we discussed subjectivism, we made the point that merely
possessing a mental state—whether a belief, a feeling, or a desire—does not
guarantee that the object of the state is really present. What we believe might
be false. What we desire might be bad or wrong. What we feel might not be
apt.
But the appeal to feelings or emotions as a source of evidence—the
fallacy of emotionalism—is one of the most tempting of subjectivist
fallacies. What explains its persistence? Why do our feelings seem to be
such reliable guides to the truth? Why do they seem to be of such searing
relevance to some thinkers, when we know that to rely on them exclusively
is to commit a subjectivist fallacy?
In this chapter, we will begin by examining some basic points about
the psychological origins of emotions. What are they and where do they
come from? How do they relate to reason and thinking? Answering these
questions will explain why emotions can create such a compelling illusion of
knowledge, even when it is only an illusion. This does not mean that they
should never be enjoyed or experienced. Far from it. But it does mean they
have a specific role that must be identified and kept in check.
What is an emotion? It is a feeling like anger, hatred, joy, fear,
embarrassment, serenity. Notably, there are things we sometimes call
“feelings” which are not the real emotions. This includes physical sensations
of pleasure and pain, for instance. While they are reactive states of
consciousness with a positive or negative content like joy and suffering, they
are different in that the same stimuli will generally cause them to come
about in all people (nobody is made to feel pleasure by a knife in the chest). .
But the causes of the emotions of joy and suffering will vary from person to
person, and emotions will remain long after the stimulus has departed. We
can also distinguish emotions from generalized moods or “funks,”
conditions which permeate our lives for lengthy periods of time. Moods may
114
result from purely physiological or environmental conditions, whereas the
cause of emotions is more cognitive.
What is the cause of emotions? The answer to this question is
somewhat controversial. To illustrate the nature
of the controversy, let’s first examine some
popular views about emotions.
One prominent attitude towards emotions
is the view that emotions have mysterious causes.
A feeling, on this view, is like a “bolt from the
blue.” This view is especially popular among
artists who speak of waiting passively to receive
inspiration for their work, and who say they
cannot express in words any emotion they do
receive. The philosopher Pascal is noted for
having said that “The heart has reasons that
Picture credit 58:
reason knows not.” Belief in this struggle
http://commons.wikimedia.org/wiki/File:C
aspar_David_Friedrich_032.jpg
between the head and the heart is not restricted to
artists and religious mystics like Pascal. One can believe in the same
struggle between reason and emotion, but, still holding that emotions have
no basis in reason, repudiate them and embrace reason. This is the attitude of
Spock from Star Trek, who is famous for his repressed demeanor and
worship of logic. (“Emotions are alien to me. I am a scientist,” said Spock
on Stardate 3417.3). It seems that Spock, thinking that the causes of
emotions cannot be understood, does not want to deal with what he cannot
understand and therefore makes an effort to
repress his emotions.
Viewing the causes of emotions as
mysterious goes hand in hand with a second
view, that emotions are uncontrollable.
“Reason has no power against feeling,” said
Charlotte Perkins Gilman. Or consider the
words of Alexander Pope: “On life’s vast
ocean diversely we sail, Reason the card,
but passion is the gale.” A “card” is a
rudder: Pope is saying that we can use our
reason to navigate through life, but our
passions make for stormy seas which we
cannot control; we can only let passion push
us along and hope that it doesn’t cause us to Picture credit 59:
http://commons.wikimedia.org/wiki/File:Rembrandt_
capsize. It is interesting that Pope uses the
Christ_In_The_Storm_On_The_Sea_Of_Galilee.jpg
115
word “passion” here, because this near-synonym for “emotion” betrays a
revealing linguistic history. Emotions have been thought of as passions
because we are thought to experience them passively as patients, just as
actions are what an active agent undertakes.
A final popular view related to the first two is that we should give in
to our emotions. This was perhaps
best enunciated by some unknown
hippie: “If it feels good, do it.” If
they really are forces beyond our
control, to resist our feelings would
be great folly. A tree that bends
with the wind may stay firmly
rooted, but one that stands firm
may snap in a gale. Following
another analogy, repressing our
Picture credit 60:
emotions is often compared to
http://commons.wikimedia.org/wiki/File:Nicolas_Poussin_004.jpg
bottling up a liquid under high
pressure: bottle up too much of it, and eventually it will explode.
Each of these three components of the popular view is closely related
to the others. If we don’t know or can’t know the causes of something, we
certainly can’t control it. Primitive people who didn’t know the causes of the
seasons or of the success or failure of their crops couldn’t hope to control
them. At best they could say prayers or offer up sacrifices to the gods of the
harvest. To this day, emotions are thought of on the same model as this
primitive understanding of the harvest. The third component of the popular
view is also related to the second. If emotions (or passions) are really
uncontrollable, then we might as well give in to them: resisting what we
cannot control will only deliver us to destruction. In the same way, primitive
people thought that if they failed to appease the gods, they would suffer
retribution or wrath.
But is this popular view of the emotions really correct? Should we
really think about them along the lines that primitive people thought of
uncontrollable forces of nature? We have since discovered the causes of
successful harvest and no longer give prayers or render sacrifices to the gods
of the harvest. Instead we find ways to introduce the causes we need to
achieve the effects we desire. We can fertilize, irrigate, even hybridize or
genetically engineer our crops for optimal outcomes. What if we could
identify the causes of our emotions? Then there would be something like an
art comparable to agriculture that would help us “cultivate” the healthiest of
116
emotions. Our reason and our emotion would no longer be at odds with each
other in the Pascalian or Spockian sense.
Cognitive causes of emotions
We don’t have an art of cultivating our emotions that is nearly as well-tested
or sophisticated as agriculture has become. Ever since the ancient Greeks,
however, philosophers have inquired into the origins of our emotions, with
varying results. The ancient Stoics, for instance, went so far as to identify
emotions with cognitive judgments of value.19 Whether or not emotions and
judgments should be so strongly identified is very controversial. But ever
since contemporary philosophers have begun to reconsider ancient views of
emotions, it has become more popular to consider how our judgments about
the world might at least figure among the causes of our emotions.
The contemporary reexamination of the cognitive dimensions of the
emotions has been supplemented by new breakthroughs on the practical side
of psychology. During the beginning of the twentieth century, behavioristic
psychologists like B.F. Skinner became famous for arguing that talk of
mental states such as emotions could be
explained entirely in terms of an
observable stimulus and response
exhibited by an organism. This meant that
unobserved internal mental states were not
judged as important components of the
causal chain. It turned out that
understanding emotions in this way proved
to be of only limited use in the practice of
psychotherapy. People, it turned out, were
not like Pavlov’s dogs, conditioned
through the right kind of rewards and
punishments. In the 1970s, a new
approach to psychology was developed by
theorists like Aaron Beck and Albert Ellis,
Picture credit 61:
variously called cognitive therapy or
http://www.flickr.com/photos/39649197@N00/44272
8348
cognitive-behavioral therapy or rational20
emotive behavior therapy. These approaches emphasized an intimate
connection between our emotions and our thinking, in particular, the basic
thinking involved in our evaluations of the world and ourselves.
19
de Sousa, Ronald, "Emotion", The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward
N. Zalta (ed.), forthcoming URL = <http://plato.stanford.edu/archives/spr2010/entries/emotion/>.
20
See Beck’s classic book Cognitive Therapy and the Emotional Disorders, Plume (1979).
117
To understand the basics of what both cognitivist theories of emotions
in philosophy and cognitive approach in psychotherapy have in common, it
is worth going through some examples of emotional responses and how they
can be analyzed into various cognitive and non-cognitive components.
Two obvious facts about emotions relevant to the cognitive view are
recognized by just about anybody. When considered in isolation, these two
facts tend to lend credence to the popular view that emotions are passions
that we cannot control. First: emotions are stimulated by things we perceive
in the world. Second: they are experienced automatically.
Imagine you are walking along a mountain trail and in the distance
you see a dark shape move around the
switchback several hundred feet in front of
you. You train your binoculars ahead, and
are able make out a large, growling grizzly
bear. The bear snarls and reveals his terrible
fangs as you realize that he is headed in
your direction. What do you feel? An
immediate shock of fear if not outright
terror pulses through your entire body.
Surely the perceptual stimulus is relevant
here: had the bear not appeared in your field
of vision, you would have gone about your
merry way, enjoying the hike. And the
experience of the terror is automatic, at
least in the moment: unless you are a
Picture credit 62:
trained animal handler for whom
http://www.flickr.com/photos/duncantoms/239275791
4/
encountering such beasts is par for the
course, there surely is a sense in which you cannot control what you feel.
If we only focused on the way emotions are experienced in the
immediate moment, we might be led to believe that emotions are
uncontrollable forces beyond our understanding. But notice that even in this
example of terror, there is already an easily understood cause: our perception
of the bear. This leads us to identify a third fact about emotions: like the
sensory perception that causes them, emotions themselves have objects. We
do not just perceive the bear and then experience a generalized fear. (A
generalized fear without object would be a sign of an anxiety attack.) We are
afraid of the bear. Objects of our emotions can be identified in many other
cases. Taking an example of the opposite quality, consider a mother’s love
for her child: she has affection for the child, she loves her son. (When it
comes to adorable little babies, most of us have a hard time not feeling at
118
least some of the same affection, even when they are not ours.) A fourth
important fact about emotions is that, like perception, they also have
physical effects: fear can make our heart race, our hands feel clammy, etc.
Affection can bring about very different physical effects.
Although in some ways, emotional responses compare favorably to
perceptual responses, they are nonetheless not identical to any perceptual
experience. What’s more, even if perception is the proximate cause of
emotion, it is not the only cause. As we shall see, the evidence for this is that
different people can perceive the same object but still experience widely
divergent emotional responses to it.
Let’s first consider an example of an emotional reaction that you
might, at first, take to be completely universal. Were you watching
television on the day of September
11, 2001? Do you remember what it
felt like when you saw that a plane
had crashed into the tower? This
was probably destruction on a scale
greater than you had ever seen
before, and you were probably felt
horror, and sorrow for what must
have been scores of victims. And
the day would only become more
Picture credit 63: http://commons.wikimedia.org/wiki/File:World- dramatic. When the second plane
Trade-Center_9-11.jpg
hit, you knew it was no longer an
accident, but a deliberate terrorist attack. You probably felt outrage and
anger at whoever had planned these attacks. When you heard stories later in
the week about the passengers on Flight 93 who had thwarted another attack
by battling with the terrorists, you probably felt inspired by their heroism.
But were these feelings completely universal? We know there were at
least some people in the world who did not share them. At the very least, we
know that those who had planned the attacks did not. When we later saw
video of Osama bin Laden describing how had planned the attacks, how he
had only hoped that parts of the buildings would collapse, and how the
eventual total collapse was “all that [he] had hoped for,” we realized that this
man’s emotional reactions were not the same as ours.21 Not only did bin
Laden not feel sorrow or horror or anger at the attacks. Since he had
undertaken them quite purposefully, and they had succeeded beyond his
wildest dreams, he seems to have actually experienced the emotion of glee.
21
CNN, “Bin Laden on tape: Attacks ‘benefited Islam greatly.’”
<http://archives.cnn.com/2001/US/12/13/ret.bin.laden.videotape/>
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But bin Laden had seen pictures of the exact same situation as we had
seen. Why did he not respond in horror in the same way? The answer is that
what we perceive with our senses is not the only fact that explains our
emotional reaction. Another element of the explanation is how we interpret
what we perceive, and this interpretation is determined by judgments of the
mind. We do not always realize that these judgments are present. Just as we
will accept the testimony of strangers automatically without thinking about
the background knowledge that makes this automatized trust possible, we
also don’t think about the background beliefs we have automatized that
condition our emotional response. Sometimes they are so well automatized
that we hold them only subconsciously. We might even have consciouslyheld beliefs that contradict our subconscious beliefs.
What are the judgments of the mind (consciously-held or otherwise)
that make a difference for our emotional reactions? Two in particular are
especially important: our identification of the object we see in front of us,
and our evaluation of it. First consider the judgment of identification. The
reason we are afraid of the bear is that we are convinced it is a real bear. If,
by contrast, we knew that it was really a fake, stuffed bear, and had
encountered it many times before, we would not feel afraid. We might feel
nothing at all, or even amused by the idea of doing something ridiculous like
stuffing a bear. It can be useful to represent the cognitive steps involved in
an emotional response in a series of box diagrams, as follows:
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The idea here is that a difference in identification of the same perceived
object makes a difference for the evaluation that results, and consequently a
difference in emotional response.
But different identifications are not the only differences in
background belief that can make a difference for the emotion we experience.
People may perceive the same object and identify it in the same way, but
still experience different emotions. Consider the difference between our
reaction to September 11 and bin Laden’s reaction. Both of us realized that
innocent people were dying in these burning, eventually collapsing towers.
Later we found out that thousands had died. But we had different evaluations
of these facts. Most of us evaluated these facts as attacks on our values. Bin
Laden evaluated them as furthering his cause. As a result, we felt sorrow and
horror, but he only felt glee:
The fact that human emotional responses can be as disparate as this is
probably one of the reasons people think that emotions are “inexplicable.”
It’s thought that they can’t be communicated by means of words, because
people’s emotional reactions are universally different. Perhaps they are
difficult to communicate, but this is not because their causes are mysterious.
Rather, it is because their causes are difficult to discover, and so differences
in emotional reaction can be very difficult to understand. The difficulty here
is heightened by the fact that most people take their basic frameworks of
value judgments for granted, without need for argument. They wear
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“ideological blinders” and do not even realize that another evaluation is
possible.
The differences in emotion experienced in response to the same object
are not limited to those among different people. There can also be different
responses for the same person. A simple example is that we can experience
distinct emotions nearly simultaneously in response to the same perceived
object. When we witnessed the September 11 attacks, we felt not only
sorrow, but horror and even anger. Perceiving the same object occasioned a
number of distinct identifying judgments, and distinct corresponding
emotions. We felt sorrow because we judged that innocent deaths are
unfortunate, horror at the thought that some human beings could do this to
others—and that they might even try to do it to us—and anger because we
judged this to be an act of intentional destruction, an act of evil:
The same individual can even have “contradictory” emotional
responses to the same object over time. For instance, suppose that bin Laden
was eventually convinced to believe that his cause was unjust and, as a
result, so were the deaths of these innocent people. In that case, he would
feel remorse and guilt, and consequently he would feel sorrow for and horror
in response to the same event over which he had once felt glee.
Of course changes of mind like this are not too frequent. One would
probably not be able to live with one self for long after assuming this much
guilt, so people who begin to feel hints of guilt for their crimes will often
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create rationalizations for themselves to encourage the belief that they are
not guilty. Still, it is possible to make relatively substantial changes in
emotional reactions by reevaluating one’s core judgments about oneself.
This is the kind of change that cognitive therapy usually aims at, and at
which it has been known to succeed.
What is a core judgment? Consider our relatively simple bear
example. Even this example involves a core judgment. One would not
respond in the typical way to the danger of the bear if one did not already
have the core judgment that one’s life is important:
It is possible that someone who is suicidal and convinced that his life is
worthless might not have the same reaction to the bear. At last, he might
think, he has found a relief from the suffering of the world. If this is
somewhat implausible, then consider other examples in which our reaction
of fear might not be as automatized. Consider the way a suicidal person
might respond to a gun pointed at his head, or simply to a couple of pills in
his hands.
Core judgments like these are usually at the root of a great number of
psychological problems. Sometimes a seemingly disparate set of problems
can even be explained by the possession of a single core belief. (This is part
of what makes it “core”.) Suppose a person has a strange complex of
problems: When he experiences a headache, he has an anxiety attack. When
he receives a bad grade on a test, he becomes chronically, clinically
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depressed. And when he sees someone else who did well on the test, or who
is doing well at life in general, he feels hatred. Interestingly, many people
who experience anxiety attacks experience them because they believe they
are going to die. Chronic depression because of life’s failures can result from
the conviction that trying harder is pointless, nothing we do will ever help us
succeed. And the hatred of success can result from the belief that another’s
success is threatening to one’s own. What single core judgment could
account for all of these identifications and evaluations? One candidate that
psychotherapists might diagnose is a lack of core self-esteem, the conviction
that one is inadequate to live life successfully, which one might hold because
of failures suffered in early life:
If you feel you are basically inadequate to live, even the littlest problems can
suddenly become enormous, insuperable obstacles. A headache becomes a
sign of looming death, a bad grade heralds the end of the world, and success
in the world seems to be of a finite quantity that one person achieves only at
the expense of another.
Cognitive therapists have realized that because our core judgments
can sometimes be so deeply buried, we might not realize that we have
them—and therefore we might not realize how our emotional reactions have
been “programmed” by beliefs that we would not accept if we brought them
to the light of day. One of the goals of cognitive therapy is to bring these
core judgments to light of day. Once we realize that we think we are
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inadequate to live, we can think about whether it is true that some failure we
suffered in childhood really makes us unequipped to handle life. As a result,
we start to see recent failures with better perspective. We realize that our
problem may not be our basic abilities, but the particular strategies we may
have chosen over the years. An unhealthy emotional response is like a
logical fallacy we have automatized, which we do not even realize we find
plausible.
Therapy is effective when it engages the tools of logic to unearth these
subconsciously-held fallacies and criticize them until we are no longer under
their spell. Of course this is easier said than done. At first the most we can
do is to separate our current judgments from our subconscious ones, and
realize that there is a difference between our mature thinking and immature,
leftover snap judgments. This can help us temper the decisions and actions
we would otherwise take on the basis of our feelings. It can take years and
years of conscientious effort to fully replace our automatized, subconscious
beliefs with others. But the principle holds fast: our emotional reactions can
change as we change our basic habits of thinking.
If all of this is true, reason and emotion are not fundamentally
opposed to each other. Emotions are only passive in relation to our thinking,
but we actively control our thinking. As soon as we learn to take more
conscious control of our thinking, our emotions are no longer experienced as
alien forces, but as allies motivating our actions in accord with the value
judgments we hold consciously.
We may also learn something of philosophical significance if different
emotions really do have different cognitive causes. Remember that in
chapter 4, we considered the plausibility of the view that value judgments
are just expressions or reports of our emotions. This is a view about value
judgments called subjectivism. If, however, it is true that emotions have a
cognitive basis, then value judgments cannot be explained by our emotions,
because our emotions are themselves explained by value judgments. We
cannot simply say that a belief in the importance of individual freedom as a
rival to theocratic dictatorship is “just an opinion” that bottoms out in
someone’s emotional reaction, if we can only explain different emotional
reactions by reference to differences in value judgments on these topics:
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There are still philosophers who might hold out for a form of value
subjectivism, insisting that the correlation between types of value judgment
and types of emotion can be accounted for by the possibility that primitive
emotions are the basis for value judgments. But these philosophers would
then owe us a special explanation for why different people experience
different primitive emotions in response to the same perceived objects. The
possibility that these responses are mediated by a third, cognitive cause
seems like the natural explanation. In the absence of the cognitive mediation,
what accounts for the difference? And why would evolution give us such
radically different automatic responses the same elements of our
environment? Of course the same question might be asked of our differing
value judgments, but we already expect judgments to be true or false, the
types of things about which people disagree. If basic emotions are primitive,
one wonders why they are not like physical sensations of pleasure and pain,
whose causes are generally the same for all people.
“Emotion” defined
We began this chapter by trying to distinguish emotions from other
phenomena of consciousness, such as physical sensations and generalized
moods. We then saw that emotions could also be distinguished from sensory
perception, because while they are generated by a stimulus and experienced
automatically, they are causally mediated by various conscious or
subconscious judgments we might hold. We are now in a position to give a
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formal definition of “emotion” on the basis of these differentiations: An
emotion is the mental/physical form in which we react to perceived objects
in light of our evaluation of them.
Because an emotion is a form of awareness, it is like a transparent
medium through which we see the world. As a result, we can forget that it
has specific causes, and that these causes are cognitive. This is the main
reason—in addition to being experienced automatically—that emotions offer
such a convincing illusion of knowledge. We see our entire world through
them, and they are difficult to analyze and modify. As a result, many of us
jump to the conclusion that the world is as they suggest it to be.
However, because our emotions are based on prior judgments, and
are not simply a transparent lens through which we see the world, this
means that they can be misleading, or inapt. Those judgments can be false.
As one philosopher put it, “an emotion that clashes with your reason, an
emotion that you cannot explain or control, is only the carcass of that stale
thinking which you forbade your mind to revise.”22 Because the judgments
behind an emotion can be false, we can be wrong that we are inadequate,
for example, and the resulting feelings of anxiety or depression or hatred
can be not only inapt, but downright unhealthy (insofar as they inhibit us
from functioning well).
This helps us explain why emotionalist subjectivism is a fallacy.
Emotionalism is the fallacy of urging action on the basis of an emotion
without assessing its source. The reason that an emotion is not an adequate
source of evidence about the world on its own is that we experience it only
because of some judgment we already have—but that judgment could be
false. So in one sense, emotionalist thinking is the ultimate form of
subjectivism through mental laziness.
From another perspective, we can see that the appeal to emotions is
a fallacy because, were we to bring the thought behind it to light and assert
it as a premise, our argument would then be blatantly circular. In the
argument, “I feel like doing X, therefore X is good,” the possession of the
feeling presupposes the judgment that X is good. That means that the
implicit argument here, were the presupposed judgment to be brought to
light, would read: “X is good, therefore X is good,” which is a circular
argument or very close to one.
22
Ayn Rand, Atlas Shrugged, pg. 953.
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Common emotionalist fallacies
Unfortunately reliance on the fallacy of emotionalism is extremely
widespread. In part this is understandable. For one thing, emotions are so
automatic that they do seem to deliver us some kind of unquestionable truth,
in just the same way that sensory perception delivers it to us. It takes care
and maturity to uncover the judgments behind our emotions, and even more
to realize that they might not be true. The illusion of emotionalism is
especially powerful because the whole biological function of emotions is
precisely to motivate action, to encourage us to act on what we know. The
problem is that not all of our beliefs are knowledge, and our emotions don’t
know the difference. Yet acting on the basis of a motivation resulting from a
false premise can be dangerous.
We cannot emphasize enough just how inapt emotions can be, or just
how many false beliefs they might presuppose. Consider the example
mentioned in the earlier section of the person who feels hatred toward a
successful person because he feels a deep sense of inadequacy. First, the
person of low self-esteem sees the successful person: this first step,
perception, is the only step in the process that does not involve any obvious
potential for error. Everything that follows does.
Consider the first judgment: the identification that she is successful. It
is one thing to see a person who happens to be successful; it is another to
know that this is what one is seeing. A person who is successful might easily
be confused with one who puts on the air of success. The only fact that our
possession of the emotion might reveal is that we have some identification
and evaluation or other of this person. And even this is not guaranteed,
because people are notoriously bad at introspection, and might not realize
that emotions have judgments as causes. Even if we know that some
judgments must be the cause, the emotion does not infallibly tell us what
those implicit judgments are. If it did, we would not need psychotherapists.
So experiencing this emotion of hatred doesn’t even tell you that you think
you’re inadequate.
Even if our emotions told us what judgments were behind them, they
would still not tell us whether those judgments were true. Does experiencing
the emotion of hatred in response to a successful person tell you that you
really are totally inadequate? No, you could be wrong about this. (Most
people who think this probably are wrong—the ones who aren’t completely
inadequate usually find ways to convince themselves otherwise!) The
implicit evaluation of the other person as negative on the grounds that her
success is threatening is likewise quite fallible, and is, in this author’s
opinion, something that only a seriously insecure person could think. It’s not
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true that there’s only a limited amount of success to go around. If that were
true, where did success come from in the first place? Are we still working
with the level of success passed down to us from cavemen?
Finally, the fact that a person experiences hatred as a result of these
implicit judgments would seem to be the most readily accessible fact that the
emotion of hatred could make obvious to the person feeling it. But even
here, there is no infallibility. Emotions do not automatically self-identify
themselves. We do not automatically know the difference between
frustration and embarrassment, between happiness and mere “kicks,”
between a feeling of genuine concern for a problem, and neurosis about it.
Making these distinctions requires forming one’s concepts of each of these
emotions carefully, and applying them even more scrupulously to the data.
Some people may even have trouble distinguishing positive from negative
emotions. A person who takes sadistic pleasure from torturing his victims, is
he really happy? Is what he experiences really joy? Or is instead a deep kind
of neurosis engendered by the need to escape from the pain of the rest of his
life?
An emotion like hatred could, however, be cited or invoked by a
rhetorician—and all too often in history, has been—in order to urge action
against some hated individual or group. Such use would constitute an
emotionalist fallacy. How else were racist Nazis able to motivate large
numbers of Germans to enslave and murder millions of Jews? Germans were
willing to believe in various conspiracy theories propounded by the Nazis
because many of them already resented or despised Jews who had
independently achieved a decent amount of material success. The same kind
of emotional appeal helped the Bolsheviks convince many Russians to
outlaw capitalist private ownership and nationalize industries in order to
establish a dictatorship.
Just about any emotion can be appealed to in an emotionalist fallacy.
But some emotions have special powers to motivate action, and because of
the widespread acceptance of some particular codes of values in the West,
some emotions are more widely used in emotionalist fallacies than others.
These include the emotions of pity, fear, humor or laughter, and inspirational
feelings associated with patriotism or heroism.
The appeal to pity
The appeal to pity is probably the most common emotionalist fallacy,
so there is much to say about it. It involves citing or invoking a feeling of
pity as a reason to help or not hurt another person. Thousands of years of
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Judeo-Christian ethics have placed a special moral premium on rendering
assistance to those who suffer. Pity is the emotion that responds to suffering
and encourages one to relieve it. Whatever one thinks of the merits of the
Judeo-Christian code, it has infused Western culture with so much concern
for suffering that the associated emotion of pity can sometimes cloud our
thinking.
Let’s begin with an example of the fallacy whose fallaciousness
should be almost entirely uncontroversial. Consider a married couple. One
spouse tends to physically
dominate the other and
frequently uses violence to
“settle” conflicts. One night
after a severe beating, the
victim calls the police and has
the abusive spouse arrested.
As the police begin to describe
the court proceedings against
the abuser, including the
potential consequences in
terms of prison time, the
abuser pleads for forgiveness. Picture credit 64: http://en.wikipedia.org/wiki/File:Cycle_of_Abuse.png
The abuse victim begins to feel pangs of remorse. Recalling the love they
once felt for each other, the victim has second thoughts and considers
dropping the charges. The argument being appealed to might look like the
following:
I feel sorry for my abuser.
Therefore, I should drop the charges against my abuser.
This is the kind of thinking that traps many abuse victims in the socalled “cycle of abuse,” in which abusers take the victim’s continued
forgiveness as a license to continue the abuse after a “honeymoon” period
between the two of them has expired. Here it is not only the emotion of
affection or love that motivates the victim to grant forgiveness, but the
emotion of pity. The victim knows that the abuser will be punished for the
abuse, and simply does not want to see him or her suffer the pain associated
with the punishment. (The victim’s affection—past or present—for the
abuser simply magnifies the effect of the feeling of pity, which some people
will have towards anyone’s suffering.)
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Whatever you think of the virtue of mercy, it remains true that were
the victim to drop the charges against the abuser simply on the basis of this
feeling of pity, he or she would be committing the emotionalist fallacy of the
appeal to pity. There are many background judgments behind his feeling of
pity that could be mistaken. What of his identification that the abuser feels
remorse? It could be mistaken. Perhaps the abuser is faking or exaggerating
his remores precisely in order to gain the victim’s favor and be released from
custody. A similar trick is used by underdogs in fights to the death in the
movies, when the party losing the fight pretends to be wounded in order to
gain the upper hand. You’ve no doubt seen Emperor Palpatine work the trick
in the Star Wars movies against both Jedi Mace Windu and the repentant
Darth Vader himself.
What of the victim’s evaluation that he should help a suffering
spouse? Even supposing that the abuser is really remorseful, the victim
knows that they have been abused. Is the victim to give up the quest for
justice and suddenly forgive the abuser because of a temporary feeling of
pity? We feel pity because we judge that a person does not deserve to suffer,
but perhaps criminals who violently abuse weaker parties do deserve their
punishment. Is an abuser suddenly no longer a threat because someone feels
pity towards him or her? Should mercy always be more important than
justice? Emotions do not answer these questions, especially the
philosophical question of the relative importance of justice vs. mercy. If the
victim has not already thought through these questions, the emotion of pity
will not give any new information relevant to the questions. The experience
of the emotion is simply a reflection of the fact that it is possible to answer
the questions passively and unthinkingly.
The point of analyzing examples of the appeal to pity is not that one
should never be motivated by pity to help someone who is suffering. The
point is just that the feeling of pity alone is inadequate logical justification
for doing so. All unevaluated, uncritically-accepted emotion are. If you think
that no one would see any logic in the victim’s forgiveness of the abuser on,
consider that many popular cultural and political viewpoints today follow
the same pattern.
It is worth briefly considering the diversity of cultural and political
arguments that rely on the appeal to pity. They deal with subjects that range
from the mundane to the incredibly controversial. You may have very strong
opinions on some of these topics already, so please try to consider them
independently of those emotions. The point here is not that the conclusions
we’ll consider are necessarily false, but that the emotionalistic arguments
presented for these conclusions are not logical.
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Consider, for example, the debate over animal rights. Many people on
the political left who favor animal rights in effect do so because they see
pictures and hear stories of the suffering animals may experience during
biological testing or in the food
harvesting process, and react with
arguments like this:
Look at how cute and harmless
this animal is.
Therefore, it would be wrong to
use the animal for medical
testing.
credit 65:
Philosophers and scientists can and do Picture
http://www.flickr.com/photos/janinevanemden/3411768141/
give extensive arguments for why
animal testing should be outlawed, or why we should never eat meat.
Whether these arguments ultimately succeed is a matter of debate. But this
emotionalist argument by itself does not come close to giving a logical
reason for the prohibition of animal testing. Just about anyone can look at
the animal and empathize with it in a way that no one would empathize with
a plant. Animals, especially mammals, look a lot like humans, and it is easy
to anthropomorphize them into having human thoughts and feelings. But do
they really? That is a matter of great debate, as is the question of whether an
animal’s suffering, to the degree that it has it, is morally significant in the
same way that human suffering is. This is especially important to remember,
given that it is often human suffering medical researchers are trying to
alleviate. If a philosopher can give an argument for why animal suffering is
as important as the human kind—if he can establish that animals have rights
or are otherwise worthy of special moral respect or legal protection—that is
one matter. But if the only basis for their protection is the feeling of pity, this
is not enough, logically speaking.
Unfortunately, the same kind of emotionalism will often plague the
abortion debate, this time usually emanating from the political right. Antiabortion advocates will show us pictures of fetuses in the attempt to generate
in us a feeling of pity. (Some will even show pictures of aborted fetuses, in
order to generate a feeling of disgust.) The emotionalist fallacy implicit in
their use of pictures in this way is as follows:
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This fetus looks weak and
defenseless.
Therefore, abortion should be
illegal.
Once again, philosophers or theologians
can and do give arguments for why the
fetus should be seen as worthy of moral
respect and legal protection. As with
arguments for animals rights, these
arguments are themselves highly
controversial. But even a controversial
philosophical argument is head and
shoulders above this emotionalistic
argument, which has not even the veneer
of logic to it. Does the fact that something
looks vaguely human mean that it really is
Picture credit 66:
a human person, and worthy of moral
http://www.flickr.com/photos/lunarcaustic/212861833
respect? Or even if it has human DNA, does
3/
that mean it is the moral or legal equivalent
of a fully-formed adult human being? Do we have obligations to assist
anything weak and defenseless? None of these questions are answered
logically by our feeling of pity. The feeling only indicates that we have
answered the question for ourselves already—but not whether we have done
so logically or illogically.
The fact that emotions can be unreliable indicators of the truth is
brought to the forefront by the fact that
people can have completely different
emotional reactions to the same situations.
Sometimes the same people can have
conflicting feelings of pity about the same
situations. Consider, for example, the
American public’s reaction to the civil war
and famine in Somalia in the early 1990s.
When TV pictures of starving Somalians
hit the air, urgent calls were made for
Western military intervention to quell the
fighting and open up lines of humanitarian
relief to starving people. Eventually the
Picture credit 67:
TV pictures found their target, and
http://commons.wikimedia.org/wiki/File:Botswana_D
efense_Force_Soldier_DD-SD-00-01033.jpg
133
President George H.W. Bush was moved to send American troops. At first
the public supported the mission, but when news of American deaths
reached home, their mind began to change. Graphic stories (and images) of
American troops being massacred in the streets of the capital city,
Mogadishu caused Americans to demand newly elected President Bill
Clinton to withdraw U.S. troops less than a year later.
This schizophrenia about a foreign policy decision is symptomatic of
a set of inconsistent moral judgments held
by the American people. On the one hand,
they were convinced they should relieve
suffering in the world. On the other hand,
they were also concerned about the lives
and happiness of their own troops. Which
of these values was to be given higher
priority? Their emotions would not
answer the question for them. On the one
hand, should we help every suffering
person in the world and become, in effect,
the world’s policeman (and aid worker)?
This would be impossible. On the other
Picture credit 68:
hand, should we withdraw from a fight
http://commons.wikimedia.org/wiki/File:Black_Hawk_
Down_Super64_over_Mogadishu_coast.jpg
whenever our troops die? This would
seem to ignore the fact that troops signed up to take these risks. Answering
these questions is difficult, and moral philosophers struggle with them. But
to struggle with them, you’ve got to think logically. It’s not enough to let
your feelings give the answer. As you can see, feelings might deliver
inconsistent answers.
Not every appeal to pity concerns deep and profound life-or-death
questions about rights, war and peace. We hear the argument every day on
just about every street corner, often delivered by panhandlers. Many people
think the poor in our own country are proper recipients of charity, but
whatever you think of this, surely you would agree that it is important to
think carefully about the proper recipients of charity, and the proper time
and place to give it. Yet some people will give to panhandlers simply
because there are accosted by them and they feel pity for them in the
immediate moment. Other motivations probably include the guilt, or the
embarrassment of not looking like a “giver” in front of one’s friends. When
they let their emotions overwhelm them in the moment like this, they don’t
stop to think about whether the panhandler is really in need, or has turned
this activity into a racket. (Many have.) They don’t stop to think about what
134
the money will be used for. (Some
panhandlers will be honest and hold
signs saying, “Why Lie? It’s for beer.”)
They don’t stop to think about whether,
by giving to panhandlers, we are
encouraging them to live on the streets
and not to seek productive employment.
And they especially don’t stop to think
about whether we should feel guilty
about the fact that we might have money,
credit 69:
and others don’t. As usual, the answers to Picture
http://www.flickr.com/photos/steveisaacs/2451061714/
all of these questions are debatable—but
they’re debates that should happen, rather than being quelled or pushed aside
by feelings in the moment.
Even something as simple as deciding with whom to attend the prom
can sometimes come down to an appeal to pity. Suppose that an unattractive
dorky character without even any redeeming personality traits—say, a
Napoleon Dynamite-like fellow who always calls everyone an “idiot”—asks
you to the big dance. He doesn’t have anyone else to go with, and looks
rather pathetic. Do you say yes, just because he’s so pathetic and you feel
sorry for this idiot who calls everyone an idiot? There’s an answer that some
people will sometimes have the courage to give to requests like this from
people who complain incessantly about their suffering about how the world
owes them a favor: “Do you hear this?
It’s the world’s tiniest violin, and it’s
playing a song. . . just for you!”
The appeal to fear
Versions of the appeal to fear
are second in popularity only to the
appeal to pity. Like pity, fear motivates
us to engage in specific actions.
Picture credit 70:
Whereas pity moves us to render some
http://www.flickr.com/photos/tgchen/2192086/
kind of assistance, fear moves us to
avoid some danger. The fallacy of the appeal to fear is to cite or invoke in
someone the emotion of fear as a reason to avoid some (alleged) danger at
all costs. As with the appeal to pity, this is a fallacy because the judgments it
presupposes (both in terms of identification and evaluation) are fallible, and
not authoritative sources of knowledge or guides to action.
135
Probably one of the oldest examples of this fallacy has been practiced
by religious mystics and preachers for millennia, when they tell us that “the
end is nigh.” We are told stories of
hellfire and brimstone, of wars and
plagues and pestilence, of Armageddon
and apocalypse. They do not merely want
to tell us a scary story, though. There is a
point to it:
The apocalypse would be scary!
Therefore, repent, sinner!
No doubt, the end of the world would be
very frightening. But what does the scary
story that’s been painted in our mind have
to do with reality or with our action in it?
Most of the soothsayers who tell of such
calamities will commit other fallacies in
order to convince us that the end really is Picture credit 71:
nigh, fallacies like the appeal to irrelevant http://commons.wikimedia.org/wiki/File:Durer_Revelat
ion_Four_Riders.jpg
authority when they cite ancient texts as
though they revealed the literal truth. But sometimes they offer the story
itself, without even an attempt at a fallacious argument to back it up, as
though it were reason enough to repent. Street preachers in particular will
resort to this tactic—perhaps they don’t have the time to catch our attention
with a scriptural argument. Of course what we ought to care about is
whether the story will actually come true, and even if we are struck by a
tinge of fear, we should know that many a fictional horror story can do the
same, and should not be taken to guide our thinking or actions. Further, our
sense of fear does not imply the truth of any evaluations we might have
about whether a looming apocalypse would threaten us. The implicit
judgment we would have to have to experience such fear—that we really are
sinners—is itself one that could be true or false, as is the presupposition that
repenting would make any difference, along with the presupposition that
there is someone or something to repent to.
Most people today do not fall for warnings of religious apocalypse.
But there are secular equivalents of these stories which are more popular.
The modern environmental movement claims to have much science to back
up their predictions of global warming, sea level rise, and looming
ecological catastrophe. Perhaps there are good scientific grounds for many
136
of these predictions (though there is sometimes more controversy over these
grounds than they are willing to admit). In any case, environmental
apocalypse scenarios are sometimes presented to the public without much
emphasis on the evidence. Instead we are told only about the terrible
consequences of failing to “repent” our
environmental sins. We are shown pictures
of entire cities being flooded by the ocean,
of coastlines receding significantly on
maps of the world. We are presented with
worst case scenarios of an uncertain
theory, even when scientists agree it is one
of the least likely scenarios. In the movie,
The Day After Tomorrow, these worst case
scenarios are all shown to occur in the
course of a few days, much more quickly
Picture credit 72:
than the seven years during which the
http://www.flickr.com/photos/rizzato/2671575856/
Biblical apocalypse is supposed to occur!
Some people are moved by the fear engendered by such stories, without
even considering the evidence for or against such scenarios. And yet all of
the same questions we asked about the religious apocalypse need answers
here, as well—and the emotion of fear does not provide the information
needed to answer these questions.
Probably one of the most realistic apocalyptic scenarios from the last
century has been the fear of a nuclear end of the world. We know that man
actually possesses the power to destroy the species several times over
through atomic weaponry. The superpower rivalry between the United States
and the Soviet Union reached a climax in the 1960s. Only two years after the
Cuban Missile Crisis, Democrat Lyndon Johnson was in a pitched battle for
the Presidency with Republican Barry Goldwater. Goldwater was an
outspoken advocate of a firm foreign policy with the Soviets. Johnson
decided to use this to his advantage, by insinuating that Goldwater would
start a nuclear war with the Russians. In a famous television commercial that
likely clinched the election for Johnson, a young girl is shown picking petals
from a daisy and counting them. Suddenly, her counting is replaced by the
countdown of a nuclear missile test. We see her looking into the distance as
a mushroom cloud rises. Then we hear the voice of Johnson, speaking the
words that amount to a premise in an argument whose conclusion is stated
by an announcer:
These are the stakes! To make a world in which all of God's children
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can live, or to go into the dark. We must either love each other, or
we must die.
[Therefore] Vote for President Johnson on November 3. The stakes
are too high for you to stay home.
The advertisement is haunting. But it is a
grand-scale example of the emotionalist
fallacy of the appeal to fear. We are told
to vote for Johnson, or we will die. No
evidence is presented that Goldwater’s
foreign policy will begin a nuclear
holocaust. No evidence is presented that
Johnson’s foreign policy is even
significantly different than Goldwater’s.
(In a great irony of history, it was
Johnson who, in subsequent years,
Picture credit 73:
escalated the war in Vietnam during
http://www.livingroomcandidate.org/commercials/1964/pe
which tens of thousands of American
ace-little-girl-daisy
soldiers died.) We are only made to feel a haunting fear, one whose object
and alternative is never specified. If this is not a dramatic example of the
danger of demagogues who exploit illogic to sway the masses, nothing else
is.
The appeal to laughter
“Laughter” is not quite the name for an emotion—it’s the name for the
physical expression that we give to the feeling we get when we express our
sense of humor. Whatever we call this emotion, there are fallacies associated
with it, too. When we listen to comedians, we naturally put down our guards.
We are looking to be entertained, not necessarily to be enlightened. But
when are listening to a political commentator or a politician who is trying to
convince us of his position, we can be disarmed temporarily by humor. A
rhetorician with a sense of humor can break through even the stoniest faces
of his opposition. This would be merely amusing if it were not for the fact
that humor is not neutral with regard to motivating us to act. To laugh at
something is to demean it, to regard it as insignificant or even contemptible.
We should, therefore, be on guard against whom we laugh at and against
whom we act on the basis of our laughter. The fact that we can isolate a
person’s foibles out of context and laugh at them does not imply that the
138
person is truly deserving of our contempt—and the actions that usually
follow from it.
Political commentary in particular utilizes the appeal to laughter. The
phenomenon is complicated by the fact that huge numbers of Americans
now rely on avowed comedy-entertainment shows like The Daily Show and
The Colbert Report for their news and commentary. Blurring the lines
between entertainment and news in this way can be dangerous, logically
speaking, because it is easier to pick on politicians foibles than it is to
engage in serious analysis of their ideas or policy proposals. The
phenomenon is complicated even further by the fact that in the recent
decade, we have encountered some fantastically humorous politicians.
It would already be outdated to speak about the foibles of George W.
Bush and Al Gore. To bring things up to date, let’s mention just briefly the
two vice presidential candidates in 2008: Sarah Palin and Joe Biden. Each
was a late night stand-up comedian’s dream come true. To the extent that we
might have relied on comedians for political advice, their arguments would
have looked like this:
Biden said, “A man I'm proud to call my friend. A man who will be
the next President of the United States — Barack America!”
“Look, John's last-minute economic
plan does nothing to tackle the numberone job facing the middle class, and it
happens to be, as Barack says, a threeletter word: jobs. J-O-B-S, jobs."
“When the stock market crashed,
Franklin D. Roosevelt got on the
television and didn't just talk about the,
you know, the princes of greed.”
Therefore, vote McCain/Palin
Of course Barack’s last name is not America,
“jobs” is not a three letter word, and FDR was Picture credit 74:
neither president during the stock market crash http://www.flickr.com/photos/barackobamadotco
m/2969826597/
of 1929, nor were television broadcasts
available. Joe Biden is quite infamous for his cantankerous gaffes, but does
this disqualify him from being Vice President? Perhaps his policy ideas do,
but these would actually need to be discussed before deciding as such. You
139
wouldn’t know this from listening to conservative talk radio, however,
which focuses all too much on the hypocrisy and hilarity of politicians like
Biden.
But let’s not pick only on the liberals. Liberal comedians had a field
day when one Sarah Palin, then-governor of Alaska, was picked as John
McCain’s running mate. Their argument for voting Obama might have
looked like this:
Palin said, “'They're our next door neighbors
and you can actually see Russia from land here
in Alaska, from an island in Alaska.''
“As for that VP talk all the time, I'll tell you, I
still can't answer that question until somebody
answers for me what is it exactly that the VP
does every day?"
Picture credit 75:
http://www.flickr.com/photos/baratunde/2826860
356/
“They are also building schools for the Afghan
children so that there is hope and opportunity
in our neighboring country of Afghanistan.''
Therefore, vote Obama/Biden!
Palin’s folksy “you betcha,” her affection for moose-hunting, and her
embarrassingly unprepared interview with Katie Couric made her the subject
of many jokes. Alaska’s proximity to Russia was only tangentially related to
Palin’s foreign policy experience, her self-described ignorance about her
would-be job description, and her slip about Afghanistan being a
“neighboring country” surely deserved to be made light of in one way or
another. But as tempting as these would be to focus on, should they really
take back seat to an assessment of Palin’s experience, her qualifications, and
her political ideas?
The appeal to inspiration
Political humor is usually wielded to cut
down an opponent; inspiration is designed to lift
up the audience to a new height. There is
absolutely nothing wrong with wanting to inspire
people. There are ways to inspire them that involve
the giving of reasons and evidence, reasons and
140
evidence to feel optimistic about the future. But not all inspiration is as
innocent as this. The fallacy we are here calling the appeal to inspiration is
something like the opposite of the appeal to fear: rather than painting the
picture of a looming danger and urging action at all cost to oppose it, the
appeal to inspiration involves citing or invoking a stirring sense
of uplift about a goal to be achieved to urge action at any cost.
The appeal to inspiration is the stock-in-trade of the political
propagandist. The great totalitarian movements of the twentieth century
employed masters in the art of political
inspiration to convince masses of people to
follow them to destruction. The Nazis told the
Germans that the Fuhrer was a glorious leader
who would lead them to establish a thousandyear Reich. Assisted by Joseph Goebbels and
masterful filmmakers like Leni Riefenstahl,
their mass rituals and print propaganda would
lead an entire nation to commit unspeakable
crimes. The communists in Soviet Russia
were no better. Stark socialist realist posters and statues, military parades,
and a national anthem as stirring as any one can find (“The Internationale”)
all helped convince the Russian people that after a revolution, their future
would be one of constant progress. Even so, Stalin murdered millions more
than Hitler, and soon led his country to economic ruin.
The legitimate use of emotion in argument
It should be emphasized that there is nothing wrong with the use of emotion
in argumentation. Emotions have a natural biological function: they motivate
us to act. People need motivation to live their lives, and for this they need
motivation even in order to think logically. So there is nothing wrong—and
everything right—with presenting logical arguments in an emotional
manner. The key here is to not let emotion substitute for the logic of the
argument. If one has well-evidenced and relevant premises that contain all of
the relevant evidence, one should feel free (in the appropriate settings) to
proclaim one’s argument in the loudest, most intense voice one can manage.
Some of history’s greatest orators have been masters of just this blend
of reason and emotion. Just so that it is perfectly clear that warning against
emotionalism does not commit us to dispensing with emotions, but instead
to the attempt to harmonize them, we will close this section with an excerpt
from a speech by the American Founding Father, Patrick Henry. We hope
you will agree with us that its structure is logical, and its rhetoric
141
inspirational. Presented merely prosaically, its argument looks like the
following:
Our countrymen have been attacked.
We may be attacked next.
Peace without freedom is not worth
having.
Therefore, we should risk our lives to
win our freedom.
But look at what Henry does with the same
statement of premises and conclusion:
Gentlemen may cry, Peace, Peace—
but there is no peace. The war is
Picture credit 76:
actually begun! The next gale that
http://commons.wikimedia.org/wiki/File:Patrick_Henr
y_Rothermel.jpg
sweeps from the north will bring to
our ears the clash of resounding arms! Our brethren are already
in the field! Why stand we here idle? What is it that gentlemen
wish? What would they have? Is life so dear, or peace so sweet,
as to be purchased at the price of chains and slavery? Forbid it,
Almighty God! I know not what course others may take; but as
for me, give me liberty or give me death!
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§3: PROOF: LEGITIMATE AND ILLEGITIMATE DEMANDS FOR IT
Chapter 7:
All the Relevant Evidence and Proof
Ben Bayer
Drafted February 20, 2010
August 15, 2010
All of the relevant evidence
We have now spent a great deal of time examining the first two requirements
of good reasoning, mainly by thinking about major ways in which each is
violated.
1. The premises of the argument must be known and known better than
the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must be likely
to establish the conclusion as true).
One of the most obvious violations of the “well-evidenced premises”
requirements is the fallacy of begging the question, and one of the most
obvious violations of the relevance requirement is the fallacy of
subjectivism. These are not the only violations, of course, but they are some
of the most seductive forms of violating these rules.
We have yet to say much about the third rule:
3. The argument’s premises must contain all of the known relevant
evidence.
Why have a rule specify not only that premises be well-evidenced and
relevant, but also that they contain all of the known relevant evidence? One
reason is that it is possible to have arguments that fit the first two
requirements but not the final. The difference between arguments that fulfill
only the first two rules, and those that fulfill all three is that while the former
may be merely decent or even good arguments, the latter are the best kind of
argument.
But what is the standard that determines whether an argument is
merely good, vs. the best? Recall why we need argument and logic in the
first place. Logic is a tool for extending our knowledge to include facts we
cannot perceive directly. It is a tool for acquiring knowledge of truths we
cannot acquire just by opening our eyes.. The better the argument is at taking
143
better known premises and transforming them into knowledge of the
previously unknown, the better the argument. There are some arguments
which, because of their relevant and well-evidenced premises, show that
something might be true. There are others that show that a conclusion is
even probably true. Finally there is a special class of arguments establishing
that a conclusion must be true.
How to know when an argument’s conclusion must be true is a
somewhat controversial question among philosophers. Many philosophers
think only a small class of arguments have this property: arguments which
merely unpack the implications already contained in their premises,
arguments called deductive arguments. For example, consider this argument
from a previous chapter:
All planets are spherical.
The Earth is a planet.
Therefore, the Earth is spherical.
Everyone would acknowledge that if we know these premises are true, then
the conclusion simply must also be true. Which is to say: if these premises
are true, the conclusion cannot be false. Provided that we know the
premises, this argument counts as a deductive proof that the earth is a
sphere.23 A proof is the best possible kind of argument, the kind that erases
all doubt about the truth of the conclusion.
Compare the deductive argument to the observation of a sailor at
sea—one who does not know the truth of either of the premises of the
deductive argument—but who sees the a ship disappearing over the horizon.
Surely he has some evidence that the surface of the earth is curved. A quick
sketch of his argument to this effect would look like this:
The ship is disappearing over the horizon
Therefore, the Earth is a spherical.
In this argument, the sailor’s premises are definitely well known to him and
better known that the conclusion: they’re based on directly observational
evidence, surely some of the best kind available. His evidence is also
23
As we mentioned previously, this particular deduction is not a good argument for someone who actually
lives on earth and does not yet have a good theory of the solar system: he would probably need to already
know the earth’s shape in order to know its place in the solar system and hence the second premise. But as
mentioned earlier, this argument could advanced by an alien astronomer who knows that all planets are
spheres, and, seeing through the telescope that the Earth is a blip large enough to have cleared its orbit
around the sun, deduces that it too must be spherical.
144
relevant to the conclusion: his background knowledge should tell him that
flat surfaces do not occlude objects resting on them.
But does the sailor possess all of the relevant evidence that he needs
to know the shape of the earth? Does he have a proof comparable to the
deductive proof considered above? No, because at this point it is still
genuinely possible that the earth is not a sphere. For one thing, until the
sailor pulls out a spyglass and looks more carefully at the dot appearing on
the horizon, it is possible that the reason he can’t see ships at an infinite
distance is simply because they are too far away to see. Perhaps they are
obscured by the atmosphere, or simply too hard to discriminate from the
surrounding sea. Only once he takes out his spyglass, and notices that the
ship disappears gradually, bit by bit, as it slowly sinks beneath the horizon,
is he able to rule out the possibility that the ship has simply been obscured
by the atmosphere. Some real kind of curvature seems to be present. But as
we shall see, more evidence is still needed.
The sailor’s argument is an example of an argument meeting the first
two requirements of good reasoning, but not the third. One reason for this is
that the argument is not a deductive argument. In deduction, we observe that
all members of some kind possess some property, and that some object is a
member of that kind. It follows that the object also has to possess that
property. In an argument like this, the conclusion follows of necessity
because these two premises are the only relevant knowledge we need to
come to this conclusion. In a deductive argument, the conclusion follows
necessarily from the stated premises, because if we know that all members
of the kind possess the property, it would be contradictory to make an
exception for this one member.
Non-deductive arguments—arguments that do not appeal to a stated
premise about all members of a kind, and its implications—require
additional relevant evidence to rule out possibilities inconsistent with their
conclusions. Because varying degrees of additional relevant evidence can be
needed, these arguments will vary in their degrees of success. Deductive
arguments trivially satisfy the requirement that their premises must contain
“all of the relevant evidence,” but non-deductive arguments have to work
much harder to satisfy it. At the end of the day, even after all of the hardest
work has been done, it may still be impossible for a non-deductive argument
to state premises listing all of the relevant evidence. All of the relevant
evidence may include the totality of one’s background knowledge, not all of
which can be (easily!) written down.
Back in chapter 4, we already discussed the role of background
knowledge in determining the relevance of our evidence, and ruling out
145
relevant alternatives to our conclusion. You may remember the example of
the argument correlating political freedom with economic prosperity which
concluded that freedom was necessary for human life—and how this was
weaker than a deductive argument from philosophical premises for the same
conclusion. We even discussed how arguments that vary in the degree of
relevance of their premises likewise vary in the degree of probability of their
conclusions. But we did not discuss how the probability of a conclusion can
improve by adding additional evidence to existing premises. In what
follows, we will present examples of arguments which are improved in this
way. By considering these examples, we will increase our sensitivity to how
the “all the relevant evidence” requirement can be violated—the subject of
the next chapter.
Proof through the elimination of possibilties
We know that our sailor needs more evidence to come closer to proving the
shape of the earth. But how much more evidence does he need, and in
particular, of what kind?
Every conclusion to be proved begins with a question, e.g., “what is
the earth’s shape?” Every question presupposes knowledge we already
possess: e.g., that the earth has a shape. With that knowledge, the question
becomes: which shape? (Notice this means that if we are missing the right
elevant background knowledge, we may not even know how to ask the right
questions.)
At this early stage of inquiry, we use our general background
knowledge about shape to generate possible answers to our question that are
consistent with the observations made so far. In the next section we will be
more explicit about what it means to “generate possible answers,” but for
now it is important to note that we begin by considering the most general
possibilities, to limit to a manageable number the options we have to
consider. What everyone thinks at first is that it the Earth is flat, but there are
other significant possibilities.
We might think of the first inquirers as considering two general
possibilities: either the Earth is flat, or not. The sailor seeing through his
spyglass how the ship disappears bit by bit under the horizon soon sees the
merit of the possibility that the earth is not flat. Seeing the resemblance
between the ship’s disappearance over the horizon and the occlusion of an
object by a sphere, he comes to rule out the possibility that it is flat, and has
evidence for an even more specific “non-flat” possibility: maybe the Earth is
spherical.
146
Of course there are many other “non-flat” shapes besides spheres in
need of consideration. The sailor must now consider these more specific
possibilities. Perhaps the earth is like a cylinder with curvature in one
direction, but not in the other. Or perhaps the earth is not perfectly flat, but
an overall flat surface which is composed of local “wavy” parts: perhaps the
oceans rise and fall just like mountains, and when the ship appears on the
horizon, it is merely cresting one of these local ocean “mountains.”24
What additional evidence
will an inquirer need to rule out
additional possibilities and to
conclude that the only remaining
possibility is actual? Our
background knowledge offers us
crucial guidance in knowing where
to look for additional relevant
evidence.
Once we have narrowed
Picture credit 77:
down the remaining possibilities to
http://commons.wikimedia.org/wiki/File:Cilinderprojectieconstructie.jpg
a manageable number, we begin to
eliminate them even further. Part of knowing where to look for the evidence
needed to do this is thinking about the meaning of the possibilities being
considered. The sailor wants to know, let us say, if the Earth spherical
(rather than cylindrical, or locally wavy). The fact that this is a question
about shape means that we must turn to geometry to eliminate further
possibilities.
Unlike flat circular disks, one knows that a sphere is distinctive in that
whichever way one turns it, it always appears circular. This is because a
plane always intersects a sphere with a circle. But furthermore, this piece of
geometrical knowledge has implications in the field of optics, which
explains what we see through the geometry of light ray diagrams. Among
other things, optics studies shadows, which we know involve the threedimensional projection of objects onto two dimensional surfaces. So it
follows that the shadow of a spherical object will always be circular on
surfaces perpendicular to the light rays. So that we would expect the earth’s
shadow on the moon during an eclipse always to be circular, never any other
shape.
24
Of course we would know this is impossible if we were to know that the surface of water remains on the
whole flat and level whatever the shape of the ocean floor beneath it, but to know that requires knowledge
about physics and even chemistry that the sailor might not yet have
147
Realizing these points of geometry, we consider that in recorded
history, there have never been eclipses involving anything other than a
circular shadow. It follows that unless the earth is a circular plane that
always just happens to be at the same orientation relative to the sun
whenever there is an eclipse (a coincidence that would cry out for a special
explanation), and unless something other than the earth is causing the
shadow in the first place, the earth simply must be a sphere.
How then would we eliminate these final possibilities? Additional
background knowledge from geometry tells us to look not just to the moon,
but to the stars as well. Just as the
disappearing ship must be
occluded by the spherical surface
of the Earth, so too must many
stars. If the Earth were flat, we
might still not be able to see some
stars—the ones underneath the
flat surface. But if that were so,
then all people in all parts of the
world would see the same
constellations on the same nights.
But it is fairly easy to observe that Picture credit 78:
this is not what actually happens: http://commons.wikimedia.org/wiki/File:Ecliptic_path.jpg
on the same night, people in the northern hemisphere will see one set of
constellations, and those in the southern hemisphere will see another. This
results from the geometrical fact that the tangent line at one point on a
sphere will veer off in a different direction than a tangent line on another
point of the sphere, intersecting different points in the distance. If light from
stars travels in a straight line, this would mean that from different points on
the surface of a curved Earth, we should see different stars. And we do.
What began as a one possibility among several others—that the Earth
is spherical—has now, through the addition of significant evidence,
increased in probability. We might now represent the argument for this
conclusion in the following way, taking care to parse premises that rely on
general background knowledge from those that involve fresh observations:
148
1. Either the Earth is flat or cylindrical or “wavy flat” or
spherical
2a. Background knowledge: If the earth is flat, ships
should not disappear bit by bit over the horizon.
2b. Observation: Ships do disappear bit by bit over the
horizon.
Therefore,
2. The Earth is not flat.
3a. Background knowledge: If the Earth is cylindrical, it
will sometimes project a rectangle on the moon
during an eclipse.
3b. Observation: The Earth is never seen to project a
rectangle on the moon during an eclipse.
Therefore,
3. The Earth is not cylindrical.
4a. Background knowledge: If the Earth is “wavy flat,”
all people will see the same constellations at the same
time.
4b. Observation: Not all people do see the same
constellations at the same time.
Therefore,
4. The Earth is not “wavy flat”
Therefore,
5. The Earth is spherical.
There are two important points to make about logical patterns in the
argument above.
First, notice that the form of argument used to establish premises (2),
(3) and (4) has the following pattern:
a. If X, then Y.
b. Not Y.
c. Therefore, not X
This is a valid form of deductive reasoning called “denying the consequent,”
or modus tollens. We will also examine it in greater detail in chapter 19. It is
a common form of testing the predictions (Y) of a hypothesis (X). If valid
predictions of the hypothesis are not observed, the hypothesis is not correct.
Of course this holds only if we know these are valid predictions. So if it
turned out that an there was reason to expect half of the people living on a
149
“wavy flat” earth to see different constellations from the other half, premise
(4a) would not be true and couldn’t be used to deduce (4). (For this reason,
we might label (4a) as only probably true, and qualify premise/conclusion
(4) accordingly.)
Second, notice that in broadest outline, the main points of the
argument, (1) through (5), have the following pattern:
1.
2.
3.
4.
5.
Either A or B or C or D.
Not B.
Not C.
Not D.
Therefore, D
This is another valid form of deductive argument called a “disjunctive
syllogism,” the logic of which we will also examine in greater detail in
chapter 19. But it is more commonly referred to as the “process of
elimination.” It embodies the wisdom once enunciated by the fictional
detective Sherlock Holmes, who said, “When you have eliminated the
impossible, whatever remains, however improbable, must be the truth.”
Holmes’ adage gives us an important formula for the construction of
proofs. One way of knowing if we have evaluated all of the evidence
relevant to a conclusion is by noting whether we have considered all of the
relevant possible rival conclusions, and the evidence bearing on them. Using
modus ponens to test these rivals, we eliminate them (in premises (2)
through (4) and are left with only one candidate standing, what must be the
truth. Much ordinary reasoning follows this pattern.
As we shall observe later, however, eliminative arguments of this type
are only as strong as the premise that lays out the possibilities in need of
elimination. In the above, we might have established premise (1) as merely
highly probable, in which case the conclusion (5) would need to be listed as
having no greater probability than the conclusion. Perhaps we must wait for
Magellan to circumnavigate the globe to increase our confidence in (5)
further. But greater confidence in the possibilities listed in premise (1) could
increase our confidence in the conclusion further still. In the section that
follows, we will discuss in greater detail how “either-or” premises of this
kind are established in ordinary reasoning.
The generation of possibilities
But how did we establish premise (1) as known to be true? There are a
variety of opinions among philosophers about how we should think about
150
proving the truth of “either-or” statements. For the purposes of assessing
ordinary reasoning, we think it is useful to think of them as listing relevantly
possible truths. In that case, evidence for premise (1) would have to look
something like this:
1a. (Possibly) the Earth is flat.
1b. (Possibly) the Earth is cylindrical.
1c. (Possibly) the Earth is “wavy flat”.
1d. (Possibly) the Earth is spherical.
Therefore,
1. Either the Earth is flat or cylindrical or “wavy flat” or spherical.
So how would we establish any of (1a) through (1d) as true? There is
also controversy among philosophers about how to think about the idea of
“relevant possibility.” Some philosophers think that anything not already
contradicted by known evidence starts out as “possible.” To them “possible”
just means “not impossible.” But there is a case to make for why even
claiming that some truth is possible requires specific evidence. We will
strengthen in the next section, but for the time being, consider again the
argument offered by our sailor at the beginning of the chapter:
The ship is disappearing over the horizon
Therefore, the Earth is a spherical.
We suggested that this argument was not good enough to prove that the
Earth was spherical, but that the premise did have some degree of relevance
to the conclusion. So it is not enough to establish the certainty or even
probability of the conclusion, but perhaps it is just enough to establish its
possibility. Here is one way of thinking about the inference pattern used to
establish such a possibility:
1da. Background knowledge: If the Earth is spherical, then
ships will disappear under the horizon bit by bit.
1db. Observation: Ships do disappear under the horizon bit by
bit.
Therefore,
1d. (Possibly) the Earth is spherical.
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Even with the inclusion of premise 1da, taken from our background
knowledge of geometry, the pattern of reasoning used here is still not
deductively valid:
a. If X, then Y.
b. Y.
c. Therefore, X
Think of this on the model of how we reason about cause and effect. If we
think of X as a cause, and Y as an effect, then if we know that the cause, X,
is present, we know its effect, Y, must be as well. But in the present
argument, we are observing the effect and inferring that it must have a
particular cause. The trouble is that many different causes can sometimes
account for the same effect. For example, we would not regard the following
as a good argument:
a. If a fire is burning, there is heat.
b. There is heat.
c. Therefore, a fire is burning.
We all know that there are many things that cause heat besides fire. A small
list of other possibilities includes electric heaters, chemical heating packs,
and living bodies. So even if premises (a) and (b) are known as well as they
can be, (c) does not follow even as a probable conclusion. But we might still
think of this as part of what we do to establish the genuine possibility that
there is a fire burning.
There is some good precedent for thinking this is how possibilities get
established. In science, we often rely on arguments from the observation of
an effect to the presence of a cause, as in the following:
If matter is composed of atoms, chemicals will decompose in
definite proportions.
Chemicals do decompose in definite proportions.
Therefore, (probably) matter is composed of atoms.
This form of inference is sometimes called “inference to the best
explanation” or “abductive reasoning,” to indicate that it is not deductively
valid but still highly reliable. Matter’s being composed of discrete elements
is thought to be the “best explanation” for the observed effects. But
philosophers think that inferences to the best explanation establish their
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conclusions only with a degree of probability that varies to the extent that
the explanation is good.
And what makes an explanation good, or the best? A variety of factors
are sometimes appealed to. But keeping with the theme of this chapter, it is
noteworthy that the reasoner’s background knowledge is highly relevant.
The chemist making the argument above presumably has independent reason
to think there are few if any other genuinely possible causes of the
phenomenon of decomposition into definite proportions worth considering.
To establish a claim of mere possibility, we may only need the background
knowledge that there are a few other possible causes—and that is exactly
what we have when we claim that maybe the Earth is spherical.
The continuum of evidence: possible, probable and certain
To examine further about why claims of possibility may need specific
evidence interpreted in the light of our background knowledge, it is worth
switching to a new example that brings out the ordinary meaning of the
concept of “possibility.”
Suppose that shortly after takeoff, a plane crashes, killing all of the
passengers. So far as investigators know, the crash and resulting deaths may
as well have been accidental. 25 But
soon after the wreckage is examined,
officials soon discover that the tail
section of the plane detached earlier in
the flight, some 1.5 miles before the
main crash site. The evidence points to
an explosion, but no defects in the
plain suggest that the explosion could
have been accidental. At this point it is
clear that the plane was sabotaged—
that this was murder, not an accident—
and the FBI begins criminal
Picture credit 79:
http://www.fbi.gov/libref/historic/famcases/graham/graham.h investigations.
tm
Uncovering the identity of the
murderer who planted a bomb is no easy task. Unlike the shape of the earth,
an impersonal fact of nature, the murderer can work to cover up evidence of
his crime. This, of course, is what makes uncovering the identity of the
25
Evidence of death is not always obvious evidence of murder; often separate evidence is needed to
establish the latter. In the legal system, a formal proceeding called an “inquest” is sometimes used to
determine if a crime has been committed, before detectives go about looking to determine the identity of
the criminal.
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murderer not just difficult, but a mystery. Notice, however, that even though
it is a mystery, we don’t begin by thinking that anyone could have been
responsible, even though every human being has the ability to hate and
engage in violence. Everyone has this power, but a mere ability or potential
is not enough to raise suspicion of being a murderer. How do we generate a
finite list of possible suspects?
We generate a list of possible shapes of the Earth by thinking about
the geometry of shape in relation to our observations of the Earth. To
identify murder suspects, we need to think about the nature of murder and
the people who commit it.
Note first that murder
is not an ordinary
occurrence. Why is it so out
of the ordinary? Committing
murder is no easy task. A
victim will resist an attempt
on his life with great energy,
and our social system is set
up to safeguard against and
punish murder. Because of
this, the energy required to
make an attempt on another Picture credit 80:
person’s life is great, and the http://www.flickr.com/photos/8533266@N04/4457182603/sizes/z/in/photostr
eam/
act will not be undertaken
lightly. Ordinarily, people have much to lose by engaging in such a heinous
crime.
Given the special obstacles faced by murderers, we expect only a tiny
fraction of human beings to be suspects. To overcome the obstacles thrown
up by the victim and society, the murderer has to have specific means,
opportunity, and motive, a famous triad of requirements repeated throughout
the detective fiction genre.
To begin with, because victims are vulnerable to attack only under
specific circumstances, and because aggressors can only escape public
notice under specific circumstances, the murderer needs to act under a
specific circumstance, at a specific time and place. This is background
knowledge obtained from basic physics and psychology. A killer, to achieve
his gruesome goal, must have some type of convenient physical access to his
victim.
Unless he is a suicide bomber, a murderer responsible for downing an
airplane must operate “long distance,” through sabotage. But sabotage still
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requires some form of physical access. In the present case, after deciding
that the plane has been sabotaged, the FBI begins to interview eyewitnesses
in the area, including control tower operators at the local airport, who
confirm having observed an explosion. Based on an examination of the
wreckage (in particular, the types of objects most powerfully disintegrated)
it is determined that the explosion originated in the cargo pit of the plane,
and that the cargo in this pit was luggage originating from the local airport,
not an earlier leg of the plane’s flight. Fragments identified as likely pieces
of an explosive device bear the chemical signature of dynamite.
At this point, every passenger on the plane is still a reasonable
suspect, and possibly others. The murderer was either a passenger who
carried dynamite on board, or someone who had the opportunity to plant it in
the luggage of someone else. The investigators
look to narrow down the list of suspects. Six of
the passengers had only recently taken out the
maximum amount of travel insurance. Attention
quickly turns to one of them in particular, one
Daisie E. King, from whom many personal
effects have been found, but whose luggage is
missing from the wreckage, suggesting that it
has been completely disintegrated. What’s
more, Mrs. King’s son, Jack Gilbert Graham, is
determined to have a criminal background. He
and is named as the beneficiary on Mrs. King’s
insurance policy. Graham is now a leading
suspect in the murder, but so far we only know
that he may have had access through possible
opportunity to access the plane through his
mother’s luggage, and that he may have had a
motive, if he knew about the insurance policy.
So far, it is genuinely possible that Graham
sabotaged the plane, but we need to know more.
Consider now the fact that a murderer has
much to lose for undertaking the crime—
ranging from his self-respect and peaceful
conscience to his freedom and even his life (in
Picture credit 81:
http://www.fbi.gov/libref/historic/famcases/gr
the event of successful prosecution). In
aham/graham.htm
Graham’s case, he would lose his own mother.
No one would undertake a plot with such obviously disastrous consequences
without the belief that they could achieve at least some apparent reward for
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doing so. That is why murder demands the highest of stakes—inheriting a
fortune, cashing in a life insurance policy, eliminating a rival for the passion
of a lover—i.e., the murderer must ordinarily have a clear motive. This is
known from our basic background knowledge about human psychology. In
the event that we can find no discernible motive for a crime, this knowledge
will lead us to look for other psychological causes besides normal beliefs
and desires: we would have to look for a suspect who is mentally unstable or
insane.
As it happens, a copy of his mother’s insurance policy is discovered in
Graham’s effects at his home, indicating his knowledge of his status as
beneficiary. He also knows that he is to receive inheritance from his mother
in the event of her death. As for the prospect of the loss of his mother, it is
learned that he does not have a happy relationship with her. They have been
known to quarrel over money he may have stolen from the family business.
Graham also apparently had no compunction against insurance fraud, having
once wrecked his car apparently to claim insurance benefits, and only
recently engaged in a check-passing scheme. Graham’s motive for killing his
mother has become clearer. So, apparently, has the nature of his opportunity.
Though he denies that he helped his mother pack, his wife tells investigators
that his mother received a gift from Graham on the day of the trip, which he
had claimed to be a tool set. Graham is also reported to have acted strangely
ever since his mother left with
the package. At this point, the
balance of the evidence appears
to establish with high
probability that Graham was the
murderer. He is now the chief
suspect.
Still, one important piece
is missing from the puzzle.
Could Graham have constructed
a bomb, and did he have access
the materials needed to do so? It
Picture credit 82:
is one thing to be in the right
http://www.flickr.com/photos/86399392@N00/109403306
place at the right time; it is quite
another to possess the tools needed to pull off a grisly crime. Speaking more
generally, most of us could probably not kill another person with our bare
hands. So we require tools: some weapon or special skills that enable us to
overcome the victim’s normal defenses. This again is a matter of physics,
and of biology. Not only are there limits on the brute force a given
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individual can exert with his bare hands, but there are also degrees of such
force that the victim’s body can withstand safely. Effective killers do not
exert force against their victims in a haphazard way. They “go for the
jugular”—or the heart, or the windpipe, etc. To undertake a murder, a killer
must not only have the tools, but know how to use them in the most effective
way. The killer must not only have the opportunity, but the means to
undertake the crime.
Upon the search of his home, the police find copper wire of the kind
used to create dynamite detonating caps. When confronted with this
evidence, Graham confesses to the crime, describing in detail the device he
constructed, including the parts used to construct it and the locations of the
businesses from which he purchased them (purchases confirmed by later
investigation). Graham had acquired knowledge of dynamite after working
with heavy equipment in Alaska. He also confesses to having slipped the
bomb into his mother’s luggage when she was not looking. When the sum
total of the evidence against him is presented to a jury, and the defense fails
to rebut any of the 80 witnesses and 174
exhibits attesting to his guilt, the jury
finds him guilty. The case has been
made that he is the murderer, and it is
far stronger than merely “probable.”
There are no genuine rival possibilities
left to consider. All of the relevant
evidence points to his guilt. We might
even say we are certain about it.26
With a case as “open and shut” as
this, ordinary people have little trouble
confessing that they are certain of the
Picture credit 83:
identity of the murderer—especially
http://www.flickr.com/photos/18796746@N05/4272817915
when the defendant confesses against
his interest. But philosophers notoriously deny that we can ever be genuinely
certain of anything but the most trivial claims of logic and perhaps
mathematics. They point to the fact that we have claimed certainty for many
conclusions in the past which turned out to be false. For instance, juries have
been known to convict men of crimes who were later exonerated by superior
evidence, most notably DNA evidence. The “means, motive, opportunity”
standard is, admittedly, not an infallible standard of proof, nor is any other.
26
In case the details of the story did not reveal it, this murder and subsequent trial really happened, in
Denver, Colorado, between 1955 and 1956.
<http://www.fbi.gov/libref/historic/famcases/graham/graham.htm>
157
But philosophers who demand infallibility as a standard of certainty
are clearly not relying on the same standards which lead ordinary people to
see a difference between the status of the conclusion about Graham when he
is one among many suspects, when he is the leading suspect, and when he is
the only suspect. True, one can always imagine that there are others to
investigate, even when no specific evidence gives us reason to do so. But
note that the ordinary legal requirement is to prove a conclusion beyond any
reasonable doubt. To cast doubt on a proof merely because another
possibility that can be imagined has not been ruled out seems to rely on a
subjectivist approach to possibility claims. There is a real, practically
important difference in degree of evidence along the continuum that we have
described that leads us to conceptualize the difference between certainty and
the lesser states, and that this difference has nothing to do with what we can
imagine. Further considerations in favor of an evidential approach to
possibility claims will be discussed in chapter 9 when we discuss the nature
of the burden of proof. Until that time, it is worth examining the particular
force deriving from one particular logical technique, implicit in the example
above: the convergence of independent sources of evidence on the same
conclusion.
Proof through the convergence of independent evidence
In the example above, detectives pieced together a case for the guilt of
Graham based on converging lines of evidence suggested by the various
fields of background knowledge implicit in the means/motive/opportunity
standard. But detectives probably do not think of themselves as consulting
physics, biology, and psychology. In the sciences, attention to the
convergence of different
scientific disciplines is more
self-conscious, and worth
pointing out with one last
example.
This last example will
help illustrate how proof is
like putting together the pieces
of a puzzle to see if they can
be made to add up to a bigger
picture. Coincidentally, the
Picture credit 84:
example involves how
http://commons.wikimedia.org/wiki/File:Plates_tect2_en.svg
scientists put together a series
of nearly literal puzzle pieces: the earth’s continents, in the theory of plate
158
tectonics. According to the theory, the present arrangement of the continents
on earth is quite temporary. These continents have been moving separately
across the earth’s crust, bumping into and bouncing off each other for
millions of years. It is fascinating to appreciate the vast diversity of evidence
that was needed for the theory to gain widespread acceptance by scientists—
and only as recently as the 1960s.
Most of us have probably looked at maps of South America and
Africa and noticed how they could fit together like pieces of a puzzle. The
observation is easy to make, and scientists have speculated for centuries that
these continents were once joined. But for a long time, this was mere
speculation. For decades, even centuries after the hypothesis was proposed,
scientists were rightly skeptical. After all, continents are massive objects, if
it is even right to think of them as separate
objects at all. Why not think of them simply as
the surface of the earth itself—and if the earth
is solid, why would its surface be otherwise?
Being able to answer this question would
eventually aid in the proof that in fact the
continents move, have always been moving,
and have crunched up against each other
multiple times.
How would you go about answering the
question of how and whether the continents of
Picture credit 85:
http://commons.wikimedia.org/wiki/File:Plate_t the earth move? As when we thought about the
ectonics_map.gif
shape of the earth and the identity of a
murderer, we would first have to think about the meaning of concepts such
as “continent” and “Earths’ surface.” Almost like the “means, motive, and
opportunity” standard for proving the identity of a murderer, we would also
need to identify the nature and mechanism of the motion. Most of the
background knowledge we need to find relevant evidence is our knowledge
of physics and other natural sciences.
Consider: well before our ultimate proof of the plate tectonic theory,
scientists had gathered evidence of rocks and fossils on either side of the
Atlantic Ocean, especially between South America and Africa, which
suggested that these continents had once been much closer to each other than
expected. Still, the main question was how they could have been so close. It
is one thing to find a murderer’s fingerprints at the scene and conclude he
could have done it. In that case we understand the causal mechanism pretty
well. It is quite another to say that a continent could have been “at the scene
of the crime.” Continents are decidedly larger and less nimble than crooks.
159
The evidence began to mount that the continents had been at different
places when scientists began to examine the bottom of the ocean across
which they would have moved. In the Atlantic Ocean, there is a parallel
series of ridges extending out from the middle of the ocean. When examined
closely, these ridges were found to have magnetic properties. It is normal for
rocks formed from molten lava to acquire a magnetic polarity in accord with
the orientation of the earth’s
magnetic field. What scientist
discovered was puzzling,
though. In one layer of ridges,
the polarity would be pointed
in one way. In the next layer it
would be in another. Scientists
already had independent
reason to think that the earth’s
polarity was known to
unexpectedly change; the
location of the magnetic North
Picture credit 86:
Pole was known to migrate.
http://commons.wikimedia.org/wiki/File:Oceanic.Stripe.Magnetic.Anomalies
This preexisting knowledge
.Scheme.gif
explained the different patterns of magnetic polarity in the rocks. If these
rocks were being slowly pushed out and formed from a central magma
source over time, then each layer pushed out would bear a different magnetic
insignia, as each was born at a different time under different global magnetic
situations.
The discovery of the differently magnetized ridges was virtually
concurrent with the discovery of the Atlantic mid-oceanic ridge, a series of
volcanic exhaust ports where lava is constantly pushed up and spread out.
This accounted for the source of the plates that had spread out over time
because of the presence of these volcanic pressure points. As more lava
flowed up and over the ridge, it would solidify in the earths’ magnetic field,
and be pushed out further and further by newer and newer magma, which
would in turn be formed under a different polarity, etc. This not only
explained the ridges along the ocean, but why the continents were
separating: a volcanic force beneath them was slowly but surely widening
the ocean floor.
As much as this evidence seemed to seal the case that the continents
moved over time, there was one important leftover question: if they earth
was spreading out on one side, what was happening on the other? Was the
earth simply getting bigger because of this ocean floor spreading, and would
160
it even be possible for that to happen? “What goes up, must come down”
was the rule of thumb here: if pressure from below the earth’s surface caused
new rocks to form above, some other force had to compensate unless the
earth was expanding at an unending pace, which it was not known to be
doing. Scientists realized that they should look at the other side of the
globe—in particular in the other big ocean, the Pacific, to see what was
happening there.
What scientists found in the Pacific—the Marianas trench—widely
confirmed their suspicions. The Marianas trench is the deepest part of any
ocean, almost 7 miles deep at one point. There, scientists discovered
evidence that the plate from the east—the same plate being expanded
through the relentless magmatic floor spreading in the Atlantic—was being
slowly pushed under the plate to the west. What comes up must go down:
this crust had been pushed up by the
Atlantic ridge, and was now slowly
sinking under the trench in the
Pacific.
All of the important elements
of the causal mechanism had now
been described. Scientists knew only
that the continents had to be in
different locations, but now also how
they had gotten there: how whole
Picture credit 87:
continents had been pushed into
http://commons.wikimedia.org/wiki/File:Oceanic_spreading.svg
each other, without something so
absurd happening as the earth itself getting bigger. To see this, scientist had
to draw on a wide array of evidence, from fields as disparate as physics,
geology, magnetometry, vulcanology, even a fair bit of biology. I’ve not
even mentioned some of the other fields relied upon to highlight other,
related evidence.
In chapter 5, we examined how we could corroborate testimony by
finding other independent witnesses who could testify to the same
conclusion as a first. We further corroborated testimony by comparing it to
what was plausible according to our background knowledge. We are
presently considering another example of the same logical technique. When
a series of independent observations and scientific disciplines converge on
the same conclusion, the whole of the evidence is almost greater than the
sum of its parts. Each line of evidence on its own establishes a probability,
but so many independently generated probabilities would be almost
impossible to explain without the truth of the conclusion they share. If one
161
source of certainty in the construction of elaborate proofs is the process of
elimination, in which a series of rival possibilities is gradually eliminated,
another is what we might describe as the process of accumulation, in which
a series of independent sources of evidence that point to the same conclusion
is gradually assembled. Taken together, these twin methods of proof are
especially hard to stop, logically.
162
§3: PROOF: LEGITIMATE AND ILLEGITIMATE DEMANDS FOR IT
Chapter 8:
The Fallacy of Ignoring Relevant Evidence
Ben Bayer
Drafted February 20, 2010
Revised August 15, 2010
Violating the “all the relevant evidence” requirement
In the last chapter, we discussed the meaning and importance of the third
basic requirement of good reasoning:
1. The premises of the argument must be known and known better than
the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must be likely
to establish the conclusion as true).
3. The argument’s premises must contain all of the known relevant
evidence.
To know when we’ve considered all of the known relevant evidence is not
easy to know. In chapter 7 we discussed examples of arguments which
appeared to consult all of the known relevant evidence, but doing this meant
bringing whole fields of background knowledge to bear on a given question,
and it is not always easy to know which of those fields are most salient.
When we think about whether or not the Earth is spherical, for example, we
know we’re facing a question fundamentally about geometry. But it is also
important to consider the implications certain facts about geometry in the
field of optics, and it is not always easy obvious what those implications are
or that we should consider them.
While it is hard to know when one has met the standard of proof for a
question in a given field, it is comparably easy to know when one has fallen
far short of fulfilling the standard. This is the topic of the present chapter.
We can call any violation of the third requirement an example of the fallacy
of ignoring relevant evidence, which is the fallacy of treating premises that
are well-evidenced and relevant to a conclusion as proving the conclusion,
without considering additional evidence that might contradict the
conclusion. There are not many named sub-types of this fallacy (and none
that we will consider directly in the present chapter), so to claim that such a
fallacy is present, no specific name is needed. We need only point out the
specific relevant evidence that an argument ignores.
163
What is the problem with ignoring relevant evidence? Why is it not
enough that one’s argument has good evidence that bears on the conclusion?
The reason is that there are many arguments that respect the first two rules
but that are, nonetheless, not good arguments. Consider for example, the
following argument about the shape of the earth:
Everywhere I’ve looked, the earth looks flat.
Therefore, the earth is flat.
Plausibly this argument can be taken as having a premise that is both wellevidenced and relevant. It’s easily conceivable that everywhere a person has
visited, the earth does look mostly flat. Even if he has seen many mountains,
he knows that these are minor exceptions to the general trend, and that at
best they demonstrate that the earth is not perfectly flat; still it may be flat
for the most part. Notice also that this person has put a great deal more effort
into his argument than the one we accused of subjectivism earlier: it’s not
that the earth just happens to appear flat nearby. Where ever he’s traveled,
still it appears flat. So the premises are relevant to the conclusion, as well.
Yet we all know that the conclusion is false.
What has gone wrong? It’s simple: even though the arguer has not
been overtly lazy, and has in fact
considered many observations, he hasn’t
considered all of the easily knowable
relevant evidence. He is looking at the
shape of the ground beneath him in many
places, but he hasn’t bothered to lift his
gaze to the horizon or to the sky above
him, or to consider the implications of
what he would see there for his
Picture credit 88:
http://www.flickr.com/photos/16175796@N00/4332122 conclusion. There are a few useful
882/
metaphors describing what the arguer here
has failed to do. He has not “taken a step back,” to look at the “bigger
picture” or “gain perspective” on his existing evidence. We might say that he
is “missing the forest for the trees.”
Sometimes the simplest examples of this fallacy arise from a failure to
see the literal bigger picture. Anytime someone shows you a picture of an
alleged flying saucer, how much does the picture actually tell you? Is the
picture so grainy as to distinguish the object from a pie plate or hat tossed
into the air or hung from some fishing wire? Or is the picture such a close-up
that you can’t see the objects surrounding or get any perspective on how far
164
away it might be, and hence how big or small it might be? The mere fact that
it is a snapshot photograph, and not video, also creates a great deal of
ambiguity. We don’t see the thing moving as it would normally, so we can’t
be assured that it isn’t some ordinary flying device
that is simply being mistaken for a flying saucer. The
same concerns apply to most of the alleged
photographs of ghosts, bigfoots, the Loch Ness
monster, etc. Each of them could benefit from
showing us more of the literal “bigger picture.”
Ignoring data in the description of patterns
So what about failures to see the metaphorical
“bigger picture”? We have encountered metaphors
Picture credit 89:
like this before. Remember the function of logical
http://commons.wikimedia.org/wik
inference? It allows us “see” (with our mind’s eye)
i/File:PurportedUFO2.jpg
what we cannot see with observation alone. Logic is the science that lets us
carefully assemble our evidence step-by-step in order to draw conclusions
that would not otherwise be observable. One preliminary step in drawing
inferences is to assemble our existing observations in a way that suggests
patterns or trends in our data, which can later be material for drawing
conclusions about the deeper nature of what we’ve observed, such as
conclusions about cause and effect relationships. We might notice, for
example, that a variation in one measurement correlates strongly with the
variation in another, and end up deciding that one of these variations is
actually responsible for the other. But to get to that point, we first need to
observe general trends of increase or decrease in the measurable factor in
question.
Unfortunately, when looking for
patterns or trends in the data, it is all to
easy to notice trends in isolated portions of
the data, without looking at the bigger
picture. This is easy to illustrate using data
represented in graphical form. Consider the
adjacent graph of oil prices during the first
decade of the 21st century. What if you
Picture credit 90:
http://commons.wikimedia.org/wiki/File:US_oil_price_i
n_dollars_from_1999_to_2008-10-17.svg
were offered this graph as evidence that in
the summer of 2008, Americans paid a
record price for crude oil? Would this be
165
enough of a big picture to come to that conclusion? Is there any background
knowledge you have that would suggest the need for additional information?
There are at least two questions that should occur to you if you have
some basic knowledge of history and of economics. Historically, we know
of previous periods in American history when oil prices spiked severely,
especially during the 1970s and early 1980s. Economically, we also know
that there is a difference between the nominal and the real price of a
commodity. The nominal price is the actual number that appears on price
tag. But prices can be increased artificially through inflation (the debasement
of the currency by government printing presses). There has been a lot of
currency debasement since the 1970s, so how do contemporary high prices
compare to inflation-adjusted prices of oil from earlier periods. The
following graph gives us a better, bigger picture:
Picture credit 91: http://commons.wikimedia.org/wiki/File:Oil_Prices_1861_2007.svg
Unfortunately this graph does not take us all the way to 2008, but we can tell
that nothing on the graph goes as high as the price of nearly $140 per barrel
experienced in June of 2008. Looking at the yellow line on top, which
represents real (inflation-adjusted) prices, we can see that prices have been
upwards of $100 or $120 per barrel in the past, so real prices above $100 a
barrel are not completely unheard of. In the 1860s, oil was expensive
because it was extremely rare and difficult to obtain. It took significant
technological and industrial development to make it more accessible and
hence, to bring down the cost of producing a single barrel. (Contrary to
conventional wisdom, the alleged oil “monopolist,” J.D. Rockefeller, was
instrumental in bringing the price of oil down over the decades.) In the
1970s, an Arab oil embargo against Western countries, along with inflation
of American currencies in general, caused oil prices to spike. In the end, it
turns out to be true that the recent oil price spike was probably an
unprecedented historical phenomenon. But we would not have known this
by simply focusing on the data from the past ten years. At the time of this
166
writing, the price per barrel is back down to lower than $80 a barrel, which
is still cheaper than what people were paying in the 1970s and ‘80s.
Another example and corresponding lesson: always be skeptical when
you hear a story in the news media stating that some economic or other
social statistic has reached its highest or lowest, best or worst rate since
some particular year. The further back
the year is in history, the more
impressive the figure sounds. But is it
that significant? Consider this headline
which appeared in a story in the Los
Angeles Times on February 24th, 2010:
“Number of banks in danger of failure
hits highest level since 1993.” The
article cites statistics from the FDIC
according to which the number of banks Picture credit 92: http://www2.fdic.gov/qbp/grgraph.asp
facing financial difficulties had reached 702. The FDIC data is listed to the
right. Clearly, there has been a trend of increasing bank problems in the last
few years. And the record of 702 problem institutions, apparently, was even
higher than the number of such banks in 1993. We can see this from the next
graph, which makes longer-term survey of the same figures, since 1991. In
1993, the number of problem
institutions was somewhere between
400 and 600, clearly lower than 702.
But what is so special here about 1993
as a benchmark year? 1991 and 1992
were clearly much worse. One
suspects that what the journalist has
done is simply to find the earliest year
in which the number of bank failures
was as bad as the current year. He
Picture credit 93:
could not go as far back as 1992,
http://www.fdic.gov/deposit/insurance/risk/2006_02/imgs/Cha
rt1.gif
when it was still higher than 702.
This is not to say that which year we pick as a benchmark is always
arbitrary. Suppose, for example, that the massively higher number of
problem institutions in 1991 had been the crest of a previously rising trend.
Had it been true that, in 2010, our number of problem institutions had
exceeded the previous crest of 1,430 institutions, this would be significant:
we would have surpassed the previously recorded highest number of
problem institutions, and be setting a new record. But that has not happened
here. Clearly we do have a worrying, increasing number of problem
167
institutions, but it is not clear what adding the “highest since 1993”
description adds to this fact. It suggests some kind of record has been
reached, but it shows a record only on the basis of an arbitrarily chosen
timeframe.
Statistics concerning natural phenomena can be just as daunting to
interpret as those concerning the manmade economy. Consider this headline
from the UK Guardian on May 13,
2008: “World carbon dioxide levels
highest for 650,000 years, says US
report.” True enough, if you look at
atmospheric carbon dioxide in recent
years, it has been increasing. But what
does the same data look like when
observed over a longer period of time--- Picture credit 94:
specifically over the past 650,000 years, http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html
as suggested by the headline? A graph, of this data, based on ice cores from
glaciers, shows that the recent figure of around 380 parts per million of CO2
is in fact greater than any figure in
the past 650,000 years—though
there have been a number of spikes
approaching 380, and we are not
too sure what the margin of error
for this data might be—especially
as we go back further and further in
time. But the story is not over yet.
The earth is very old indeed, much
Picture credit 95:
http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html
older than 650,000 years. Some
scientists think they can assemble
data from other sources showing CO2 concentrations as far back as 600
million years. According to this data, at least, carbon concentrations
regularly exceeded 1000, 4,000, and even
6,000 parts per million in periods much
earlier than 650,000 years ago. 27 Of course
this is what we should expect. In these
earlier periods, plants had not been around
long enough to have converted much
carbon dioxide into oxygen and water
27
See William L. Broad, “In Ancient Fossils, Seeds of a New Debate on Warming,” The New York Times¸
November 7, 2006. <http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html>
Picture credit 96:
http://commons.wikimedia.org/wiki/File:Phanerozoic_Ca
rbon_Dioxide.png
168
through the process of photosynthesis. And surely life on earth at that time
would have been differently adapted to this radically different climate. But
examining this data is relevant when considering whether carbon
concentrations correlate well with temperature. If carbon concentrations
were on the order of twenty times higher then they are now, were
temperatures also twenty times higher, or at least some proportionate amount
higher? If not, what are the implications for the current hypothesis that our
climate’s temperature is highly sensitive to changes in carbon dioxide
concentration?
Not every instance of ignoring relevant evidence has to involve
statistics! An exceedingly simple and everyday example is the practice of
quoting out of context. In the same way that statistics can be misleadingly
presented to suggest a significance that is not there, quotations can be
misleadingly cropped to suggest a meaning that is not there. The practice is
widespread, but is especially notorious in movie advertisements which quote
from published movie reviews. Often these advertisements quote the words
of the review in a way that suggests a more favorable view of the film than
is warranted. Here are just a few examples of original quotations, followed
by the full context, which you should easily be able to tell does not have the
same glowing aura to it:
Quotation: "'The Big Bounce' is like a paid Hawaiian vacation."
-A.O. SCOTT, THE NEW YORK TIMES
Original: “Coming at the end of a dismal and frigid January, 'The Big
Bounce,'…is like a paid Hawaiian vacation—somebody else's.
Everyone involved with this picture…seems to have had a good time
making it, which was nice for them, but it may not do you much
good.”
Quotation: “[Analyze That is] Absolute perfection. Here surely is the
perfect holiday season movie."
-Jeff Simon/THE BUFFALO NEWS
Original: “Absolute perfection of a sort—the perfect way to kill 95
minutes. You don't have to pay attention to it or care about it one whit
or remember it afterward and you'll still find it a diverting and funny
way to rest your weary feet. It's television by other means—and not
good television either."
169
Ignoring general background knowledge
Finding trends or patterns in data is not an end in itself. We try to find trends
in order to correlate them with still other trends. Noticing correlations—say,
between increasing carbon concentrations and increasing temperatures, or
between numbers of failed banks and interest rates—can sometimes be a
clue to finding causal connections. Finding cause-and-effect relationships is
one of the most important goals of acquiring knowledge, because knowing
them can help us act successfully in the world. We understand causal
connections in a general form: All cases of X (the cause) are cases that bring
about Y (the effect).
We will spend more time in a chapter 14 discussing more about how
knowledge of causal connections is discovered and justified inductively. In
chapter 15, we will also discuss fallacies related more specifically to
inductive reasoning. For now, it is worth mentioning that arguments that
help us acquire causal knowledge need to be based on evidence like any
other. And like any other argument, arguments seeking to establish general
causal knowledge can ignore relevant evidence like the previous examples
we’ve considered. Often the evidence ignored is that which would be seen as
relevant in light of background knowledge which the arguer fails to consult.
We know from chapter 8 how background knowledge is often needed to
make connections between premises and distinct conclusions in the first
place. But sometimes evidence that appears to establish a conclusion may
appear to do so for superficial reasons.
Consider a fairly simple example of an argument from some simple
physical premises, both of which known better than the conclusion and at
least somewhat relevant to the conclusion:
All heavy bodies are pulled towards
the earth.
Airplanes are heavy bodies.
Therefore, airplanes are pulled towards
the Earth (and cannot fly).
Picture credit 97:
http://commons.wikimedia.org/wiki/File:LeBris1868.jpg
We know that it is false that airplanes
cannot fly. Yet the conclusion that they
are pulled towards the Earth at first suggests that it is true. What relevant
evidence does this argument ignore? From one perspective, there is some
extremely obvious evidence it ignores: anyone who has seen or ridden on an
170
airplane knows that they fly. The conclusion itself contradicts easily
knowable evidence. Very well, but what is wrong with the argument for this
conclusion? There is some piece of more general background knowledge it
ignores, the ignoring of which makes it plausible that the premises here are
establish the conclusion.
You don’t need to know a great deal about physics to know what is
being ignored here. It’s true that gravity pulls heavy bodies towards the
earth, and that the plane is a heavy body.
But does being pulled toward the earth
have to imply that a thing will fall, and
therefore cannot fly? No. That’s because a
thing can be pulled in opposite directions.
If there is a force opposing the downward
force of gravity—say the force of lift
generated by the aircraft’s wings—then it
will remain suspended. This is no different
Picture credit 98:
from the way in which a ball you hold in
http://commons.wikimedia.org/wiki/File:Accelerated_
your hand is prevented from falling by the stall.gif
force your hand exerts in opposition to the force of gravity.
Let’s consider a few more examples of arguments with generalized
conclusions that ignore background knowledge, and thereby fail to support
the conclusions they seem to support. Let’s begin with some generalizations
that relate to some common ethical doctrines.28
Hedonism is the doctrine that we ought to pursue pleasure. Consider
this argument that might be advanced by a hedonist:
Taking this cocaine will give me pleasure
Pleasure makes me happy.
Therefore, taking this cocaine will make
me happy.
As usual, both of the premises may be
better known and relevant to the
Picture credit 99:
conclusion. Cocaine really does cause
http://commons.wikimedia.org/wiki/File:Bacchanal_1627_
Moses_van_Uyttenbroeck.jpg
physical pleasure, and physical pleasure
is the kind of thing that lend to one’s overall well-being as a person
28
Recall from chapter 4 that there is some controversy about whether and in what way we can make logical
arguments for conclusions that embody value judgments. Though there is no reason to assume that value
judgments are crudely subjective, you’ll note that the arguments presently examined only relate to ethical
theories: they do not argue for them.
171
(happiness). But can pleasure resulting from drug like cocaine do this for us?
We might think so, but only if we ignore some fairly important relevant
evidence. The most obvious is the knowledge we may have of the long-term
health effects of the use of the drug. Cocaine is highly addictive, and
because it is unregulated, its quality can be unknown, and users may be
easily subject to overdose. More generally, seeking to dull one’s senses
through mindless behavior can threaten one’s long-term happiness, because
we need our minds to plan and successfully pursue that happiness. Regular
cocaine users may not even be trying to pursue happiness. Realistically,
many who are addicted to drugs are really only trying to escape some kind
of pain, and the absence of a negative is not the same as the achievement of
a positive.
Note also that in this example, the fallacy of ignoring the relevant
evidence is combined with a kind of emotionalistic fallacy—“it’s good
because I feel like it”—and this is likely the case with all examples of
emotionalistic fallacies. Emotions are responses to something in the world.
The problem is that we can respond to overly limited aspects of things.
Under normal circumstances, pleasure is good to pursue, and wanting to
pursue it makes sense. But we can experience a normal desire without
noticing that the circumstances are abnormal. Part of the reason we need to
unearth and analyze the judgments presupposed by our emotions is to
determine whether they take into account the full range of facts about the
present circumstance.
Just to make it clear that logic is not necessarily opposed to having a
good time, consider the following argument
related to an opposite ethical theory, asceticism:
The pursuit of ambitious goals leaves us
open to frustration.
Frustration leads to suffering.
Therefore, only by not pursuing ambitious
goals can we avoid suffering and
achieve contentment.
It is true that we never have guaranteed success
in the pursuit of our ambitions. Does this imply
that we should never pursue them? What if we
are successful in our pursuit? Isn’t this
possibility sometimes worth the risk of failure?
Perhaps the ascetic will counsel that we might
Picture credit 100:
http://commons.wikimedia.org/wiki/File:Tempt
ation_of_Saint_Anthony_by_Bosch.jpeg
172
occasionally experience joy, but that it is only fleeting. True enough, but
many people do not mind that their pleasures are only fleeting: they enjoy
not only their achievement, but their actual pursuit. Wouldn’t a life of
complete bliss in which everything we want is given to us without effort be
rather boring? And: if contentment is merely the absence of suffering, then
it’s true that people who don’t pursue any ambitions will be “content.” But a
comatose patient also feels no suffering. Is he content?
Moving from ethics to economics, here is an argument that has
seemed plausible to more people than you might imagine:
Breaking the window makes the store owner have
to replace it.
This gives a job to the window glazer, who spends
his money on other goods, etc.
Therefore, breaking the window is good for the
economy.
Economists who have arguments like this often note
that the premises take note of what is seen, but not
take what is unseen: in particular, the wealth that is
not created because of the vandal’s destruction. The
shopkeeper, who was planning on buying a new
suit, needs to replace the window instead. And
Picture credit 101:
http://www.flickr.com/photos/theuptake/2
while the window glazer obtains a job, the tailor
820893751/
who would have made the new suit loses one. At
best the end result is a wash: the gain is balanced out by the loss. But
probably there is also net loss, because not only is the tailor out of a job, but
the shopkeeper is out of the suit, and can no longer use it to impress
customers, who may end up patronizing another business as a result. This
argument ignores that generally, it is production, not destruction that creates
wealth and leads to prosperity.
Just in case you think this is an obviously fallacious argument that
nobody would fall for, you might remember the high school history teacher
who told you that nothing is better for the economy than a war. Indeed it’s
true that increased war production can create temporary manufacturing jobs
to produce munitions, not to mention employment in the armed forces. But
remember that the end of this production is destruction: not just the
destruction of a single window, but of thousands if not millions of them. The
war producers will temporarily profit, but their profit comes at the expense
of the destruction of whole infrastructures and populations who would have
173
otherwise contributed to production and trade.29 And in case you think that
the fallacy here is confined to the champions of the military-industrial
complex, what do you think about contemporary advocates of “green jobs”
who say these jobs are needed to stimulate the economy? The idea is that if
we give a subsidy to a wind turbine manufacturer, this will lead the
manufacturer to hire more people, which will further stimulate the economy.
But where is this subsidy coming from? It’s being taken from taxpayers,
who would have used the same money to invest or hire or otherwise create
economic opportunities of their own. At best one job is merely substitute for
another—and one can argue about which of the two types of job would be
more productive.
Moving from economics to foreign policy:
Hitler signed a peace pact in
exchange for territory
This will make him happy.
Therefore, there will be “peace in
our time”
This was an argument originally made,
in effect, by British prime minister
Neville Chamberlain after he signed an
Picture credit 102:
agreement with Hitler in 1938, just
http://commons.wikimedia.org/wiki/File:Bundesarchiv_Bild
before the outbreak of World War II.
_183H12751,_Godesberg,_Vorbereitung_M%C3%BCnchener_A
Hitler was allowed to occupy a large
bkommen.jpg
portion of Czechoslovakia (the
Sudetenland) in exchange for a promise to be peaceful. We all know that this
did not happen. Should Chamberlain have known any better? Even though
Hitler had not overtly invaded any other countries at the time of the peace
accord, it was not as if he had no track record by which to judge his
intentions. His Nazi party had gained political power in Germany through
acts of violent intimidation. He had preached his racism and desire for
dictatorship openly. And even in the absence of a specific track record for
Hitler, there is nonetheless a long and unfortunate history of how dictators,
or bullies of any kind, respond to appeasement. When you give them an
inch, they usually take a mile. They are not deterred by rewards, but by
punishment alone. The lesson seems simple enough that a child on a
29
None of this is to say that war can never be justified: if an aggressor nation is threatening to kill a
retaliating nation, then the destruction of war may be the only way to prevent still further destruction: but
this should not be confused with actual progress.
174
playground could learn it, but it is surprising to what extent various forms of
appeasement are proposed to guide Western foreign policy with
dictatorships.
Finally, an environmental example. In the 18th century, Rev. Thomas
Malthus finished a study of the deer population in England and concluded,
probably on the basis of viable evidence, that whereas the local deer
population would increase exponentially over time, the production of food
resources needed for the deer to live would only increase at a constant rate.
This meant that at some point the population growth rate would outstrip the
resource production rate, at
which time there would be
Food needed for growing
population
mass starvation and the surplus
population of deer would die.
Malthus himself, along with a
number of neo-Malthusian
Food produced
doomsayers, predicted much
the same for the fate of
Malthusian trap
mankind in our present age. It
is an interesting argument, but
arguably ignores some very
important background
knowledge about the
difference between deer and human beings. Whereas deer must adjust
themselves to their environment, human beings adjust their environment to
themselves by creating new technology. One prominent scientist in the 20th
century, Norman Borlaug, did this on an unprecedented scale when he
invented new breeds of wheat that ended up turning countries like Mexico,
India and Pakistan, all of which were
once net food importers, into net food
exporters. Malthus also ignored the
fact that unlike animals, we are not
slaves to our reproductive capacity.
When we use more resources to create
wealth, the resulting prosperity
permits families to live with fewer
children, no longer needing extra
children as farmhands and laborers.
While it is true that global population
has probably not yet reached its
climax, demographers are now
Picture credit 103:
http://commons.wikimedia.org/wiki/File:World-Population1800-2100.png
175
predicting that sometime in the 21st century, owing to these economic
factors, it will probably begin to decline.
176
§3: PROOF: LEGITIMATE AND ILLEGITIMATE DEMANDS FOR IT
Chapter 9:
Shifting the burden of proof and the argument from ignorance
Ben Bayer
Drafted February 28, 2010
Revised August 16, 2010
The burden of proof
We have now completed our survey of the three basic requirements of good
reasoning.
4. The premises of the argument must be known and known better than
the conclusion (they must be well-evidenced).
5. The premises must be relevant to the conclusion (they must be likely
to establish the conclusion as true).
6. The argument’s premises must contain all of the known relevant
evidence.
As the requirements of giving a good argument, these presuppose that there
are circumstances under which we need to give an argument. Fulfilling all
three, especially for non-deductive arguments, can be a difficult task. We
may have to think through the entirety of our background knowledge on a
given topic, about the meaning of the conclusion we are trying to prove, and
about the implications of accepting the conclusion
for our different areas of knowledge. This can be an
exhausting process. It is in part for this reason that
logicians will say that proof is a kind of burden we
must carry if we want to claim to know some
conclusion.
As with any burden, we should be sure to
carry it only when we need to. When do we need
to? You’ll recall from our opening discussion about
why we need logic that the main reason is that
human beings have limited cognitive faculties: we
can only take in so much information at a time
through our senses. For this reason we need a tool
to gather the information we can and piece it
together in a way that lets us “see” further than we
Picture credit 104:
would be able to with our unaided vision, in the
http://commons.wikimedia.org/wiki/File
:Port_merion_atlas.JPG
177
same way that a ladder or tower lets us see further by climbing it. And we
only need the assistance of the tool under this circumstance: otherwise our
eyes will do just fine. Though it sounds odd to say it in a textbook devoted
to logic, there is a way in which proof is only a second class kind of
knowledge. It is only what we have to resort to using when we have no first
class, directly evident knowledge on a given topic.30 Since the demands of
proof carry with them a heavy burden, we should after all be happy when we
do not need to resort to meeting them.
A simple example of when we need not bear the burden of proof is
when we form a judgment directly from sensory observation. If I see a table
before me, it does not require any “proof” to
conclude on the basis of this observation, “There
is a table.”31 This is a conclusion reached without
any special inference, only by applying one’s
concept of “table” directly to what one observes.
For judgments like this in contexts like this, there
is no burden of proof, because there is simply no
need for proof. Under ordinary circumstances, if
someone demands a proof that you are looking at
a table (the lighting is normal, your vision is
20/20, and nobody is drinking too much) he
doesn’t really understand the concept of “proof.”
Asking for a proof of what requires none—and
Picture credit 105:
for what is, in fact, the basis of all proof32—
http://www.flickr.com/photos/esther17/190
would be like asking for a ladder to get back to
47228
the ground. There’s no point in going through the effort of climbing up a
ladder and then down again to just to get where one was in the first place.
30
I borrow the idea of proof as something we “resort to” from Harry Binswanger, with gratitude.
There are philosophers called “anti-foundationalists” who deny that sensory data is the rock-bottom basis
of all knowledge. They insist that perceptual-level judgments may sometimes need justification.
Knowledge, on this view, is not hierarchical in structure, but a vast, interconnected, circular web. This
author disagrees with the anti-foundationalists, but thinks it is possible to make the present point without
stepping on too many toes. Even anti-foundationalists are typically “contextualists” about the justification
of our beliefs. They’ll say that in ordinary contexts we treat perceptual-level judgments as unshakeable—
they just insist that there can be special circumstances in which such a judgment may be challenged by
another person, who should then be given a special justification. So we’ll speak here only of perceptual
judgments in ordinary circumstances, which anti-foundationalists agree do not need justification.
32
Not every philosopher thinks that basic sensory judgments are the only kind not in need of proof. Others
think we may have a kind of “rational intuition” about basic claims in mathematics (“1 + 1 = 2”) in logic
(“Nothing can be both A and non-A at the same time and in the same respect”) and in the formulation of
definitions (“A bachelor is an unmarried male of marriageable age”). We will not here examine what other
sources of foundational knowledge there might be, but in chapters 12 and 13, we will examine the nature of
definitions, and show how there may be sensory-based knowledge that is relevant to assessing their
adequacy.
31
178
There can be other ways in which claims of various kinds do not need
proof. In the examples above, basic perceptual claims need no proof because
they are so obvious as to not need it. In other examples, claims may be so
irrelevant as to not be worthy of consideration—and certainly not in need of
proof. This point holds especially a kind of proof that a claim would need is
utterly impossible to provide.
. For example, it is sometimes said that it is impossible to prove a
negative claim. Strictly speaking this is not true. We can prove quite easily
that a substance does not contain any acid if we apply litmus paper which
turns blue. Because the litmus test shows that the substance is basic or
alkaline, this implies that it is not acidic. But note that this kind of a negative
claim is demonstrated by showing that an incompatible concept (“base”
rather than “acid”) applies. Independent of
inference from positive incompatible
knowledge, however, these negative
claims cannot be inferred from anything
else. We cannot point to “negative facts,”
to the bare “non-acidity” of a substance,
to show that it is not an acid. As we shall
later see, however, some requests to prove
a negative are made in contexts in which
no recourse to positive evidence is
permitted. In these cases, the demand for
Picture credit 106:
proof demands the impossible. These,
http://www.flickr.com/photos/pranavsingh/1288182406/
then, form a separate class of cases for
which there is no burden of proof: we cannot prove a negative without
reference to a positive, and so we cannot be expected to try.
We can think of such inappropriate demands for proof—especially of
the kind involving a request for what cannot be proved—as involving the
attempt to shift the burden of proof. To “shift” a burden is to slough it off on
to someone whose task is not to carry it in the first place. This kind of
burden-shifting involves a conceptual mistake about what proof is and why
it is needed, but it is not yet a logical fallacy, because it is a mistaken
demand, not a mistaken argument. However, as we shall shortly see, the
attitude implicit in the demand is used to make several forms of argument,
each of which is, as a result, a fallacy.
179
Shifting the burden of proof in argument
We can illustrate a form of fallacious reasoning that is often expressed
in the act of shifting the burden of proof by noting the difference between
examples. You will concede, we assume, that
there is an important difference between the
following two arguments:
Abigail says you tormented her
magically.
Therefore, you are guilty of witchcraft
There is no proof that you aren’t a
witch.
Therefore, you are guilty of witchcraft.
The premise of the first argument contains
the typical kind of testimonial evidence that
was used to prove women guilty of
witchcraft in a bygone era. This is doubtless Picture credit 107:
http://commons.wikimedia.org/wiki/File:TheSale
evidence of questionable reliability, and
mMartyr-Noble.jpg
33
doubtful relevance to the conclusion. But at least it is something.
We can’t say the same for the second argument. Usually a prosecutor
would not state an argument in this explicit form. But the way witch trial
prosecutors would accuse defendants would imply as much. Consider this
passage from the transcript of the trial of Bridget Bishop, the first woman to
be executed for Witchcraft in Salem, in 1692:
Q: Have you not to do with familiar Spirits?
A: I have no familiarity with the devil.
Q: How is it then, that your appearance doth hurt these?
A: I am innocent.
Q: Why [do] you seem to act witchcraft before us, by the
motion of your body, which seems to have influence upon the
afflicted?
A: I know nothing of it. I am innocent to a Witch. I know not
what a Witch is
Q: How do you know then that you are not a witch?
33
For considerations about why such testimony might not be reliable, see chapter 5’s discussion of
corroborating testimony by reference to background knowledge. Reports to have seen the Devil may fall
into the same category as reports about having seen men walk through walls.
180
A: I do not know what you say.
…
Q: Tell us the truth in this matter how come these persons to be
thus tormented and to charge you with doing
A: I am not come here to say I am a witch to take away my life.
Q: Who is it that doth it if you do not they say it is your
likeness that comes and torments them and tempts them to write
in the book. What Book is that you tempt them with?
A: I know nothing of it, I am innocent.
Q: Do you not see how they are tormented? You are acting
witchcraft before us. What doe you say to this? Why have you
not a heart to confess the truth?
A: I am innocent. I know nothing of it. I am no witch I know
not what a witch is.
Q: Have you not given consent that some evil spirit should do
this in your likeness?
A: No I am innocent of being a witch. I know no man woman or
child here.34
Notice the pattern of reasoning here. A suspect would, for example, be
presented with claims from so-called “spectral evidence”: other witnesses
would claim to have seen the accused appear to them in a dream or vision
and cast spells on them, for instance.
Presented with the claim that her
“appearance” somehow hurts the victims,
Bridget Bishop denies the charge, but is
rebuffed by her cross examiner, who asks
her how she knows that she is not a witch.
She does not have an answer, and it is not
clear how she could. She can prove that she
is a woman, but how could this contradict
the charge that she has communication
Picture credit 108:
with the Devil? By its nature, the claim
http://commons.wikimedia.org/wiki/File:Salem_witch
2.jpg
cannot be disproved. In the worldview of
her accusers, witches have magical powers that allow them to communicate
with the supernatural forces of evil through extraordinary means, all while
having the normal appearance of a woman.
34
<http://etext.virginia.edu/etcbin/ot2wwwsalemname?specfile=/texts/english/salem/public/salem.o2w&act=text&offset=1001011&textreg=div2&que
ry=bisbri >. Spelling and punctuation modernized —BB.
181
Suppose, for example, that on the night of the witness’ vision, the
accused had an alibi. Let’s say that the accused was busy making dinner for
her husband at the time of the vision, and so could not have visited her
physically. But the interrogator could simply allege that the accused was
casting the spell in her mind while making dinner, a possibility still
consistent with the claim that she consorts with the devil. Notice, for
example, in the second half of the exchange, when the interrogator is willing
to concede that Bishop did not appear before her victims directly: he
accounts for this by insisting that she must have then consented for some
separate evil spirit to appear in her absence. How could she now disprove
this? By constantly adjusting accusations against Bishop, she is rendered
incapable of showing that she is not a witch, because she is deprived of the
normal means of proving a negative: i.e. deriving it from some positive fact
that is inconsistent with it.
In such a case, there really is no proof that the accused is not a witch:
and the accusers have made sure that there could be no such proof by the use
of “spectral evidence.” And yet nothing actually follows from the mere
absence of this proof. The
assumption that something does
follow from the absence of proof is
at the root of this act of shifting the
burden of proof, and a number of
other forms, each of which we will
examine in the next section.
To speak of shifting the
burden of proof presupposes an
identification of what the proper
burden of proof is. This is often
formulated in a principle known as
the burden of proof principle or the
credit 109:
onus of proof principle: the burden Picture
http://www.flickr.com/photos/swanksalot/4883039221/
of proof is on the person who
asserts a claim. It is not anyone’s burden to prove the denial of some claim,
especially if no real evidence has been presented for it to begin with. This is
why we have the presumption of innocence rather than guilt in our court
system. It is telling that in practice defendants enter not guilty pleas, rather
than innocence pleas: we presume they are not guilty unless someone proves
otherwise. We will explore the meaning of this requirement in the sections
that follow.
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The argument from ignorance
If we cannot prove a negative independently of deducing it from
positive facts, we shouldn’t demand it. It is a form of shifting the burden of
proof from those who are claiming what is so (for example, that someone is
a witch) to those who make no such claim. If it is improper to shift the
burden of proof in this way, it follows that two different forms of argument
are fallacious, because they rely on an implicit demand for an impossible
form of proof. Each of these is a form of the argument from ignorance (also
called the appeal to ignorance or argumentum ad ignorantium), which is the
fallacy of inferring some conclusion from the mere absence of evidence,
rather than from real evidence. The argument from ignorance comes in two
main forms, each of which is presented schematically as follows:
Type 1: “There’s no proof that X is not so, therefore X is so.”
Type 2: “There’s no proof that X is so, therefore X is not so.”
Notice that each type begins with the premise that there is no proof for
some claim. The difference is simply with regard to what kind of claim there
is no proof for. If there is no proof that X is not so, it is inferred that X is so.
If there is no proof that X is so, it is inferred that X is not so. The assumption
here is that the absence of proof for a claim allows us to conclude in favor of
its logical alternative, as if the absence of proof for a claim implies the
negation of the claim. But each of these is a fallacy. We may understand
why the first is fallacious by invoking the old saying, “Nothing comes from
nothing” (“Ex nihilo nihil fit”). So no positive conclusions can be drawn
from a sheer absence of evidence. Likewise we can understand why the
second is a fallacy through another saying: “Absence of evidence is not
evidence of absence.” The sheer fact that a thing does not show itself does
not imply it is not there. Nothing, not even the truth of negative claims,
comes from nothing!
Unfortunately examples of both forms of the argument from
ignorance are sometimes too easy to find. Here are a few examples of Type
1 argument from ignorance we have heard even in this century, so many
years after the Salem witch trials. Recall that the form of Type 1 is “There’s
no proof that X is not so, therefore X is so.”
You can’t prove your money didn’t come from selling drugs.
Therefore, you must be a drug dealer.
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There’s no reason not to jump out of this airplane.
Therefore, I should jump out of this airplane.
No one has ever shown that God does not exist.
Therefore, (maybe) he does.
The first example is probably the most pervasive. It is an argument
routinely used by drug enforcement officials who discover irregularities in
the finances of the accused and invoke asset forfeiture laws. The mere
presence of the irregularity is taken as a sign of involvement in the drug
trade, and suspects are sometimes expected to forfeit cash or assets that they
cannot prove to have come from somewhere other than the sales of drugs.
The government has no legal obligation in such cases to prove that the
money actually did come from drugs. Now in practice there may be ways to
show where the money really comes from. But even when someone
advancing this argument does not make the proof of the negative impossible,
it remains true that nothing follows from nothing, and a mere inability to
show where money comes from does not show that it did come from drug
sales.
The second example is not in the form that it is usually asserted. But
there is a certain type of person who, when asked why he wants to do some
surprising or even dangerous activity, will
simply shift the burden of proof onto the
person asking the question, and ask “Why
not?” Of course it’s not that reasons against
such a proposal can’t ever be given. (For
instance: Jumping out of an airplane could kill
you.) They can be given, but there is a deeper
logical question here: the person is proposing
using a great deal of energy at great risk, and
we would hope there is something to achieve
by doing it. Perhaps there really is a
justification—it would be fun—but rather than
state this, he’d rather find out reasons against
his proposal. Of course, having fun is an
Picture credit 110:
http://www.flickr.com/photos/29667181@N05/3
emotion, and we know that emotions do not
859685426/
offer us an independent source of evidence. So
a missing answer to “Why not?” plus the desire to have fun does still not
give us a clear reason.
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The last example is again not stated as many might hold it explicitly.
Often people will hold out only the possibility of the existence of God
simply because his existence has never been disproved. This assumes that a
possibility is merely the absence of impossibility—the absence of the proof
that something cannot be. As we will discuss later, however, even possibility
claims may need specific positive evidence. If that is true, the burden of
proof may be on the theist who wishes to show that God does exist, not on
the atheist who wishes to show that he does not.
The end of what is often regarded as the worst movie ever made, Plan
9 From Outer Space, features a speech by the narrator Criswell, which
hammers home an argument from ignorance:
You have seen this incident, based on
sworn testimony. Can you prove that it didn’t
happen? Perhaps on your way home, someone
will pass you in the dark. And you will never
know it, for they will be from Outer Space!
Many scientists believe that another world
is watching us this moment. We once laughed at
the horseless carriage, the aeroplane, the
telephone, the electric light, vitamins, radio, and
even television. And now some of us laugh at
Outer Space!
God help us, in the Future!
The second part of Criswell’s statement is
especially interesting version of the appeal to
Picture credit 111:
http://commons.wikimedia.org/wiki/File:Plan_
ignorance. He points out that many facts we
nine_from_outer_space.jpg
know about today were previous unknown,
implying that our absence of knowledge of about his subject matter (aliens
from outer space) does not mean there are no aliens. We’ll leave this one for
you to think about. Presumably you’ll agree that there were and are many
yet-to-be discovered facts. But does this imply that we have a reason to
believe in aliens?
Sometimes it can be tricky to determine if a given argument really is
an example of the appeal to ignorance. It is not something we can determine
simply by the form of the argument. For instance:
There’s no evidence that the fire has been put out.
Therefore, the fire is still burning.
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This argument appears to have the form, “There’s no proof that X is not so,
therefore X is so.” But is it a fallacy? Suppose that at one moment, you see
the fire burning, and then turn your head from it for just a moment and are
asked if the fire is still burning. Suppose further that you remember having
seen it burn, and know that when you saw this, it had a ready supply of fuel,
and would only have been extinguished by, say, a large quantity of water.
So, not having heard the gushing of a flood putting it out, is this arguer
justified in concluding that it is still burning? Is this an appeal to ignorance?
Arguably this is not a fallacy. Pay attention to the definition of the
argument from ignorance: it is the fallacy of inferring some conclusion from
the mere absence of evidence, rather than from real evidence. In this case,
the arguer may be appealing most immediately to the absence of some
evidence to infer that the fire is still burning. But, as we have often seen in
other examples of both good and bad reasoning, there can background
knowledge or beliefs at work. In this case the arguer is not appealing to the
mere absence of evidence.
Implicitly, he may also be relying
on several additional sources of
positive evidence: his having seen
the fire burning, his having seen it
with a good stock of fuel, his
knowledge of what it would take to
put the fire out in spite of the fuel,
and, in particular, his knowledge
that if a nearby fire were put out by
water, he would soon after acquire
Picture credit 112:
the evidence of this. Not having
http://www.flickr.com/photos/gardenbeth/4661474559/
acquired this evidence, the arguer
has a very justified belief that it is still burning. (And if, by chance, the fire
has been put out, and he just hasn’t gotten the news yet in the narrow
timeframe required, his belief is still quite justified, even if false.)
Whether or not one has all of this background knowledge, then, is
crucial for determining whether or not an argument from ignorance is being
committed. So consider a slightly different argument:
There’s no evidence that my long-lost, obscure, and elderly friend is
dead.
Therefore, my friend is alive.
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Would we have the same knowledge about the friend here as we did about
the fire? We remember once having seen our friend, but when we saw him,
we knew he didn’t have many years to live, we knew he was obscure, so not
many people knew about him, and it is now been many years since we have
seen him. Unlike the fire, he did not have a lot of “fuel” left to burn. And
because he was obscure (and so easy to lose touch with), we do not have the
same conviction that if he were to die, we would hear about it. This, then, is
not backed up by the same kind of positive background knowledge that
backs up the fire example. At best it is backed up by our once having known
the friend in the distant past, which is something rather than nothing. But
being that far in the past, it is questionable whether that evidence is really
relevant or operative any more. Which leaves us only with the absence of
evidence in the present. So all we really have now is ignorance.
Now let’s consider some prominent examples of Type 2 appeal to
ignorance. Recall that Type 2 is of the form, “There’s no proof that X is so,
therefore X is not so”:
I haven’t heard any prominent news stories about rain falling in the
south Pacific.
Therefore, there must be no rain there.
There are no confirming news reports from the 1960s of hippies
spitting on returning Vietnam vets.
Therefore, it never happened.
There is currently no Darwinian explanation for a complex
molecule.
Therefore, there must be no Darwinian explanation. (God must have
designed it.)
Unlike the examples of Type I argument from ignorance, these examples go
from the absence of evidence to a negative conclusion. At first they would
seem to be more logical: the absence of one kind of thing is connected with
the absence of another. But are they more logical? Should we think that
absence of evidence is evidence of absence?
The mere absence of evidence is not evidence of absence. Consider
the first example about the rain storm in the south Pacific. To come to a
conclusion that there is no rainstorm in such a distant place is to make a very
strong and definite claim not only about what isn’t there, but what is. When
we claim that there is no rain storm in the south Pacific, we claim that there
187
are clear skies and sunshine. If we could know so much about the weather in
a distant place just by checking on what stories we haven’t heard, we could
make a fortune as a weather forecaster. We have to take this absence of news
in conjunction with our background knowledge that we don’t usually pay
attention to weather in faraway places, and probably wouldn’t hear about
such a storm if it happened. Actually, we probably don’t have that
background knowledge at all. It’s more relevant that we lack the background
knowledge that we would hear about such a storm if it happened. So in this
case, this really is an appeal to mere ignorance, which is not a good basis for
argument.
A similar problem infects the second argument. Some time ago, a
prominent journalist wrote a critique of rumors that used to circulate to this
effect.35 It is true we have no journalist’s reports of such terrible incidents.
But we wouldn’t necessarily expect journalists to have been on the scene to
report such incidents, and we wouldn’t expect them to report them even if
they had witnessed them (for reasons of patriotism, perhaps). This doesn’t
mean that we should conclude that there were incidents of such harassment.
It means, at best, that we should be agnostic about them, especially if we
have heard at least some plausible rumors that they occurred (which is why
most people at least consider it to be a possibility).
The last example is actually a major pillar of a contemporary
philosophical theory advanced by theists, the so-called theory of “intelligent
design” (which is a really a variant of a philosophical argument called the
“argument from design,” which goes back at least as far as the 18th century,
if not further). There are some microbiological structures—the flagellum (or
swimming tail) of certain bacteria,
for instance—which at one time,
at least, biologists could not give
an evolutionary explanation for.
The molecules were said to have
an “irreducible complexity” to
them, such that it was hard to
imagine how they could have
arisen from smaller, simpler
molecules. Hence intelligent
Picture credit 113:
design theorists concluded that
http://commons.wikimedia.org/wiki/File:Hands_of_God_and_Adam.j
these molecules had to have been
pg
designed by God, since they could not have evolved by natural selection.
35
Jack Shafer, “More Spit Takes: Searching the News Archives for Evidence of Spat-Upon Returning Viet
Vets,” Slate, February 12, 2007. <http://www.slate.com/id/2159470>
188
The trouble is that the absence of an explanation is just a form of ignorance,
the fact that we don’t know how a structure like this could have arisen.
What’s more, an evolutionary explanation is a lot like a rainstorm in the
south Pacific: even if there is such an explanation available, it’s not obvious
that we would readily know it (because the events behind it would be buried
in the distant past). Whatever you think of the theory of evolution, this
particular argument isn’t enough to call it into question or support design
theory, because no relevant background knowledge tells us to expect
anything other than ignorance of the existence of a difficult explanation.
As with examples of Type 1 appeal to ignorance, it is not always easy
to tell when a given argument is appealing to mere ignorance. We have to
take a careful look at what kind of background knowledge may or may not
be involved. Consider, for example, the following:
There is no evidence that there is a large pink elephant in this room
Therefore, there is no large pink elephant here!
Here again we have an argument that
is roughly of the form, “There’s no
proof that X is so, therefore X is not
so.” But is there additional
background knowledge that could
inform the arguer’s conclusion here?
The example is very similar to our
previous example of the fire, though
this time perhaps the logical status is
even more obvious. Given what we
know about large pink elephants,
Picture credit 114:
there is good reason to think that if
http://www.flickr.com/photos/oddsock/2242056191/
there were such a large and noisy
beast in the room, we would know about it! In that case, there is no evidence
of the elephant, true, but there is evidence of the ordinary contents of the
room, and the background knowledge that these ordinary contents would not
easily hide a large malodorous pachyderm. Note that this stands in contrast
to the following argument of similar form:
There is no evidence that there are atoms in this room.
Therefore, there are no atoms in this room.
189
We do not have any general conviction that if there were atoms in the room,
we would know about it. They are by definition some of the smallest
particles of matter, and therefore invisible. If they are there, we wouldn’t
know about them very easily, and our scientists in fact did not know about
them until the 19th century.
As a final exercise for the reader, suppose that we have no evidence
for the existence of Santa Claus. Can we conclude that he does not exist. Is
he more like the elephant, or the atom? Do we have background knowledge
about whether or not we would possess evidence of his existence, were he to
exist?:
There is no evidence that Santa Claus exists
Therefore Santa Claus must not exist.
Depending on what background
knowledge you think we have, you
will conclude that this argument is
a fallacy, or not. But for the sake of
further exercise, suppose further
that arguments like the argument
from design fail, and no other
arguments for the existence of God
work. We would then be in a
position to assert the following
premise, and some might add the
following conclusion:
Picture credit 115:
http://commons.wikimedia.org/wiki/File:Where_Santa_Claus_lives.j
pg
There is no evidence that God exists.
Therefore, God does not exist.
What background knowledge do we have here? Would we know about God
if he existed? If you think the argument about Santa Claus is a good one
(since most of us don’t believe in Santa Claus), what is your view of the
second? Is there any difference between the way we think about Santa, and
the way we think about God?
Appeal to the arbitrary
It’s very rare that an arguer will appeal to nothing other than his ignorance
in order to establish some claim. Even in the examples from witch trials, we
noticed that accusers appealed to something called “spectral evidence” to
190
motivate the original charges against alleged witches. In actual fact
appealing to someone’s dream or vision is not a form of evidence. There is
no reason to think that a dream connects one to reality any more than
hallucination or reverie. But a dream is at least something. Combining the
dream with an appeal to ignorance (the point that these women can’t show
they aren’t witches) makes it look as if the “spectral evidence” provides
some kind of positive background such that they are not appealing to mere
ignorance.
Of course because “spectral evidence” is not real evidence, the witch
trial argument really is an appeal to ignorance—it just might not look like
one at first. The example of spectral evidence illustrates a more general point
about the usual practice of shifting the burden of proof through the argument
from ignorance: it usually requires the mirage of positive evidence to make
it plausible-sounding. We may think that the use of “spectral evidence”
today is outmoded and that none would ever find it admissible.
Unfortunately, our age has its own equivalent. Consider these partial
arguments for various conspiracy theories:
Maybe you’re lying when you say you were in New York on
November 22, 1963.
Therefore, you can’t prove you weren’t in Dallas.
Therefore, (maybe) you were in Dallas.
Maybe witnesses who saw a plane crash into the Pentagon were part
of the conspiracy.
Therefore, you can’t prove a missile didn’t hit the Pentagon.
Therefore, (maybe) a missile hit the Pentagon.
Picture credit 116:
http://www.flickr.com/photos/50203533@N00/2936677990
In the first example, the arguer
is attempting to establish the case that
the person he accuses had the
opportunity to kill JFK. Suppose that
the accused says he has an alibi.
Suppose further that his alleged alibis
will even back him up. At either
point the conspiracy theorist can
allege that the accused or the alibis
might be lying, in which case the
accused really could have been in
Dallas, and really did have the
191
opportunity to help kill JFK. Much the same is actually done by those who
assert conspiracy theories about 9/11: the second above represents an actual
argument made by actual conspiracy theorists today. But what is the basis
for any of these “maybes”? Ultimately, the first “maybe” in the first premise
is arbitrary.
An arbitrary assertion is a claim devised by the imagination, asserted
in defiance of the need for evidence. “Spectral evidence” may be out when it
comes to making claims about the actual presence of a witch casting a spell
in one’s bedroom. But an equivalent is still judged by many to be
permissible about possibilities: as long as all we are asserting is a possibility,
it is thought to be the privilege of
imagination to determine such
possibilities. And it is true that there is
some sense in which that is the job of the
imagination. When we ask if it is possible
for us to walk through some door we’ve
never walked through before, for instance,
we imagine ourselves fitting through the
circumscribed space. But this imagination
is informed by some general background
knowledge of physics, as well as specific
knowledge of the shape and size of both us
and the door. Is there any equivalent
knowledge behind imagining the
credit 117:
possibility that we could be members of a Picture
http://www.flickr.com/photos/bibliodyssey/3783620795/
conspiracy to cover up the truth about the
JFK assassination or the 9/11 attacks?
The trouble is that apart from background knowledge, we also do have
a way of gathering specific evidence for specific possibilities. For instance:
A lot of money is being paid to cover up the break-in.
Therefore, maybe people were part of a conspiracy.
This was the nature of the actual evidence used by Woodward and Bernstein
to uncover the Watergate conspiracy. They began by “following the money”:
it led to the highest White House sources. Once they heard word from Deep
Throat and noticed a discernable money trail, there was a definite, wellevidenced possibility that there was a conspiracy to cover up the
involvement of the White House in the Watergate break-in. But that kind of
evidence was not constructed by imagination. As we discussed in our
192
previous chapter on the nature of proof, “possibility” is a concept we can use
to denote when we have gathered some evidence for our conclusion, if not
all of it.
Some imagination, however, is not some evidence, not unless it is
itself based on some background knowledge and evidence of the specific
circumstances. The mere fact that we can imagine people lying and
participating in a conspiracy does not establish a genuine possibility that
there is a conspiracy here. At best, it illustrates our power to invent fiction.
In the end, a claim that claim X is possibly true made simply on the grounds
that claim X has not been disproven, and that we can imagine its being true
is another version of the argument from ignorance. But it is a particularly
dangerous version of the argument, because, like spectral evidence, it allows
us to let into our mind thoughts that are not really thoughts. Insofar as they
can be made to fit with any of the evidence we do have, arbitrary
possibilities have no identity constrained by the genuine thinking we have
done.
This point that claims to know what is possibly true need to be based
on specific evidence, not just imagination, is
important for bigger issues in logic and
philosophy. Recall from chapter 8 that there
is some question about whether we can ever
really prove anything besides trivial
deductively-demonstrable claims. Can we
ever really prove that someone is a murderer,
that men are mortal, or that the earth’s
continents once fit together into a
supercontinent? Proof involves ruling out all
of the rival possibilities to a given conclusion,
leaving only one that must be true.
Philosophers who say that proof is ordinarily
impossible for the knowledge we acquire
from observation will say this because they
Picture credit 118:
say there are always a number of logical
http://commons.wikimedia.org/wiki/File:Goya__Caprichos_%2843%29_-_Sleep_of_Reason.jpg
possibilities that the evidence cannot rule out.
We cannot prove that we will all die someday, they say, because maybe
there is or will be someone who is immortal. All too often in the history of
philosophy, however, these imagined possibilities produce monsters—for
instance, claims that we can really know nothing at all.
As the Goya painting above illustrates, however, it is the sleep of
reason that produces monsters. Imagination is crucially important for
193
envisioning genuine possibilities, but it cannot do the job on its own. Reason
needs to guide our attitude toward what is possibly true, in the same way that
it guides our attitude toward what is probably true: by reference to the
evidence. And if reason can help us eliminate some possibilities as not
generating “reasonable doubt,” it may also be able to guide our attitudes
about what is certainly true.
194
§3: PROOF: LEGITIMATE AND ILLEGITIMATE DEMANDS FOR IT
Chapter 10:
The pseudo-proof of crackpot conspiracy theories
Ben Bayer
Drafted March 7, 2010
Revised August 17, 2010
Proof and pseudo-proof, illustrated by conspiracy theories
We have now examined all of the basic requirements of good reasoning
(though more nuanced requirements are yet to be discussed). We have also
looked at the conditions under which good reasoning or proof is appropriate
to demand or provide. When it is necessary, we have given sketches of the
systematic survey of different bodies of knowledge that proof requires.
For each element of human reasoning presented so far, we have
presented model examples of good reasoning and contrasted them with
associated fallacies. It is worth giving the same contrast on a broader level.
Just as a full proof that meets all three requirements will likely contain many
observations, inferences, and systematic interconnections among them, it is
possible to give a systematically interconnected phony “proof.” It is one
thing to use a single fallacy to generate an argument containing evidence
with illusory support and relevance. It is quite another to use a whole series
of such fallacies held together in a self-reinforcing way. When one is subject
to criticism, still another can be invoked to provide a smokescreen.
Elaborate “pseudo-proofs” are the mainstay of what is called a
“crackpot” theory, a theory so at odds with the ordinary evidence that it
requires extraordinary means to be made even plausible-sounding. We can
understand why paranoid schizophrenics resort to such proofs to construct
their pathological world views. It is less excusable when sane individuals do
the same. Still, they do. In the present chapter, we will illustrate the
difference between a legitimate and a “crackpot” proof by reference to the
topic of conspiracy theories.
Though the term “conspiracy theory” sometimes suggests otherwise,
not all conspiracy theories are “crackpot” theories. Some can be motivated
well by real evidence. A conspiracy is just a plan of joint action involving
two or more people, usually made in secret; so a conspiracy theory is just
someone’s claim that such an event has actually transpired. The fact that
such events are often planned and executed in secret is what makes them
195
mysterious, and what makes them need an unusual amount of evidence to
establish their truth.
This characteristic—that a conspiracy theory usually represents the
solution to a mystery—is what makes them ripe for abuse. If there is much
we do not know in the first place, there is ignorance to be exploited by the
fallacy of the appeal to ignorance. By contrast, a good detective solves a
mystery not by reveling in ignorance, but by finding real evidence that adds
up to a conclusion about the guilty part.
For this reason there surely can be legitimate conspiracy theories
based on real and relevant evidence.
Prominent examples include the
theory first articulated by Woodward
and Bernstein regarding the
perpetrators of the Watergate breakins. There really was a plan by
officials high up in the Nixon
administration to break into
Picture credit 119: http://commons.wikimedia.org/wiki/File:CesarDemocratic Party offices and cover
sa_mort.jpg
up the crimes. There really was a
communist conspiracy to infiltrate Hollywood in the 1930s and 1940s.
Though McCarthyism was no doubt paranoid in many respects, revelations
from the Soviet archives have revealed evidence of serious Soviet espionage
during that period, often with the assistance of the American Communist
Party.36 Last but not least, perhaps the most famous conspiracy in all of
history was that planned by a cabal of Roman senators to assassinate Julius
Caesar on the Ides of March, 44 BC.
But the bulk of famous conspiracy theories
are probably based on much less credible evidence
and argument than the previous well-documented
theories. These theories are grist for the mill of
recent Hollywood movies, like The DaVinci Code,
in which the fictional portrayal of a crackpot
conspiracy does often make for an entertaining
yarn, but not a scientifically verified account of the
truth. Sadly, crackpot theories are also grist for the
mill of many internet web sites whose authors take
36
Picture credit 120:
http://commons.wikimedia.org/wiki/File
March
1, 1999
:Judeo-Masonic_Conspiracy.jpg
See Joshua Marshall, “Exhuming McCarthy,” The American Prospect,
<http://www.prospect.org/cs/articles?article=exhuming_mccarthy>; and Ronald Radosh, “The Persistence
of Anti-Anti-Communism,” Front Page Magazine, July 11, 2001
<http://97.74.65.51/Printable.aspx?ArtId=24006>.
196
them seriously. There are those who think the moon landing was faked at a
sound stage under the direction of Stanley Kubrick. There are those who
think that the government has plotted to cover up evidence of the existence
of aliens from outer space (e.g. a crashed alien space craft at Roswell, NM).
And when it comes to speculating about who controls the world economy
(as if any single set of individuals
could possibly do this), the usual
candidates are: the Freemasons, the
Bavarian Illuminati, the Trilateral
Commission, and of course (following
in a tradition of anti-Semitic
conspiracy theories), the Jews.
Sometimes one can imagine that in the
minds of some conspiracy theories, all
Picture credit 121:
http://commons.wikimedia.org/wiki/File:World_conspiracies_
of these conspiracies are linked, to the
pyramid.jpg
point where everything of any
importance in the world is under the control of one massive secret plot.
Usually when conspiracies expand to include so much, keeping them secret
requires more and more people to be part of the conspiracy. After a while,
you get the sense that you might be the only one not part of the conspiracy
(or you’re part of it and you don’t even know)!
Clearly some conspiracy theories are better than others, logically
speaking. In the remainder of this chapter, we will examine two conspiracy
theories, each dealing with the same basic topic. This author takes one of
them to be quite convincing, but not the other. Both concern the terrorist
attacks of September 11, 2001. Before evaluating the difference between
them we will first sketch the case given for each.
Conspiracy theory #1: Al Qaeda planned
and executed 9/11
This first theory is “official”
conventional wisdom. For that reason it
sounds strange to describe it as a
“conspiracy theory,” since that term is
usually reserved for theories of the
crackpot variety. But a conspiracy theory
it is: Al Qaeda is said to have plotted the
attacks in secret over a period of years,
and their success required that a number
of different parties conspire to make sure
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http://www.nasaimages.org/luna/servlet/detail/NSVS~3~3
~9978~109978:Landsat-7-view-of-Ground-Zero
197
that separately planned events occur simultaneously. The moment that we
saw a second plane hit the towers, we knew there was a conspiracy involved.
Though this is a conspiracy theory, there is a great deal of evidence
supporting it. Since the conspiracy involved a plot to commit mass murder,
we can use the same standard of proof for establishing the identity of a
murderer as we would for more ordinary crimes. To find the guilty party, we
need to identify a party with the means of undertaking the specific crime, the
opportunity to do so at the specific time and place, and a motive for
undertaking such high stakes actions.
The evidence in support of the “official” theory is well-known
enough, so we do not need to belabor the details.
Evidence concerning the means and opportunity was obvious enough.
We have pictures—many of them broadcast on live television—of two
planes slamming into the World Trade Center
towers, of a flying object slamming into the
Pentagon, and of wreckage of a plane in rural
Pennsylvania. As soon as the attacks occurred, we
were able to quickly look up the passenger
manifests to identify the suspects. On each flight,
there were four or five names of unmistakable
Middle Eastern origin, one of whom on each plane
(Atta, Hanjour, Jarrah, and Al Shehhi) had also
received instruction at various flight schools in
America, many of whom at received funds from
known Al Qaeda sources, and some of whom had
been known to have trained at Al Qaeda camps.
Evidence of Al Qaeda’s motive for
Picture credit 123:
http://commons.wikimedia.org/wiki/Fil
committing the crime was also fairly clear.
e:Hamid_Mir_interviewing_Osama_bi
Throughout the 1990s, Al Qaeda tried to make a
n_Laden.jpg
name for itself as the leading advocate of Islamic
totalitarianism as a rival to American global power. It openly complained
about the American military presence in the Persian Gulf after the first Gulf
War, and America’s continuing financial and moral support for Israel. Al
Qaeda did more than complain: it acted on its grievances, and is known to
have been connected with, if it did not claim outright responsibility for, a
variety of terrorist attacks against American interests throughout the 1990s,
from a series of coordinated bombings of American embassies in East Africa
in 1998, to the attack on the U.S.S. Cole in the harbor of Aden, Yemen, in
October of 2000. Bin Laden himself is known to have issued fatwahs
(scholarly religious decrees) calling for fellow Muslims to attack Americans
198
around the globe, and admitted to as much in a television interview with an
ABC news reporter in May of 1998, where he even said “We do not have to
differentiate between military or civilian. As far as we are concerned, they
are all targets, and this is what the fatwah says.”37
We usually resort to the means, motive and opportunity standard of
proof when the murderer is trying to elude capture and cover up evidence of
his guilt. Our case is simplified for Al Qaeda, because in many cases the
leaders and members of the organization claimed direct responsibility for the
9/11 attacks, directly testifying against their own interest to their guilt. This
includes not only captured members of Al Qaeda, such as Khalid Shaik
Mohammed and Zacarias Moussaoui, but bin Laden himself, who described
in detail his planning for the attack and subsequent elation about its success
in a video captured by American intelligence,38 and on several other
occasions released tapes claiming official responsibility for the attacks.39 In
one of these tapes, some of the terrorists known to have been on the planes
are shown reading their wills.40
The evidence against Al Qaeda, or at least against some Middle
Eastern terrorists inspired by Islam, is damning. But there is at least some
reason to be hesitant about all of the
evidence mustered in favor of this
theory. Much of it comes from the
testimony of U.S. government
investigators, who have claimed to
associate the names of the terrorists
with Al Qaeda, and who have
translated the relevant messages in
which bin Laden claims
responsibility. Since we do not have
credit 124:
first hand access to this evidence, we Picture
http://commons.wikimedia.org/wiki/File:Richard_Nixon_candid_i
n_the_Oval_Office.jpg
can take it as evidence only if we
regard the testifier in this case as reliable and honest. There is little reason to
doubt the reliability of the U.S. government as a testifier. It has at its
disposal the most expertise of any investigation agency on the planet. But
37
PBS Frontline, Interview with bin Laden (in May 1998),
<http://www.pbs.org/wgbh/pages/frontline/shows/binladen/who/interview.html>
38
CNN, “Bin Laden on Tape: Attacks ‘Benefited Islam Greatly,” December 14, 2001,
<http://archives.cnn.com/2001/US/12/13/ret.bin.laden.videotape/>.
39
BBC News, “Excerpts: Bin Laden Video,” October 29, 2004,
<http://news.bbc.co.uk/2/hi/middle_east/3966817.stm>; The Times of India, “Osama Claims Responsibility
for 9/11,” May 24, 2006, <http://timesofindia.indiatimes.com/articleshow/1550477.cms>
40
CBC News, “Bin Laden 9/11 Planning Video Aired,” September 7, 2006, <
<http://www.cbc.ca/world/story/2006/09/07/al-qaeda-tape.html>.
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there may, at least sometimes, be reason to doubt its truthfulness. Americans
can remember cases in which their own government has not always been
honest with them. A prime example is the very Watergate scandal cited as an
example of a legitimate conspiracy theory above. The Watergate scandal
shook American’s confidence in the honesty of their leaders, and was
followed in the 1980s and 1990s with a number of other scandals in which
government officials were accused, often with justification, of lying about or
covering up government activities. (Prominent examples include: the
Iran/Contra scandal under the Reagan administration, and the Lewinsky
scandal under the Clinton administration.) In addition to this general concern
about the trustworthiness of the U.S. government, critics of the first theory
have described holes in the official explanation given by the government.
These shortcomings, in fact, constitute much of the basis for the second case,
a rival conspiracy theory.
Conspiracy theory #2: Elements of the U.S. government planned or
permitted 9/11
Claims about U.S. government involvement in the 9/11 attacks range from
the radical claim that Bush himself directly planned the attack, to the more
moderate claim that at least some government officials had evidence that the
attacks were being planned, and purposefully declined to do anything to
prevent them. In either case,
malicious intent would obviously be
necessary.
What evidence suggests that
the U.S. government had the
opportunity either to plan or permit
such attacks? It is now well known
that government intelligence pointed
the President himself to the looming
threat of an Al Qaeda attack, as early
Picture credit 125:
http://www.flickr.com/photos/thegreenpages/2740311600/
as August of 2001, when a
Presidential Daily Briefing title “Bin Laded Determined to Strike in U.S.”
went so far as to mention the use of hijacking a plane as a tactic.41 You may
have also heard of the story of FBI agent, Colleen Rowley, who made
repeated attempts to warn her superiors that the man they had held in
custody in Minnesota since August 2001, Zacarias Moussaoui, was part of a
41
Thomas S. Blanton, “The President’s Daily Brief,” April 12, 2004, The National Security Archive,
<http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB116/index.htm>. Actual Briefing document here:
<http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB116/pdb8-6-2001.pdf>.
200
wider plot.42 Sadly her attempts fell on deaf ears. Other attempts to warn of
the attacks were ignored or, seemingly, stonewalled.
Perhaps, you may suggest, the U.S. knew something about the
possibility that these attacks could occur, but this does not mean that they
acted on their knowledge or had the means to do so. One theory suggests
that the U.S. did: it had secretly planted bombs in the basement of the World
Trade Center. They argue that Columbia
University recorded a strange seismic spike
before the collapse of the towers, and that
planes crashing into the towers could not
have brought them down by themselves.
Here they will often cite the fact that in
1945, when a B-25 bomber crashed into the
Empire State Building, there was a fire but
nothing close to a collapse (since the
Empire State Building still stands to this
day). They will cite the fact that the
temperature at which jet fuel burns is not
hot enough to melt structural steel. And
they will cite the fact that World Trade
Picture credit 126:
Center #7, a third building close to the
http://en.wikipedia.org/wiki/File:Empirestate540.jpg
Twin Towers, also collapsed later in the
day on September 11th, even though it was never struck by any planes. All of
this, they think, points to a plot—usually it’s the CIA who is responsible—to
bring down the towers using a bomb and to blame it on Islamic terrorists.
But the U.S. conspiracy would not need to be as devious as involving
a bomb under the World Trade Center to satisfy some critics. Even if the
planes could have brought down the towers, it would be sufficient to let
them do this, assuming that the government knew what was going to happen.
In addition to the stonewalling of various pre-September 11th investigations,
there is also evidence that on the day of September 11th, officials who were
charged with the nation’s air defense appeared to wait unnecessarily long
before ordering fighter jets into the skies to intercept the planes headed for
New York and Washington, after the first plane had hit the first tower.
Critics allege that this supports a more plausible, less radical conspiracy
theory: that the government could have stopped the attacks, but chose not to.
The same kind of story is sometimes told about the events at the
Pentagon. One eyewitness who saw the Pentagon struck used the phrase
42
Time Magazine, “Coleen Rowley’s Memo to FBI Director Robert Mueller” (dated May 21, 2002),
<http://www.time.com/time/covers/1101020603/memo.html>.
201
“cruise missile” to describe what he saw. Other evidence from the scene of
the crime is mustered to suggest that it really was a cruise missile, and not an
airplane, as we are usually led to believe. Very little debris is seen on
pictures of the Pentagon lawn on the day of the attack, and the hole
punctured by the incident object appears to be too small given the wingspan
of the plane. Questions are even raised about the crash of Flight 93 in
Pennsylvania, about a small white plane that was seen flying near the scene
of the crash, and about the relative absence of debris at this crash site. It is
suggested that the plane was shot down by a missile, rather than having been
forced to crash because of a passenger rebellion against the hijackers.
Of course the most pressing evidence the advocates of this second
theory would need to find would be evidence of motive. Why, after all,
would the U.S. government plan attacks on its very own soil, killing its very
own citizens—and in the case of the Pentagon, its very own employees? The
expected payoff would have to be very high to motivate such drastic action.
Here critics will mention that the military had pre-existing plans to invade
both Iraq and Afghanistan, and
remind us that the U.S. has long
had oil interests in both countries
(in Iraq, which is a major producer
of oil, and in Afghanistan, where a
proposed oil pipeline from Central
Asia to the Indian Ocean had been
stymied by the resident Taliban
government). Critics will also
marvel at the rapidity with which
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domestic spying legislation like the
http://commons.wikimedia.org/wiki/File:Bush_War_Budget_2003.jp
g
Patriot Act was passed after
th
September 11 . The bill itself ran for hundreds and hundreds of detailed
pages, as if it had been written before the attacks themselves. The military
also had plans to build new weapons systems, such as an anti-missile
defense system, but was concerned that it could not justify spending the
money on such systems unless a “New Pearl Harbor” attack occurred on
U.S. soil. And unless it still seems implausible that the U.S government
would consider anything like a terrorist attack in order to justify new wars or
military spending, critics will point to the existence of “Operation
Northwoods,” a plan by the CIA in the 1960s (never implemented) to launch
terrorist attacks in U.S. cities in order to justify war with Cuba.
What do you think? Is the evidence for this second theory—that the
U.S. planned or permitted the 9/11 attacks—at all convincing? In the next
202
section, I will offer an evaluation of the evidence and comparison with the
first theory.
Comparison of the two conspiracy theories
We have already noted one major problem for the first (official) theory
about the perpetrators of the 9/11 attacks: much of its evidence has to be
accepted on the basis of testimony by government agents, and the
government is not always the most trustworthy testifier. The second theory
is not without its own problems. As it happens, it has enough problems to
warrant an entire section of discussion. This should give you a hint as to
which theory we’ll argue is more plausible.
Much of the evidence for the second theory is based on anomalies:
strange facts or occurrences that defy the usual expectations. Because they
seem unusual, the theorists have to posit extraordinary explanations to make
sense of them. However more often than not, these occurrences can be
explained in a simpler way—showing that perhaps they are not as
extraordinary as the critics seem to think.
Consider, for example, the fact that pre-September 11th warnings of
terrorist attacks were neglected or sometimes even stonewalled. There are at
least two fairly simple explanations for these facts, explanations which we
would not hesitate to offer for other
government failures: many
government workers could be too
busy or too incompetent to handle
every piece of intelligence that
reaches their desk. Government
bureaucracies are notoriously
inefficient. This could explain the
negligence, but what about active
stonewalling? What reason could
government officials have to resist
the investigation of an Islamic
terrorist plot, apart from wanting it
Picture credit 128:
actually to occur? This is harder to
http://www.flickr.com/photos/kongharald/3821492016/
speculate about, but there is at least
one reason that comes to mind. When allegations of terrorism are registered
against foreign nationals or members of an ethnic minority, complaints of
racism or xenophobia are likely to be registered in turn against those
performing the investigation. This occurred both before 9/11 and has
happened since. It is not unreasonable to expect that government officials,
203
leery of being accused of racism or other forms of political incorrectness,
could have resisted the investigation in order to preserve their reputation
without “rocking the boat.” This is a simpler and much less devious motive
that would explain how early warnings could have failed to be heeded. We
all know that government officials have these motives, and we can easily see
how they could have played out in this circumstance.
What about allegations of mysterious occurrences on September 11th
itself? Here, we move from alternative explanations that are “simple” to the
layman, to explanations that are at the very least fairly simple to experts on
the subject. First, the mysterious seismic “spike.” Researchers at Columbia’s
Lamont-Doherty observatory, who
recorded seismic activity that day,
say that conspiracy theorists who
claim that this is evidence of an
explosion triggering the collapse of
the buildings do not know what they
are talking about. First, they mention
that the graphs only appear as spikes
when looked at in the context of
larger amounts of time. Since the
building collapses only occurred over
Picture credit 129:
http://www.ldeo.columbia.edu/LCSN/Eq/20010911_wtc.html
a period of 10 to 12 seconds, they
would look like spikes in the context of a half-hour to an hour. Second, they
mention that explosives needed to bring down buildings would not register
as much on the Richter scale to begin with. Explosives used to attack the
World Trade Center in 1993, and the Oklahoma City Federal Building in
1995 barely registered.43
What of the comparison drawn to the crash of a bomber into the
Empire State Building? Here again, the conspiracy theorists ignore relevant
evidence from experts and only engage in armchair mechanical engineering
themselves. The people who designed the Trade Center towers contend that
they only designed them to withstand the impact of a Boeing 707, an
appreciably smaller plane than the Boeing 767s that actually struck, and that
in their design, they also neglected to plan for a full load of burning jet fuel.
The construction of the Trade Center was also different from the Empire
State Building, relying on an external frame to bear most of the load of the
building, rather than internal steel beams. When the planes punctured this
external frame, much of load-bearing structure was endangered. There were
43
See Dunbar and Reagan, Debunking 9/11 Myths: Why Conspiracy Theories Can’t Stand up to the Facts.
(New York: Hearst Books, 1996), pp. 50-2.
204
other important differences between the Boeing 767s which struck the Trade
Center towers, and the B-25 which struck the Empire State Building: they
were much larger, flying at much faster speeds, and carried much more jet
fuel (the primary agent in the collapse of the Trade Center towers).44 What
of the contention that jet fuel does not burn hot enough to melt steel? This is
true, but not relevant. One does not need to melt the steel frame of a building
to cause it to collapse: one only needs to weaken it, and the crash along with
the subsequent fire did this. (The fire was intensified because sprayed-on
internal insulation had been knocked free by the crash.)
What about the mysterious collapse of World Trade Center #7.
Admittedly, engineers still do not understand this completely. (Note that
what we have here is a lack of understanding: we’ll come back to this later.)
What they do know is that this third building was dramatically damaged by
the collapse of the main towers of the Trade Center. Some pictures reveal at
least 25% of the front of the building was missing before its collapse. It also
had an unusual design to accommodate other structures it was built on top
of. And it contained large fuel tanks designed to help the building maintain
power in the event of an electrical outage, tanks which would have burned
for a long time in the event of a cataclysm, and which would have then
caused even further structural damage.45
What of the more moderate claim, that the government conspired not
to plant a bomb underneath the World Trade Center, but simply to permit the
planes to crash into it. It is true that after
the first plane hit the tower, fighter jets
did not appear in New York until well
after the second plane had already hit.
Critics will say that simple math shows
that fighter jets flying at maximum
speed from the nearest air based could
have reached New York in time to
intercept the second plane, but the math
is not the whole story. First, how would
the military know where to send these
planes? Until the second plane hit, no
Picture credit 130:
one realized that the country was
http://commons.wikimedia.org/wiki/File:060306-F-4109Kactually under attack or that other planes 076.jpg
might be coming. The FAA did know which planes in the sky to suspect,
and it would have taken time for them to realize that another had left its
44
45
Dunbar and Reagan, Ibid., pp. 30-32.
Dunbar and Reagan, Ibid., pp. 53-56.
205
scheduled route. Even if the FAA had contacted the military in time to warn
them of the second plane, they would not have known automatically that it
was headed to New York. And since all of the hijacked planes had turned off
their transponders, they would have been difficult to locate even if we knew
their destination. Even if fighter jets knew where to fly, they still would have
had trouble shooting them down, since they were not authorized to shoot
down civilian planes until later in the day, and did not regularly carry the
munitions to do so, anyway. 46
Last of all, to the Pentagon and Pennsylvania. Unlike the attacks at the
World Trade Center, we have no definite footage of a plane striking the
building. We do have a video showing something striking it, but it moves
too fast for the low resolution, elapsed-time camera to capture its shape. One
eyewitness to the crash did say something about a cruise missile, but here
the critics who make reference to this are clearly guilty of quoting out of
context, for this is the full context of the quotation:
I looked out my window and saw this plane, this jet, an
American Airlines jet, coming. And I thought, “This doesn’t
add up. It’s really low.” And I saw it. I mean, it was like a
cruise missile with wings. IT went right there and slammed
right into the Pentagon.47
It is true that there was little debris on
the lawn in front of the Pentagon, but
some was photographed, and since the
plane crashed into the building, that is
where we would expect to find most of
it. It is also true that the external hole
punched by the plane was small, but
this can be explained by the fact that a
commercial airliner’s wings are
Picture credit 131:
relatively weak compared to its
http://commons.wikimedia.org/wiki/File:Flight_77_wrecka
fuselage, and would simply fold
ge_at_Pentagon.jpg
towards the fuselage when collapsing
into a strong enough structure (and the Pentagon had just been reinforced),
leaving only a hole where the fuselage would have been.48 As for the scene
in Pennsylvania, there was relatively little debris because during a crash at
46
Dunbar and Reagan, Ibid., pp. 22-25.
Mike Walter, to CNN, as reported by Dunbar and Reagan, Ibid., pg. 62.
48
Dunbar and Reagan, Ibid., pp. 62-70.
47
206
such a speed from such a height, most of the plane does typically
disintegrate, leaving only engines and larger parts of the plane. There was a
white plane observed near the crash sight, but it had been en route in the
neighborhood and asked by tower controllers to observe the scene.
For a theory based so heavily on evidence concerning anomalous
(unexpected, difficult to explain) occurrences on the day of the attack, it
turns out to be easier to explain the alleged anomalies than advocates of this
second conspiracy theory admit. This shows that the evidence they cite fails
to be relevant. Apart from the ease of proving these alternate explanations,
there are several broader problems with the second theory related to
violations of other basic requirements of good reasoning. Those who say that
the U.S. could have planned the attacks, planted bombs, or ordered planes
not to intercept the terrorist jets also have the burden of proving their claims,
a burden they have not often attempted to shoulder.
If a massive amount of explosives brought down the World Trade
Center Towers (and it would have required even more explosive power than
the bombs that sought to do the same in 1993), surely someone might have
noticed large quantities of explosives being trucked in or otherwise installed
in the building. But there is no evidence provided for this. If the government
had paid off terrorists to engage in these attacks, perhaps there would be a
money trail to follow, as there was during
the Watergate cover-up. Again, there is no
evidence provided of such a money trail.
If American planes had shot down Flight
93, tower radar may have registered it.
Again, no evidence for this is provided.
An arbitrary explanation for the lack of
evidence in each of these cases would be
that the conspiracy has succeeded in
covering it up. Where is the evidence of
the cover up? (The completely arbitrary
response is: “It’s been covered up, too!”)
credit 132:
Further, suppose we accept that there has Picture
http://commons.wikimedia.org/wiki/File:Secret_Servic
e_agents_stand_guard.jpg
been a massive cover up. Would we not
then expect that the size and scope of the conspiracy has grown to an
unimaginable size? Wouldn’t we expect to see evidence of an effort so large
and organized (just as we would expect to see an elephant in the room)?
Whatever the means of the attack, it would have involved many people—
officials at the FAA, at NORAD, in the Air Force—and such massive
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conspiracies are rarely ever able to contain evidence of themselves. Why is
there no evidence of such large scale devious collusion?
Apart from failing to provide well-established, relevant evidence,
advocates of the second conspiracy theory also fail to consider all of the
relevant evidence. We have already seen this to an extent, when they failed
to consider all of the relevant science needed to understand the seismic
activity resulting from the collapse of the buildings, and the science needed
to understand why the World Trade Center buildings collapsed, when the
Empire State Building did not. But there is even further evidence they
neglect. What about all of the many other eyewitnesses at the Pentagon who
insist they saw a plane (not a cruise missile)? Are they to be discounted just
because one spoke of a cruise missile (when even he only said that the plane
was “like a cruise missile”)? What of the passengers on that plane who
called their loved ones before the crash? Were their phone calls also faked?
Are these people not really dead? Were they perhaps not even alive in the
first place? This would be hard to square with the fact that one of them who
made a phone call was Barbara Olson, a famous conservative political
commentator, whose husband was a prominent government bureaucrat. And
what of all of the evidence presented in the earlier section pointing the finger
of blame at Al Qaeda?
One last category of relevant evidence the second conspiracy theory
ignores is that concerning the motives of the alleged conspirators. We expect
people to undertake extraordinary measures only in to accomplish
extraordinary goals. What were the
goals of the alleged American
conspirators? To secure some money
through military contracts or oil
contracts. It is noteworthy that oil
companies have not much profited in
either country yet, and military
contractors like Halliburton have only
more closely scrutinized since 2001.
But leaving this aside, would the
Picture credit 133:
terrorist attacks as enacted that day
http://commons.wikimedia.org/wiki/File:Professor_Lucifer_Butt
have been the most effective means to
s.gif
accomplishing this goal? If you want to justify a war in Iraq and
Afghanistan, why plan an attack involving mostly terrorists from a country
that is our putative ally (and a target usually singled out as involved in the
conspiracies), Saudi Arabia? Why bother having these terrorists smash a
plane into the World Trade Center towers, if you are really going to cause
208
them to collapse using a bomb? Why not just use a bomb, especially since
that was how the terrorists attempted to destroy the same target in 1993?
Why bother using a missile rather than a plane to attack the Pentagon, if
you’ve already used a plane at the World Trade Center? Surely it could not
be because you did not want to spare the lives of the passengers—you’ve
already just killed many such passengers in New York. And, last but not
least, why cover up the fact that you’ve shot down a civilian airliner in
Pennsylvania when the critics are otherwise complaining that you did not
intercept and shoot down the planes that attacked New York and
Washington? Why bother covering it up when it would make you look more
conscientiously responsible, having prevented yet another attack? In general,
why bother going through all of these complicated steps that resemble the
workings of a Rube Goldberg machine when simpler, more efficient means
to the same ends are available.
Here, then is a summary of the two conspiracy theories before us:
 Al Qaeda theory:
 Based on overwhelming, uncontested evidence
 Simple explanations available for evidential anomalies
 No contradictions between actions/motives of AQ
 U.S. theory:
 Motivated mainly by irrelevant anomalies of the AQ theory,
 Key provisions of theory not based on any independent,
relevant evidence.
 Neglects relevant evidence, especially concerning the
relationship between the means and motive.
Based on this survey of the evidence, it is the conclusion of this author, at
least, that the theory that Al Qaeda (or some foreign terrorist force) almost
certainly plotted and enacted the September 11th terrorist attacks, and the
U.S. government almost certainly did not. The only doubts that remain
concern the exact identity of the plotters. It is at least possible that some
terrorist plotters other than bin Laden were responsible. Bin Laden initially
denied any involvement in the plot, and only later confessed. It is at least
plausible that he took responsibility in order to gain the prominence and
respect this would have afforded him among other supporters of the terrorist
attacks. But even if he himself did not plot the attack, we know that he
plotted others, and continues to plot new attacks.
209
Lessons from the consideration of “crackpot” conspiracy theories
For all of the reasons presented above, we think it is safe to say that the
second (U.S.) conspiracy theory about 9/11 counts is a “crackpot”
conspiracy theory. As such, it exhibits a number of general problems shared
by other theories of the same worth.
Generally speaking, the bigger the conspiracy, the more intricate of a
plot it must involve, and the more difficult it becomes to enact. But the scale
of the difficulty here has to be gauged to the alleged goals the conspirators
are seeking to achieve. If all that the conspirators sought to achieve by
killing so many people was to make some money from military or oil
contracts, one would think they could have found easier ways to make
money, say, in the stock market or the housing bubble (at the time). It is
especially difficult to believe that anyone could be motivated to kill so many
innocent countrymen for the sake of a relatively small amount of money.
Generally, the bigger the conspiracy, the
greater the number of people involved, and the
greater the number involved, the harder the
conspiracy is to keep under wraps. People who sit on
big secrets have an incentive to tell about them,
especially after time passes. Yet we have not yet
heard any leaks about a conspiracy by the U.S.
government to attack America and justify foreign
wars. Many smaller conspiracies have been
discovered by leaks in this way, when the stakes
Picture credit 135:
were much smaller. Nixon
http://commons.wikimedia.org/wiki/Fi
could not keep the Watergate le:Bill_Clinton.jpg
scandal under wraps. Bill Clinton, the most powerful
man in the world at the time, could not stop one
woman from letting the public know about one
soiled dress—and as a result his entire presidency
almost collapsed. If Clinton couldn’t deal with
Monica Lewinsky, why have the Bush (and Obama!)
administrations been able to successfully silence
Picture credit 134:
http://commons.wikimedia.org/wiki/F every single leak from the allegedly much larger
ile:Monica_lewinsky.jpg
9/11 conspiracy?!?
Last of all, in the second 9/11 conspiracy theory, we also see many of
the traits of poor reasoning characteristic of other such crackpot theories. We
see shifting the burden of proof in the form of the appeal to ignorance. We
can’t understand some anomalous fact (about how the World Trade Center
collapsed, about why the planes weren’t intercepted earlier, etc.), the critics
210
will say. Therefore it must have been the U.S. government that did it! But
nothing follows merely from a lack of knowledge. We also see shifting the
burden of proof in the form of arbitrary explanations. Whenever we point to
a lack of evidence for a crucial claim of the second theory, its supporters will
say, “This evidence has simply been covered up by the conspiracy.” But
where is the evidence of this cover-up?
A final methodological note is that even when “crackpot’ conspiracy
theorists seek to provide evidence for their theory, it is obvious that they
look for it only in places that favor their pre-determined views. Many or
most “truthers” about 9/11 were also critics of the Bush administration. They
would have loved it if they could tar Bush or his cronies with a crime of this
scale. As a result, they ignored simpler explanations of the same evidence
that did not point in the direction of Bush, and ignored other evidence that
completely contradicted their theory. This selective “cherry-picking” of the
evidence indicates a drive to confirm what they want to confirm, which is,
from the broadest perspective, an obvious form of “wishful thinking”
subjectivism.
Incidentally, crackpot conspiracy theories are not the province of one
side of the political spectrum or another. Many of the marks of crackpot
theories that we see on the political left among “truthers” we now see today
on the political right among “birthers”—those who contend that Barack
Obama was not born in the United States, or that he is secretly a Muslim.
Examining their claims would be material for an entirely separate chapter,
however, which we do not intend to write.
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§4: THE ROLE OF MEANING IN LOGIC
Chapter 11:
The role of meaning, and fallacies of interpretation
Ben Bayer
Drafted March 9, 2010
Revised August 17, 2010
The importance of good interpretation
In the last two major subsections of this book, we have examined the
principles of good reasoning and of proof. These principles are tools for
determining whether or not conclusions reached through inference are true
or false, since the function of an inference is to give us knowledge about
what we cannot observe directly. We know that an inference has failed in
fulfilling its function if it does not follow one of the key principles we’ve
outlined.
But before we can evaluate an argument, we need to be clear about
what argument we are evaluating. This is
not an obscure point known only to
logicians. If we are traveling in a foreign
country, and we want evaluate the
directions we get from the locals, first we
need to be sure what directions they are
giving us. We need to be sure that we
understand the local dialect. The same
issue arises even for speakers of the same
language. We can speak clearly or
Picture credit 136:
unclearly to others who share a mother
http://www.flickr.com/photos/dmaudsley/159644052/
tongue. We can even think clearly or
unclearly to ourselves, and logic plays a role in separating the clear from the
unclear.
This is not the first time we’ve spoken about the role of meaning in
logic. At one point in chapter 2 we mentioned the possibility that logic was
not concerned only with evaluating inferences or arguments. In one
example, we talked about how making an effective inference also involves
the formation of the correct concepts, and that these too are subject to
evaluation. You may recall the example of the formation of the concept of
“eclipse.” Early astronomers needed to distinguish lunar eclipses from the
ordinary phases of the moon and identify what they had in common with
solar eclipses. They needed to do this before they could understand that the
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shadow cast by the Earth on the moon during its eclipse was circular, part of
the evidence for the claim that the Earth is spherical.
Logic, then, evaluates and hopes to guide the entire rational process,
from concept-formation on up. It is, therefore, not only concerned with
whether or not premises are known and relevant, but whether they are
cognitively meaningful. In the present chapter, we will introduce the issue of
identifying the meaning of the premises or conclusions in our arguments,
and evaluating the role this meaning plays in the overall logic of an
argument. For the time being, our focus is on showing that meaning matters.
Ultimately, we will be concerned with understanding the meaning of
individual concepts by analyzing and even evaluating their definitions. But
we will work our way into this issue by first dealing with questions about the
meaning of concepts (and occasionally, of whole propositions) that don’t yet
presuppose the precise analysis of their definitions. As we shall see, there
are a number of confusions and even fallacies possible to reasoners who do
not pay careful enough attention to the role of meaning in argument.
Here is a simple example. Suppose your friend calls you a troglodyte.
If you have never heard the word before and never learned its meaning, you
simply don’t know what their overall claim means, and therefore you can’t
assess if the claim is justified or unjustified, true or false. Suppose instead
that you have a rough idea of what the word means, but you’re not sure of its
precise meaning. Is the person saying that you are rude and crude? Are they
making an even more startling claim about your level of mental
development? You won’t know unless you know the meaning of the word.
How do you learn the meaning of the word? One obvious way is
simply to look it up in a dictionary. Here’s what you find if you go to
Merwin-Webster.com:
1 : a member of any of various peoples (as in
antiquity) who lived or were reputed to live
chiefly in caves
2 : a person characterized by reclusive habits or
outmoded or reactionary attitudes
Picture credit 137:
http://commons.wikimedia.org/wiki/File:
Caveman_8.jpg
From the looks of it, the term can mean one of
two things, depending on the context. Your friend
might be calling you a literal caveman, or she
might be using the word more metaphorically, to
suggest that in some ways you behave like a
caveman would. So what is the context? Perhaps
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your friend’s larger statement was as follows:
You are such a troglodyte! Can’t you eat
anything but fast food, or watch anything on
TV but Jerry Springer?
So it should be clear that your friend was using the term in more of a
metaphorical sense. Presumably cavemen didn’t have fast food or Jerry
Springer, but perhaps if they were around today, this is what they would
prefer to Whole Foods and PBS.
Notice that pinning down the meaning of the word being used here is
important for evaluating inferences involving the word. Consider:
You are a troglodyte.
Therefore, you live in a cave.
If we know that the term is being used in a metaphorical sense, we would
have to classify this as an invalid inference: the premise is not relevant to the
conclusion, because the metaphorical use of the term does not imply literal
cave-dwelling. The act of determining the meaning of a word or phrase is
interpretation. Sometimes arguers can fail to interpret words and phrases in
the correct way, and commit erroneous inferences.
The questions about meaning we’ll deal with are sometimes broader
than language or confusions that arise when dealing with other people. Some
philosophers dispute the idea that there can be meaning or cognition
independent of language, but we may also be able to make many first-person
assessments of meaning apart from its expression by others linguistically. In
particular, we will spend a great deal of time talking about the personal,
cognitive importance of definitions.
Interpreting terms
We will first discuss errors in the interpretation of terms, so we need to say
what we mean by a term. A term is a special part of linguistic expression,
but not just any part. For example the “e” in the following is not a term:
Fred is a troglodyte.
Of course each of the letters in a sentence is needed to spell out the whole
sentence. But the letter “e” is not a term because it contributes no meaning
214
of its own to the meaning of the sentence. The same is true even of most
syllables, e.g.:
Fred is a troglodyte. (
“Dyte” is not a meaningful expression, even though etymologically,
“troglodyte” comes from the Greek for hole-creeper. A “dyte’ is someone
who creeps into something. This meaning is now lost to us, and when we
hear the word, we don’t think of its etymology. If we know the word, the
meaningful portion is the whole word:
Fred is a troglodyte. (a term!)
But don’t think that every separate word is a term, and every term, a
word. Consider the following pair of sentences:
I earned my bachelor of arts.
I earned my bachelor of arts.
Normally when someone says he has earned a
bachelor of arts, he does not mean that he has
purchased for himself an unmarried male with
aesthetic talents. He means that he has been awarded a
college diploma. “Bachelor of
arts” functions as an entire
Picture credit 138:
http://commons.wikimedia.org/wi
term, even though it involves
ki/File:1846-single-bachelorsolitude.jpg
three words separated by
spaces. Some terms can be composed of more than a
few words. Note that in the following case, however,
we really are dealing with separate terms:
I am a bachelor with a degree in the arts.
We simply have to go by our knowledge of English
idiom, and of the context of usage to determine what is a term and when.
The fallacy of equivocation
In the previous section, we saw that the term “troglodyte” could be
used somewhat ambiguously. The difference between literal and
metaphorical uses of terms is a potential source of ambiguity, though not one
215
that usually leads to confusion. There are other sources of ambiguity that are
not as easily identified in advance. Consider this pair of sentences:
Bob is responsible for this mess.
Bob is a responsible fellow who would never make this mess.
What’s curious is that each uses the same word to say something very
different about Bob: the first says something bad about him, the second,
something good. This happens because the word “responsible” has multiple
senses or meanings. In the first case, to say that Bob is responsible for
something is just to say that he was the cause of something. But when we
say that he is a responsible fellow who would never make a mess, we mean
that he is someone who acts with attention and care for the consequences of
his actions. There is a loose connection via analogy between these two
senses. Someone who is said to be responsible in a virtuous way is one who
is willing to acknowledge responsibility in the generic sense for his
mistakes, and thus takes care to avoid them in the first place. But this
connection in meaning is a loose one, and some words in the language with
distinct senses have not even an analogous relationship to each other
(compare “bat” the animal with “bat” the sports implement).
Many words in English are ambiguous, but few are ambiguous in the
previous sense of having nearly the opposite sense. But, just for the fun of it,
here is a second example of the same phenomenon, taken from two recent
newspaper headlines:
HEADLINE: Report on MD police tuition aid cites poor oversight,
abuse.49
HEADLINE: Academy: Farrah Fawcett omission was ‘not an
oversight’.50
In the first sense, to exercise oversight means to oversee something, to
supervise it and make sure all goes as planned. In the second sense, to
commit an oversight or be guilty of an oversight is to pass over or overlook
49
Washington Post, March 8th, 2010. < http://www.washingtonpost.com/wpdyn/content/article/2010/03/08/AR2010030804986.html>.
50
USA Today, March 8th, 2010.
<http://content.usatoday.com/communities/entertainment/post/2010/03/academyfarrah-fawcett-omissionwas-not-an-oversight/1>
216
a problem that one should not have overlooked, i.e., to fail at one’s duty to
exercise oversight in the first sense.51
Normally ambiguity does not pose any special logical problem
provided that different senses of the same term are confined to recognizably
different contexts. But sometimes two different uses of the same term can be
mashed together, and cause logical confusion. This example is somewhat
artificial (no one would ever fall for it), but it illustrates in the starkest of
terms the type of confusion we are about to examine:
I keep my money in a bank.
Banks are beside rivers.
Therefore, I keep my money beside a river.
What is the ambiguity here? It results from two different senses of the word
“bank.” The premise here is surely known to be true, so the question is
whether or not it is relevant to the conclusion. The conclusion doesn’t seem
to follow from the premise. Maybe some people do keep their money by the
river, but it doesn’t follow from the fact that banks are besides rivers. Why
does this person think it follows? Because in the first premise, “bank” means
“a repository for money,” while in the second, it means “a sloping surface of
earth” (something often found besides rivers). Obviously, the fact that
something is a bank in one sense doesn’t mean it is a bank in the other. This
means that the conclusion doesn’t follow, though it looks like it does to
someone who doesn’t realize that the word
“bank” has these two sentences.
The argument about banks above is an
example of the fallacy of equivocation, the
fallacy of relevance resulting from using different
senses of an ambiguous term interchangeably. It
is called “equivocation” because the arguer uses
two senses of a word with “equal voice,” as if
each meant the same. But they do not, and so the
fact that one sense of a word applies correctly to
some object in some situation does not mean that
every sense of the same word does; nor does it
mean that the implications of the second sense
Picture credit 139:
hold of the same object in the same situation. We http://commons.wikimedia.org/wiki/File:My_
Wife_and_My_Mother-InLaw_%28Hill%29.png
51
Please don’t think that all cases of ambiguous language concern exercising one’s duties carefully, or not.
It’s just a surprising accident that these both “responsibility” and “oversight” happen to both involve this
topic.
217
can have our money in a financial-institution kind of bank, without having it
in a by-the-river kind of bank. Equivocation exploits the ambiguity of
language in the same way that optical illusions exploit the ambiguity of
visual scenes: we know that something cannot be an old woman and a young
woman at the same time, even though the famous optical illusion makes it
look like it.
Consider some trickier examples of equivocation:
Alligators are not found in Illinois.
Therefore, you won’t find your pet alligator in Illinois if you lose it.
The premise is true, but the conclusion is quite false—and people have
found lost alligators in Illinois.52 The equivocation here is over two different
senses of “to find,” though it is subtle. In the first premise, to say that
alligators are not found somewhere is just to say that they are not naturally
occurring. But when we speak of finding something that is lost, we mean
that it can be located, or at least that it can be collected by someone who
wasn’t trying to locate it. (There is really a second, implicit premise
involved in this argument, that “things that are lost are not found.” Including
this doesn’t let the argument sound so funny, though.) Clearly, species that
are not naturally occurring in some region can still be lost and then located
in that region.
Here’s a similar example:
This is a large mouse.
Mice are animals.
Therefore this is a large animal.
Suppose it’s true that we really do have a large mouse in front of us. Some
mice are larger than others, so suppose we’ve got one of those. Then the
premise is surely true. Mice are also, surely, animals. But the conclusion
here is clearly false. A mouse is not a large animal. A false premise can’t
follow logically from two true premises, so something must have gone
wrong here.? “Large” is a fairly straightforward quantitative term, but
quantitative terms come with qualifiers. “Large” and “small” are relative
terms. Something is large or small compared to some relevant standard. So it
may be true that a given mouse is a big mouse, i.e., big for its species. But
52
Troy Taylor, “Mysterious Creatures of Illinois, < http://www.prairieghosts.com/gators.html>. See also
Sufjan Stevens, “Decatur, or Round of Applause for Your Step Mother!,”
<http://www.songmeanings.net/songs/view/3530822107858542812/>
218
that does not mean it is big for a mammal or for an animal. When we call the
mouse large in premise 1, we mean it is large-for-a-mouse large, but this is
consistent with it being quite small-for-a-mammal small or small-for-an
animal small. It is surely quite small compared to the biggest animal, the
blue whale. Hence the conclusion does not follow.
Here is one more example of an equivocation, this time one that has,
from time to time, actually been accepted in different forms by real people:
Everyone should be equal.
People are of unequal heights.
Therefore, differences in height are unfair!
The term that plays the crucial role
here is “equal.” To the extent that we
accept the Declaration of
Independence (“all men are created
equal”) and the 14th Amendment to
the Constitution (“nor deny to any
person within its jurisdiction the
equal protection of the laws”), we
think people should be afforded
Picture credit 140:
equal rights. But this is not what we
http://commons.wikimedia.org/wiki/File:CCRugby1940.jpg
http://commons.wikimedia.org/wiki/File:All_men_are_created_equ are talking about in the second
al.JPG
premise: rights are not the same as
heights! In case you think it is implausible that people actually accept an
argument like this, consider the views held by some about inequality in
income or intelligence.
Here is another potential example of equivocation, one that is even
more widely accepted than the previous example—and one with very
significant philosophical implications:
There are laws of nature.
Every law is made by a lawmaker.
Therefore, someone must have written the laws of nature
What are the terms that are crucial for making it seem like the premises are
relevant to the conclusion? Why are these terms ambiguous? If they are
ambiguous, are different senses of the terms being appealed to in different
parts of this argument? Is this, therefore, an example of the fallacy of
equivocation?
219
Here’s one last example of potential equivocation to think about, one
that many people, including many philosophers, take very seriously.
Depending upon the political theory you adopt, you’ll either think it’s
perfectly logical, or that it involves an equivocation. What terms in the
following argument might be ambiguous and used equivocally?:
Anyone who forces you to labor makes you a slave.
Industrial workers are forced to choose between work and starvation.
Therefore industrial workers are slaves to their employers?
One last observation about equivocation: it can be funny! This is not
uncharacteristic of logical fallacies. We are rational animals, but we are also
animals with a sense of humor because our rationality allows us to get the
point of a joke. We are able to get the point of a joke because we can
perceive various inconsistencies and incongruities in the words or actions of
others. We laugh when someone slips on a banana peel because there is an
inconsistency between his self-assured attitude and what actually happens to
him in practice. What’s more, the reason that plays on words or puns can be
funny is because they purposefully exploit ambiguities in language to evoke
the ridiculous. Consider the following equivocal statements. Each has an
implicit argumentative structure that makes us laugh.
Questioner: What do you think
of Western Civilization?
Gandhi: I think it would be a
great idea.
I’m not the member of any
organized political party. I’m a
Democrat.
--Will Rogers.
(Beavis, watching a music
video, is dancing on the sofa.)
Butthead: Get down, Beavis!
Beavis: I am getting down!
Picture credit 141:
http://commons.wikimedia.org/wiki/File:1885_Punch_threevolume-novel-parody_Priestman-Atkinson.png
220
Merely verbal vs. real disputes
When two people engage in argument with each other, and find that
they are in disagreement, it is possible that a version of equivocation
explains the nature of their disagreement. There is, for instance, an important
difference between the following two kinds of disagreement:
Dispute #1.
A: Not everyone is equal.
B: Sure we are! It’s guaranteed by the constitution.
A: No we’re not! Look how we all have different heights, strengths,
and levels of intelligence.
Dispute #2.
A: Not everyone is equal.
B: Sure we are! It’s guaranteed by the constitution.
A: No we’re not! The constitution is supposed to protect everyone
equally, but some people get to exercise freedom of speech, while
others do not.
In dispute #1, the term in play is “equal,” just like in one of the
previous examples of equivocation we considered. Notice that person A
could be taken as committing that fallacy by urging that not everyone is
equal in height. But then again, perhaps he only means to be speaking of the
inequality of such characteristics in the first place. Perhaps person B is the
one who changes the subject to politics. Whoever is at blame here, it is clear
that the two parties are talking past each other. (Or: they are like two ships
passing in the night.) One is talking about equality of one type, the other of
another. The result is that the dispute is merely verbal, not real. They seem
to disagree only because they are talking about different kinds of equality.
But because they are different kinds, they may both be right: one kind of
inequality and another kind of equality might exist at the same time.
But compare this to dispute #2: here the dispute is not verbal, but real.
There is not simply a disagreement about which sense of the word “equal” to
use, but whether or not people are really equal in one specific respect—in
this case, the political respect. Person A charges that not everyone is
afforded equal protection of the laws, whereas person B thinks they are.
Sometimes when two rival parties assume different definitions of a
concept, people are quick to remark that it is a “mere semantic dispute,” and
that parties to the dispute are “playing semantic games.” Sometimes that is
true, as is the case in dispute #1 above. Sometimes, however, there can still
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Picture credit 142:
http://commons.wikimedia.org/wiki/File:1846single-bachelor-solitude.jpg
be a real dispute even in the presence of a
disagreement about definitions. It’s possible
to have the same general subject matter in
mind while disagreeing about how to define
it. This is often the case in philosophic
disputes, when philosophers debate about
how to define important philosophical
concepts like “knowledge” and “the good.”
We will have more to say about these
definitional disputes, and their philosophical
significance as we proceed through to
chapter 13.
Interpreting sentences
There is not as much to say about errors in interpretation of whole sentences
here, but it is worth noting the possibility for the sake of completeness.
We have already encountered the prominent example of
misinterpreting the views of others’ by quoting them out of context:
Coming at the end of a dismal and frigid January, 'The Big
Bounce,'…is like a paid Hawaiian vacation—somebody else's.
Everyone involved with this picture…seems to have had a good time
making it, which was nice for them, but it may not do you much
good.”
I looked out my window and saw this plane, this jet, an American
Airlines jet, coming. And I thought, “This doesn’t add up. It’s really
low.” And I saw it. I mean, it was like a cruise missile with wings. IT
went right there and slammed right into the Pentagon
Were you to focus on just the highlighted portions of the passages rather
than the whole, you might come to a very different conclusion about the
author’s meaning.
Another way that sentences can be misinterpreted stems from a kind
of grammatical ambiguity. In just the same way that individual terms can be
ambiguous by possessing multiple meanings, so whole sentences can be
ambiguous because of different ways of understanding their grammar.
222
Sentences which exhibit this ambiguity are called amphibolies, or are said to
exhibit the trait of being amphibolous. Here is a famous example:
Woman without her man is lost.
This sentence illustrates the importance of good punctuation for avoiding
grammatical ambiguity. One meaning can be clearly discerned by adding a
few punctuation marks in strategic locations:
Woman: without her, man is lost.
The other can likewise be seen through a different punctuation:
Woman, without her man, is lost.
Notice that the meaning of each is very different! One puts woman quite
literally “on top”—the other does not.
A famous story is told of an author who wrote a book with the
following dedication inscribed at the beginning:
To my parents, Ayn Rand and God.
Presumably the author intended to thank three separate parties, but by
neglecting the serial comma (after the name of the atheistic philosopher,
Ayn Rand), she implied that she had a most unlikely pair of parents.
Other humorous examples of amphiboly can be found in newspaper
headlines, which because of their space limits, can often be forced to
economize on grammar as well:
Headline: Lawyers Give Poor Free Legal Advice
Headline: Collegians are Turning to Vegetables
Last but not least, let’s turn to a professional humorist who knows
how to twist logic for the explicit purpose of getting a good laugh:
Last night I shot an elephant in my pajamas.
What he was doing in my pajamas, I’ll never know.
--Groucho Marx
223
Interpreting arguments
Never mind mere terms and sentences: whole argument are open to
misinterpretation as well.
Unjust or “uncharitable” interpretation
In chapter 3, we considered the role of implicit or suppressed premises
in argument, in particular in connection with a form of the question-begging
fallacy that involved failing to state the very premises most in need of proof.
You may recall how the following argument relied on a suppressed premise:
Most people are offended by flag burning.
Therefore, flag burning should be outlawed.
We suggested that the suppressed premise was “Anything people are
offended by should be outlawed.” On that basis, we criticized this argument
as begging the question, because this suppressed premise would be far more
controversial than the conclusion.
But what if we are wrong that this is the premise being relied upon?
Sometimes people do subconsciously assume premises like this
controversial in the course of arguments like this. But what if we knew more
about the author of this argument in particular? What if we knew that he was
also a defender of the free speech rights of political minorities, but a
proponent of laws censoring obscenity in public? In that case, it would be
unfair to attribute to him the general premise “Anything people are offended
by should be outlawed.” A more likely premise would be “Any profane
sights forced on bystanders in public should be outlawed.” We might still
find this premise controversial and worthy of criticism (how do we draw the
line between the two forms of offensiveness?), but it is less controversial
than the earlier attributed premise. The author sees a difference between
expressing unpopular ideas in print for the consumption of willing readers
on one hand, and making public displays against the wishes of the viewers
on the other. He may see flag burning as more akin to the second than the
first.
So while it is a fallacy to suppress a controversial premise in the
manner described in chapter 3, it is also a fallacy to accuse someone of
begging the question by suppressing a controversial premise when there is
insufficient reason to attribute to him that particular controversial premise.
This is a mistake that philosophers sometimes call “uncharitable”
interpretation. On their view, we should attribute to arguers those views that
224
make their argument the most likely to turn out to be reasonable. Of course
there are many irrational people in the world, and so we should not always
assume the best of anyone. Sometimes people really do suppress incredibly
ridiculous premises, and in those cases, we should call them out for it.
Arguers do not deserve unearned “charity”: they deserve justice. If we have
special reason to believe that they hold the more reasonable premise (as with
the profanity premise above), then we should reassess our interpretation, but
not otherwise.
The straw man fallacy
Sometimes misinterpretation of another’s argument is less innocent
and more malicious than failing to see that a suppressed premise may be
more reasonable than the one we elected to criticize. Sometimes an
interpretation of an argument can be outright misleading and tar an arguer
with a view that there is little if any reason to believe they hold. Often the
purpose of such misrepresentation is to discredit the implausible version of
the argument, and by association, discredit its conclusion—even if a better
argument was actually offered. Compare these two examples:
Original argument:
We don’t need to believe in God to justify a moral code.
Believing in God doesn’t automatically make us happy.
There are no good philosophical arguments for God’s existence.
There are no good scientific arguments for God’s existence.
Therefore, there are no good reasons for believing in God.
Misrepresentation:
People who say we have no reason to believe in God think we don’t
need him to justify a moral code. They must think we don’t need a
moral code at all. But we do. Therefore ignore these people.
In this case, the misrepresentation occurs primarily through a
misrepresentation of the first premise. The original arguer probably doesn’t
mean that we don’t need morality, only that we don’t need knowledge of
God’s existence to justify our knowledge of morality. We might still need a
moral code, but be able to justify it on the basis of other (say, scientific)
facts. The point here is not that the original argument is necessarily a good
argument. People might take issue with any of its premises, or their
relevance to the conclusion. The point is that the response to the argument
considered above is not a logic response. It misconstrues the meaning of the
225
first premise when an obvious alternative explanation is available. It’s not
simply that this interpretation fails to discover special facts about the arguer
that suggest a more reasonable interpretation; it actively distorts the meaning
of the argument into something that few if any people believe—just to make
its conclusion look less defensible.
Misrepresenting an argument in this
way commits what philosophers call the
straw man fallacy, the fallacy of attributing a
controversial assumption or implication to
some view in order to make it easier to
refute. The reason it is called this is obvious
enough: it is much easier to knock down a
straw man than a real man. Likewise it is
easier to “knock down” (or refute) a “straw”
argument—one that is a misrepresentation of
the real argument—than it is to refute the real
argument.
Picture credit 143:
Sometimes it is not always easy to tell
http://commons.wikimedia.org/wiki/File:Scarecrow_%28
when a person is committing a straw man
PSF%29.png
fallacy, or making a legitimate critique of
another’s argument by drawing some absurd implication from it to show it is
false. (This is a technique called reductio ad absurdum, which we will
review later in chapter 19.) Here, just for the sake of full disclosure, is an
original argument, followed by two criticisms. One involves the straw man
fallacy, and the other does not obviously involve it:
Original argument
We must limit the role of government.
Government’s antitrust power gives it unlimited power
Therefore we should repeal antitrust laws.
Response A:
He thinks government power is unnecessary. Those who advocate the
repeal antitrust law must believe in anarchism. We me uphold
antitrust!
Response B:
If we permit businesses to form trusts and monopolies, they will have
too much power. Those who advocate the repeal of antitrust law
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would give private interests too much control over our lives. We must
uphold antitrust!
Response A involves a straw man fallacy. It is easily possible to
believe in the limitation of government power without believing that
government should be eliminated entirely. So the responder here is imputing
a premise to the original argument that he need not impute. Since it is much
easier to refute the idea of anarchism than it is to refute the idea of merely
limiting government power, this is clearly a straw man fallacy.
But what about Response B? Surely someone could disagree with
respondent B, and argue that there is nothing to worry about with respect to
corporations’ accumulation of more and more economic power. (They could
argue, for instance, that there is a real difference between economic and
political power.) Still, to disagree in this way would not be to register the
charge that respondent B is committing a straw man fallacy. B is not
claiming that the original argument argues something that it doesn’t; he is
simply urging that this argument has an unpleasant implication which the
original argument may not acknowledge.
Misc.: The ad hominem fallacy
One last fallacy to consider in this chapter is not really a fallacy of
interpretation. As such, many of the observations we have made about the
determination of meaning do not really apply here. We include this fallacy in
the present chapter only because it does not fit well in any of our other
chapters, and because it does have some not too superficial resemblance to
the straw man fallacy we’ve just examined, in that it is also a fallacy by
which some will unjustifiably dismiss the arguments of others. In this case,
however, the motivation for dismissing the argument has nothing to do with
a misrepresentation of its meaning.
Here are three examples of what is called the ad hominem fallacy:
A: I think all men have rights, so slavery is unjustified.
B: Don’t pay attention to Mr. A’s argument against slavery. He’s a
known philanderer!
Pro-war: We should go to war because it will protect us from
terrorism.
Anti-war: You’re a chickenhawk! I don’t see you going off to fight!
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Kerry: I have a plan. Here are reasons to adopt it.
Bush: Kerry is a flip-flopper. First he plans to do one thing, then
another.
The ad hominem fallacy is the fallacy of arguing against a conclusion
by attacking the character of the person making the argument, rather than
refuting the argument. The phrase “ad hominem” means literally “at the
man” in Latin. It is a fallacy because the shortcomings in a person’s
character do not imply that he is incapable of presenting a logical argument.
Even if, through some psychological corruption resulting from his poor
moral character, the arguer is not capable of appreciating the logic of a good
argument, we are still capable of appreciating it. So we cannot just dismiss
the argument by saying that the person making it is a bad person in one way
or another.
Notice that the same pattern is present in each of the arguments above.
It is quite clear in the first case, where the arguer’s straightforward (and
widely accepted) argument against the morality of slavery is dismissed
because of alleged sexual promiscuity on the arguer’s part. Maybe the arguer
is a philanderer. What of it? That might be reason not to vote for him as a
political leader (maybe), but it is not a reason to dismiss his argument. The
merits of an argument are its premises and method of inference, not the
moral merits of the man making it.
The second argument, otherwise known as the “chickenhawk”
argument, is a popular one made by anti-war protestors against those who
speak up in favor of wars. It is especially easy to use against pro-war
advocates who live at home where it is peaceful, and since most anyone with
time to make arguments in public is not in combat overseas, the argument is
guaranteed to find targets unless 100% of civilians are pacifists. The
allegation is that because the pro-war advocate is not fighting himself, there
is some hypocrisy involved in his speaking in favor of someone else going
off to fight.
Suppose that there is some hypocrisy involved. What of it? The
original arguer might still have presented good reasons to fight, for instance,
by giving a sober assessment of the threat faced by the country, and the need
to oppose the threat out of the right self-defense. So his moral shortcoming
is not logically relevant to the worth of his assessment of the threat and our
right to oppose it. (Of course, he may not even have the alleged moral
shortcoming: not everyone who believes in the justice of a war can be
expected to go and fight it, no more than everyone who believes in the
importance of police or fire protection should become a policeman or
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fireman. If everyone did this, the soldiers, police, and fire personnel would
not have anyone left to protect! And there is a division of labor in our
society, where some people are simply better at soldiering than others.)
The last example is a clear example of what is called “circumstantial
ad hominem,” so called because it highlights the character shortcoming of
the person’s logical circumstance: they now appear to disagree with
something they used to believe. They
“speak from both sides of their mouth” or
“flip flop.” Even here, even where it is
logically clear that the politician
contradicts his old belief, it doesn’t follow
that his present belief is false. It could be
that he has abandoned the old belief
because it was false. There is no telling
whether a new belief is false or true simply
by comparing it to an old belief. What we
need is to compare it to the evidence.
Sadly, many politicians and political
Picture credit 144: http://www.flickr.com/photos/commentators never get past the habit of
eugenia-/4715842330/
charging their opponents with hypocrisy in
this way. It detracts from much substance in our nation’s political debate.
One last qualification: it is not always logically irrelevant to attack a
person’s character. It is if one’s purpose is simply to create a smokescreen
that obscures the logic of another’s argument. But when we are simply
evaluating the testimony of another person—who is not giving us an
argument, but asking us to take his word that what he reports is the truth (see
chapter 5)—in this case his moral character is quite important, because it
tells us whether or not he has a track record of dishonesty. For this reason,
the following charge made against a testifier is not an example of the ad
hominem fallacy:
A: I saw my brother commit the murder.
B: Don’t believe Mr. A! He’s been telling lies about his brother for
years.
Can you distinguish between ad hominem and the valid dismissal of
unreliable testimony? Which of the following is which?:
Politician A: Here is evidence that my opponent takes bribes.
Politician B: Don’t listen to him. He takes bribes, too!
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Politician A: If elected, I promise to cut taxes.
Politician B: Don’t listen to him. He’s broken many campaign
promises before.
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§4: THE ROLE OF MEANING IN LOGIC
Chapter 12:
Rules of definition
Ben Bayer
Drafted March 14, 2010
Revised August 18, 2010
Definitions in argumentation
In the previous chapter, we examined at least one kind of fallacy that
resulted from inattention to the meaning of important concepts used in an
argument, the fallacy of equivocation:
Everyone should be equal.
People are of unequal heights.
Therefore, differences in height are unfair!
We realized that in this example, premise 1 uses the term “equal” with one
meaning in mind, premise 2 uses a distinct meaning. The problem is that
equality of political rights is simply not the same as equality in other
respects, such as physical characteristics.
(It would require a whole set of special
philosophical arguments to show that the
two were somehow related.)
The fallacy of equivocation is not
the only example we’ve seen in which
inattention to a definition results in a
fallacious argument. Consider, for
Picture credit 145:
instance, this (condensed version) of a
http://www.flickr.com/photos/hippie/3314189655/sizes/m
previously discussed example of the
/in/photostream/
fallacy of begging the question:
Capitalism is the superior social system. This follows from the fact
that it helps preserve the free market system.
Citing the fact that establishing capitalism helps maintain the free market
system as a reason for the superiority of capitalism counts as a form of
question-begging because “the free market system” and “capitalism” mean
the same thing. We know they mean the same thing by consulting the
definitions of each.
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Both of the previous arguments are examples of fallacious
argumentation resulting from inattention to definition. Sometimes, however,
attention to definitions is needed to make sure that a good argument can be
presented. Consider, for example, the following:
All human beings are mortal.
Socrates is a human being.
Therefore, Socrates is mortal.
This is a famous deductive syllogism:
if the premises are true, the conclusion
has to be true, as well. And we can tell
that the conclusion follows from the
premises simply as they are presented
here. However, to know that the
premises are true in any given case
sometimes requires work. We know
that all people are mortal—all people Picture credit 146:
will die some day—through a process http://commons.wikimedia.org/wiki/File:David__The_Death_of_Socrates.jpg
of inductive generalization from our
observations of particular people and facts about their biology. (We will
discuss the mechanics of inductive reasoning in more detail in chapter 14.)
But how do we know that the second premise is true?
From one perspective, we might simply look at Socrates and realize
that he has that “human” look to him: he has a body of a certain shape, and
speaks like human beings speak. As we’ll see later, though, just going on the
basis of the simple look of a thing can sometimes not be inadequate
(especially since not all human beings look exactly the same). Once we
become fully mature adults, we organize our understanding of concepts
using definitions. Inserting a premise containing the definition of “human
being” might help shore up our inference here about Socrates’ mortality:
All human beings are mortal. (Generalization)
A human being is a rational animal (Def.)
Socrates is a rational animal. (Observation)
(Therefore,) Socrates is a human being. (From 2 & 3)
Therefore, Socrates is mortal. (From 1 and 4)
We don’t always need definitions to know when we’re dealing with an
example of a given concept, but sometimes it can help. If we didn’t speak
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Greek, for instance, and Socrates’ behavior in the marketplace looked and
sounded very alien to us, we might need that definition to help us know what
kind of signs to look for.
Just to show that we sometimes do need the help of a definition to
make a better argument, consider the following argument that might have
been advanced by pre-philosophical Greeks:
Human beings are creatures who look like us. (Def?)
This barbarian does not look like us. (Observation)
Therefore, this barbarian is not a human being.
Most ancient peoples had trouble recognizing
foreign peoples as human. The Greeks called such
foreigners “barbarians” because they spoke a
different language, which to them sounded like
nonsense (“bar bar bar….”). Because foreigners
may look very different and make noises that are
difficult to understand, we can understand why it
Picture credit 147:
would be difficult for primitive peoples to see them
http://www.flickr.com/photos/alkalisoap
as of the same species. But when modern people
s/3317394622/
still adopt the same attitude today, knowing
everything we know, the result is racism. As it turns out, then, deciding
which definition of “human being” to adopt makes a difference for
something as important as the ethical or political ideology one adopts.
A different definition of “human being” would lead to a very different
conclusion. For example:
Human beings are rational animals. (Def?)
This barbarian is rational (Observation)
Therefore, this barbarian is a human being.
It may take a little time to recognize how foreign peoples are rational. It will
take, for instance, enough observations to realize that the sounds they make
are also a language. You probably wouldn’t need to fully translate the
language to realize this: you’d just need to observe them long enough to see
that the sounds facilitate communication and cooperation in just the ways
that ours do. It will take some time to realize (especially in an ancient time)
that foreigners engage in other distinctively human behaviors, like the
building and use of tools, or the practicing of religions. Once this is realized,
and if we understand that human beings have characteristics beyond a very
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specific visual appearance, the first cross-cultural bridges can be built and
the motivation for racism begins to disappear.
So if we think that the non-racist position is superior to the racist
position, doesn’t this mean that we consider the “rational animal” definition
to be objectively superior to the other? If so, what makes one definition
better than another? Or do we prefer one simply because it leads to our
desired political conclusion, while the other does not? Many people think
that how we define our terms is just a matter of playing an arbitrary semantic
game. Is this true? Is our reason for rejecting racism just an arbitrary choice
on our part? Or is there actually an objective good reason for it? In the
chapter that follows, we will begin to introduce some genuinely logical
considerations that should help us decide whether a definition is good or
bad. This chapter won’t exhaust what logic has to say about definitions. But
it will get the ball rolling.
Just in case you aren’t yet convinced that the definitions we adopt will
make a difference for the conclusions we arrive at, here are just a few more
examples. Different definitions don’t only make an anthropological
difference (as in the example above). Consider the following example from
another field of science, astronomy:
A planet is a round body in orbit around a star.
Pluto is a round body in orbit around a star.
Therefore, Pluto is a planet.
A planet [1] is a celestial body that: (a) is in
orbit around the Sun, (b) has sufficient
mass for its self-gravity to overcome
rigid body forces so that it assumes a
hydrostatic equilibrium (nearly round)
shape, and (c) has cleared the
neighbourhood around its orbit.
Pluto has not cleared the neighborhood
around its orbit (etc.).
Therefore, Pluto is not a planet.
Picture credit 148:
http://commons.wikimedia.org/wiki/File:Pl
uto_animiert.gif
The first argument involves the traditional definition of a planet; the second
involves one recently adopted by the International Astronomical Union,
which had the effect of demoting Pluto from the status of planethood.53 Once
53
“IAU 2006 General Assembly Votes: Result of the IAU Resolution votes.
<http://www.iau.org/public_press/news/detail/iau0603/>.
234
again, scientists adopted the new definition because they thought that it was,
in some sense, objectively better than the old definition. They thought that
this definition somehow reflected new astronomical knowledge, new
discoveries about numerous other orbiting bodies that are distant from the
sun, and how similar Pluto is to them. Presumably these scientists do not
think they are just playing an arbitrary semantic game. So what kinds of
logical considerations could lead one to think one definition is better than
another?
Perhaps the reason many people think disagreement over definitions is
arbitrary is because some disagreements
result from deep philosophical
disagreement about, disagreements about
the source of our knowledge of basic
philosophic principles. Two pairs of
arguments concerning contemporary
controversies show this clearly. The first is
the controversy over same-sex marriage:
Picture credit 149:
http://commons.wikimedia.org/wiki/File:Sergebac7thce
ntury.jpg
Marriage is a legal-romantic union between a man and a woman.
A same-sex union is not a legal union between a man and a woman.
Therefore, same-sex “marriage” is not marriage.
Marriage is a legal-romantic union between two consenting adults.
A same-sex union is a legal union between two consenting adults.
Therefore, same-sex “marriage” is
really marriage.
The second is the controversy over abortion:
A human being is any organism with
human DNA.
Human embryos have human DNA.
Therefore, human embryos are human beings.
Picture credit 150:
http://commons.wikimedia.org/wiki/File:
Equine_reproduction_services_fetus.jpg
A human being is a fully-formed rational animal.
Human embryos are not fully-formed rational animals.
Therefore, human embryos are not human beings.
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In both cases, the first party gets the definition (of “marriage” or of “human
being”) from a philosophic tradition that is inspired in one way or another by
religion. The second, by contrast, sees natural observation of the world as a
more exclusive source of definitions.
How and whether it is possible to settle these deeply entrenched
philosophical debates is a matter of some controversy, one we cannot settle
in a text on logic. So it is somewhat understandable that some will think that
choices of definitions—especially choices of definitions of very abstract
philosophical concepts—will not be objectively decidable. We will say more
about this issue in the chapter 13. For the time being, it suffices to mention
these examples as still further cases in which a difference in definition
makes a difference to the outcome of an argument. Even if we can’t settle
these very entrenched definitional disputes in the present chapter, the
examples should at least motivate us to look for simpler kinds of definitional
dispute that we can settle. Any simpler rules of definition that result from
considering these simpler disputes might help us inform more sophisticated
rules, which could help settle the sophisticated disputes.
Function 1: Definitions state the meaning of concepts
Definitions are constructed by human beings to serve specific purposes.
Though some think that anything constructed is by that very fact “arbitrary,”
we should not leap to that conclusion. We construct tools and buildings, but
some are better than others, because some serve their purposes better than
others. A hammer with a head made of metal is a far better than one made of
wood, because this mode of construction will succeed far better in driving
nails into wood. It follows that if we can identify the function or functions
served by definitions, we will be able to tell whether or not definitions serve
these functions well or poorly, and hence whether definitions can be good or
bad at what they do.
The first function of a definition is implicit in our earlier examples of
arguments that succeeded or failed depending upon how terms of their
premises are defined: definitions state the meaning of concepts. This
function will help us identify at least one crucial rule of definitions. The first
examples we’ll consider will be examples where a definition fairly
obviously fails to state the meaning of the concept. But evaluating a
definition by reference to this function and the rule associated with it will
not always be obvious, because in some cases the meaning of some concepts
is harder to know than others. So we will begin with examples in which the
meaning is relatively uncontroversial.
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It is important to bear in mind that concepts will often have meanings
that precede the statement of their definitions. The idea, then, is that a good
definition will capture that preexisting meaning. Consider the following
diagram, which indicates the most obvious examples of human beings, if
you are, say, a pre-philosophical Greek:
At the earliest stages, Greek people will see the strongest perceptual
similarities between a Greek man and a Greek woman (Socrates and
Xanthippe): both will be considered as human beings. There will be some
question about whether or not to consider the “barbarian” to be a human
being, because of some clear perceptual differences. Adopting the definition
that human beings are rational animals reflects a decision to draw the line in
one definitive way:
How do we decide to draw the line this way and adopt the definition that
reflects it? It is useful to remember that we do not define a concept in
isolation. We define it as against other nearby instances of other concepts
which clearly fall outside the boundary of the concept being defined. For
example:
237
Nobody would say that a dog (e) or a plant (f) is a human being—the
differences between us and them are too perceptually obvious. When we
decide to include “barbarians” as among human beings, we would do so by
judging that the similarities between these foreigners and native Greeks are
clearer than those between them and dogs or plants. (Another way of putting
this is: the differences between Greeks and barbarians are far smaller than
those between Greeks and dogs or Greeks and plants.) And these similarities
are overwhelmingly strong in spite of any differences between Greeks and
barbarians in appearance or language. There may still be some undecided
cases: do we consider a human embryo to be a human being? That is the
question that the debate about abortion hinges on. But we would also settle
that debate by deciding whether the similarities between the embryo and
other human beings are stronger than those between it and the non-humans.
The need for definitions becomes even stronger when we deal with
concepts whose meanings are more abstract, and for which the perceptual,
pre-definitional meaning is not as obvious. We need a definition to make a
fairly intangible meaning more tangible and definite. Consider questions one
might raise about the definition of the concept “science.” We cannot see a
science in the same way that we can see a human being. We may start out
with some paradigm cases of science, like physics and chemistry, and have
initial questions about whether biology counts as a science. This was the
case until the 19th century, when it looked like biology might only be a
system of categorizing various species:
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When Darwin’s theory of evolution by natural selection was proposed,
however, there was suddenly a framework for explaining and understanding
why species were to be classified as they were. To decide, then, that biology
is a science would depend upon adopting a formal definition of science as
the systematic, observation-based search for natural explanations of natural
events in the world.
As before, this definition would serve to distinguish science from other
forms of inquiry, such as those based on supernatural explanations of
natural events, like astrology and voodoo. As before, this may leave certain
cases unresolved. Is intelligent design theory a form of science, or not?
Some say it involves a supernatural explanation, while at the same time it is
allegedly based on observations (about the complex functionality of living
systems). Once again, to decide whether or not it counts as science, and
whether or not the definition needs to be revised, we will need to decide
whether resemblances between intelligent design theory and paradigm cases
of science are stronger than those between it and astrology or voodoo. In
either case, if we were not able to propose various definitions of “science,”
we would have a very hard time even keeping hold of the meaning of the
concept. We cannot literally line up physics, chemistry and these other
239
examples in front of us and look at their perceptual resemblances. We have
to think about what they have in common at a more abstract level.
Rule 1: Definitions must be equivalent in meaning to the concept being
defined
Knowing that a definition’s function is to state the meaning of a
concept helps us to state our first rule of definitions, that there must be an
equivalence in meaning between definition and the concept it defines. So in
the definition of “human being” as “rational animal,” the concept “human
being” must pick out the same examples the definition, “rational animal,”
and vice versa. That is to say, it must be true both that all human beings are
rational animals, and that all rational animals are human beings. This is
also to say: it must be true that all and only human beings are rational
animals.54
The rule that definitions must reflect this equivalence of meaning
implies that there are a number of ways in which they can fail to achieve this
goal.
a. Definitions must not be too narrow
Consider the definition of a “table” as a piece of furniture with four
legs intended to support smaller objects. Can you point out any problems
with this definition? Is the meaning of “table” equivalent to the meaning of
“a piece of furniture with four legs intended to support smaller objects”? Is it
true that all and only tables are pieces of furniture with four legs intended to
support smaller objects?
If we think about it, we will realize that, at the very least, there is a
problem with saying that all tables fit this definition. Do all tables have four
legs, for instance? It doesn’t seem like it. There are some pretty obvious
examples of tables with more than four legs, with fewer than four legs, or
54
Many philosophers will object to the idea that definitions state equivalence classes for things in the
world, and insist that these classes must be put in terms of classes of objects across all possible world.
There is merit in this view, in that we suppose our concepts to mean all of their possible instances. After all
we can think counterfactually about what would have happened if human beings had made different
choices than they actually did in the past (e.g., what would have happened to the human race if the U.S. and
the Soviets had started a global nuclear war in the 1960s). Nevertheless, it is the opinion of this author that
reasoning about counterfactual situations like this is asymmetrically dependent on our knowledge of actual
human beings, and that the primary form in which this knowledge is to be formulated is in terms of
Aristotelian categorical propositions. (For more on the difference between Aristotelian categorical
propositions and hypothetical statements used by counterfactual logic, see chapter 18.) In any case, there is
widespread agreement that categorical propositions can be made rough-and-ready equivalents of
counterfactual conditionals, and since they are easier to understand by the student, I will use them here.
240
even with no legs at all (if, for instance, the table is sticking out of a wall, as
at a diner). If that is true, then this definition of “table” unjustifiably
excludes many examples of tables that it should not exclude. It focuses on
too narrow a subset of tables. That is why we say this definition is “too
narrow.”
We can represent this mistake visually with the following diagram:
Notice how the class of “tables” is broader than the class of “four-legged
small object supporters.” That means that a definition based on the latter
class would be too narrow in light of many other examples that are
uncontroversially accepted as examples of tables.
Here are some other examples of
definitions that involve the same error. Can
you see why? Can you think of examples of
both games and works of art which are
unjustifiably excluded by the following
definitions?:
A game is a form of recreation in which two
players compete for obtaining an object.
Picture credit 151:
http://commons.wikimedia.org/wiki/File:Jan_V
ermeer_van_Delft_011.jpg
Art is a form of expression depicting visual
objects.
b. Definitions must not be too wide
If definitions might be too narrow, obviously they might also be too
wide. Consider the definition of “table” as a piece of furniture for supporting
things. Is it true that all and only tables are pieces of furniture for
supporting things? This time, the problem is not so much with the “all”
quantifier as with the “only.” Is it true that only tables are pieces of furniture
for supporting things? Can you think of other pieces of furniture that are
241
obviously not tables, but nonetheless serve the function of supporting
things?
Clearly there are other types of furniture that serve this function.
Chairs, for instance, help support our bodies when we sit. Beds support our
bodies when we sleep. And shelves support things like books and other
knick-knacks. So it is not true that tables are the only pieces of furniture for
supporting things: there are others as well. That means this definition is no
good. It is too wide. To say it is too wide means that it includes examples of
other things that are obviously not examples of tables: it would define
“table” in such a way as to include many non-tables, such as chairs, beds,
and shelves.
As before, we can also represent this with a visual diagram:
And here are further examples of other definitions that break the same
rule. Can you see how they are too wide? Remember: to show that a given
definition is too broad or too narrow, you need to be able to give a
counterexample to it: in this case, an example of an obvious non-table which
the definition unjustifiably includes:
A game is a form of recreation involving
the achievement of a goal.
Art is a form of expression of emotion.
Picture credit 152:
http://en.wikipedia.org/wiki/File:The_Scr
eam.jpg
242
c. Definitions must not be too wide and too narrow
It may sound counterintuitive at first, but it is actually possible for a
single definition to violate both of the previous requirements at the same
time. Consider the definition of a table as a piece of furniture for holding
books. Is it true that all and only books are pieces of furniture for holding
books?
In this case, we can find fairly obvious problems with both the “all”
and the “only” conditions. It is not true that all tables are pieces of furniture
for holding books. Surely few are limited to holding only one kind of objects
or another: they can be used to hold many such objects. Even if some tables
are better suited for some objects than others, there are clearly many that are
used with other specific objects in mind: for example, dinner tables are used
for holding food and dishes. But it is also true that tables are not the only
pieces of furniture for holding books. An obvious counterexample here is the
bookshelf, which is not a table, but still a piece of furniture for holding
books.
It might be hard to imagine how a definition that is too wide and too
narrow at the same time is to be represented visually, but this diagram shows
it:
Notice that the definition is shown as being too narrow, because the “book
supporters” category overlaps only a small portion of “table,” leaving out
many other examples of tables that the definition should not leave out. But
notice that it also includes many examples outside of the concept of “table,”
showing that it is also too wide.
Can you tell why these are
definitions that are both too wide and too
narrow?:
A game is recreation involving several
people.
Art is the production of beautiful objects.
Picture credit 153:
http://www.flickr.com/photos/anneh632/3163678441/in/
photostream/
243
Special note on “too wide” and “too narrow”
Many students who first learn the rules against definitions that are too
wide or too narrow (or both) sometimes apply these rules in a systematically
mistaken way. Consider again one of the mistaken definitions of “table”
we’ve considered:
A table is a piece of furniture with four legs intended to support
smaller objects.
We have already noted that a problem with this definition is that it
neglects the possibility of two-legged or six-legged tables. Students making
the systematic error in question will say that this makes the definition too
wide. (Notice that we classified it as too narrow up above.) What is their
rationale for classifying it in this way?
The idea these students are working with is that the problem with the
definitions is that it says too much. It specifies “four legs” when it should
not—there are many tables that have a greater or smaller number of legs.
Their idea, then, is that this definition is too broad because it is too long, it
contains too many words doing too much specification. Really it should be
“narrower,” in that it should contain fewer words doing less specification.
From one perspective, there is nothing wrong with thinking of the
problem this way. The definition does give too many specifics. The problem
is just that this way of stating the problem is not what we originally meant
by “too broad.” We think of a definition as too broad because it counts too
many things as a table, and we can see that this example counts too few
things as a table. Another problem with this way of describing the error in
the definition is that it assumes that excessive specification will always come
by way of an excessive number of words in the definition, but that is not
true. After all, we could eliminate its overspecification by using the exact
same number of words:
A table is a piece of furniture with some legs intended to support
smaller objects.
It is better, then, to think of “too broad” and “too narrow” as
describing the number of examples improperly designated by a definition.
The key here is not to think of the problem with the definitions language, but
with its meaning—with the way it covers more or less territory than it
should.
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Function 2: Definitions interrelate concepts in a hierarchy
We already saw hints of this second function of definitions in the previous
section. Recall how, when we formulated definitions of “human being” and
of “science,” we were concerned to contrast obvious examples of the
concept in question from obvious examples not included in the concept.
One function of a definition is precisely to indicate differences and
similarities between instances of one concept and those of nearby concepts.
The definition of a human being as a rational animal, for instance, suggests
that there are animals other than rational animals. This reflects the fact that
the concept is being contrasted with other concepts, such as “dog” and
“bird”55:
The definition also suggests that there are similarities between human beings
and dogs and birds. All of them, for example, are animals:
And of course suggesting this similarity also suggests a further contrast,
since human beings, dogs, and animals, are animals as against plants. And
we would only think to compare animals to plants in the first place because
they too had something in common: all of these things are living organisms:
55
One of the usual criticisms of the “rational animal’ definition is that there are non-human animals that
exhibit signs of rational behavior. Whales and dolphins are thought to communicate. Chimpanzees and
gorillas can learn rudimentary forms of sign language. In some cases, chimps even seem to be able to learn
symbols for relatively abstract concepts. There are, of course, controversies about how to interpret the
experiments suggesting all of this, but even if the results are in accord with the usual interpretation, these
examples do little to challenge the point of the definition. Even if chimpanzees, for instance, possess
rudimentary forms of rational cognition, it is not their characteristic faculty by which they function
systematically, in the way it is for human beings. Chimpanzees may be an interesting borderline case
between characteristically rational animals and fully non-rational animals, but the existence of such a
borderline case does not call into question the fact that there is a chasm of difference between the
characteristic cognitive functioning of human beings and that of the rest of the animal kingdom. We will
explore the significance of this difference under Function and Rule #3.
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The component of a definition which suggests the most immediate
concepts whose instances are similar to those of the concept being defined is
called the genus. The genus is the wider class of which a species is a
member. In our definition of “human being” as a “rational animal,” animal is
the genus.
Picture credit 154: http://taxonomicon.taxonomy.nl/TaxonTree.aspx
The other component of the definition is the characteristic that
distinguishes the species from other members of the genus, which is called
the differentia. In our definition of “human being,” rational is the
differentia.
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Here are some other examples of definitions, with their respective
genera (the plural of “genus”) and differentiae (the plural of “differentia”):
It turns out that there are different levels of generality at which we can
specify the wider class of which a given species is a part, so there will be
multiple genera which one could choose. (We could conceivably define a
table as a kind of item of furniture, but also as a kind of man-made object, or
even as a kind of physical object.) The ones listed above are the most natural
genera, and the reasons that make them most natural are complicated. But
we should note that there are several extremely generic (to use the word in
its most literal sense) “ultimate genera”:
Aristotle argued that these ultimate genera (along with a few others) were
the ultimate “categories of being” into which the referents of any concept
would ultimately fit.
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Rule 2: Definitions should have a genus and differentia
This is the rule that follows most obviously from the fact that definitions
help us interrelate concepts from others in their neighborhood by means of
similarity and difference relationships. On one hand, it’s hard to imagine that
we could have a bad definition that violated this rule, because it’s hard to
consider a string of concepts didn’t have both genus and differentia as a real
definition, good or bad. On the other hand, there are examples in which
unclear or overly general genera are stated, and these are examples of poorly
formulated definitions. For example:
A game is where you follow a rule to obtain an object.
A government is what has authority to make and enforce laws.
Happiness is when you get what you want
Notice that “where,” “what,” and “when” are merely pronouns and,
therefore, unclear. Which “where,” “what” or “when” do these terms refer
to? They are also misleading. “Where” refers to a location. Is a game a kind
of location? No, it is an activity, and we can be more specific than that: it is
a form of recreational activity. The same considerations apply to the other
examples. A government is a what—i.e., a thing—but it would be better, at
least, to say that it was a kind of thing, and even better to say that it is
something like an institution. Likewise for “happiness,” an example
considered in the box above.
Appendix: how reflecting on interrelations among concepts helps us
define them
When we considered how to define “human being” and “science,” we
were already working implicitly under the view that definitions serve to
interrelate concepts. We wanted to make sure, for instance, that our
definition of “science” captured the fact that it was very different from
astrology and voodoo. This helped us pick, in particular, a differentia. But
considering the broader hierarchy of concepts of which a particular concept
is a part can also help us fill out the rest of the definition.
Consider, for example, the concept “game.” The philosopher Ludwig
Wittgenstein once noticed that the many things we call “games” look very
different from each other. This is true:
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But Wittgenstein concluded that because we could not “look and see” a
similarity between poker, soccer, tic-tac-toe, and video games, there must
not be any similarity between them, and so definitions must ultimately be the
product of a mere “family resemblance” among the examples.
We can’t just “look and see” and see a similarity among these
examples. But why should every similarity be one that is directly visible? A
good definition of “table,” for example, is not simply in terms of the look of
the table, but in terms of its function, what the object does. Tables are used
to support objects of one kind or another. In the case of tables, its function is
intimately related to its visual appearance: we can easily see people sitting
on tables, and understand that they are able to do this because of the table’s
shape. Not every object has a function that is as directly observable as a
table. Sometimes members of a kind act or are used in ways that are not
perceptually similar. Still, we can observe the diversity of uses and abstract
from them to determine the more abstract similarity in function they exhibit.
Wittgenstein assumed that only if we could stare at games and see a
perceptual similarity in their function could we define them. But many
definitions are not gotten merely by staring: it helps also to look at examples
of nearby concepts with which the concept can be compared and contrasted.
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What kind of thing is a game? We would distinguish, for example, a game’s
function from the function of labor or study: it is a form of recreation. We
play games in order to relax or unwind. This is not to say, of course, that one
could not play a game professionally, but the possibility of professional
game playing is only made possible by the fact that many people enjoy
playing games and sports for fun on their own and want to watch others who
are virtuosos do the same. So a game is fundamentally a form of recreation.
This helps us grasp the genus of “game.”
Of course there are many other forms of recreation apart from games.
As you may have discovered by considering some of the improper
definitions of “game” in previous sections, there are forms of recreation like
hobbies, parties, and travel, all of which are also done in order to relax and
unwind, but which are different from games. How do games differ from
these? One thing to note is that hobbies and travel both involve pursuits that
are enjoyable in themselves. We enjoy using our hands to build model ships,
seeing friends at parties, and seeing new sites when we travel. This may be
true for games, as well, but there is something special about the nature of the
fun involved in games. Games involve activities that we would not normally
enjoyable in and of themselves. What is so special about moving a ball
across a line (an end zone) in football? Normally, doing this would not give
us any special pleasure. In fact we would normally regard as burdensome
running back and forth across a field. So why do we enjoy playing games?
In games like football, the “object of the game” (or goal) is picked
arbitrarily, though perhaps with some analogy to the achievement of real
goals in real life (the action of football is loosely analogous to action on a
battlefield). But the game also involves rules which describe the ways in
which it is acceptable or not to achieve the object: it is difficult to score a
touchdown, involving as it does physical activity we would otherwise try to
avoid in everyday life. If we are willing to participate in such a game in spite
of the exertion it requires in the absence of an inherently enjoyable end, it
must generate a special kind of enjoyment. It must be the activity rather than
the end that is enjoyable, and since physical exertion per se is not
necessarily enjoyable it must be the activity of exerting energy to overcome
obstacles in the pursuit of goals that is the reward. These obstacles are
created by the rules, which make them crucial to generating the fun of the
game. This explains, for instance, why cheating at the game ruins its fun.
For this reason, a good definition of “game,” derived from the
considerations of comparisons and contrasts with other nearby concepts,
would be something like: A game is a form of recreation deriving from the
following of rules about how to obtain an arbitrarily chosen object (whose
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achievement may be analogous to real-life action). This is not a definition
that can just be gotten by looking and seeing, but it reveals a distinguishing
characteristic which is much more than a mere “family resemblance.”
Function 3: Definitions condense knowledge
So far we have considered two related functions of definitions: to state the
meaning of our concepts, and to interrelate them with other concepts. These
functions are related because part of what we need to do in order to
determine the meaning of our concepts is to remember what other concepts
they are contrasted with (see our exercise with the concept “game” above).
But it might be wondered: why do we need to state the meaning of our
concepts at all? What good does it do us? One answer is that some people
might not fully know the meaning of words they have learned from other
people. A definition allows them to take a word learned from another, and
understand it in terms of more readily knowable concepts they may already
understand.
But the function of definitions is not merely to help us be on guard
against parroting the words of other people. There are other personal,
cognitive reasons for being able to state the meaning of our concepts in a
short, easily manageable formula.
Consider one last time our definition of a human being as a “rational
animal.” Notice that there are many things we know about human beings
apart from their having a certain kind of mind and their being members of a
certain kingdom of living things. In particular there are many other things
we know about human beings that are distinctive of them: they use tools,
they use language, they are the only animal with a sense of humor, they are
the only animal that gets married. And there are many other facts like this.
If, in order to use and understand a concept like “human being,” we
would have to memorize a long list of facts like the above, it would be very
difficult if not sometimes impossible to manage. We need concepts to serve
as repositories of our knowledge, but sometimes our knowledge about a
given concept is massive. Definitions help solve this problem by condensing
our knowledge down to its essentials.56
How? Consider the relationship between the property of being a
rational animal, and the longer list of their other distinctive traits. The fact
that we are rational beings in one way or another actually helps explain these
other distinctive traits. We are (just about) the only animal that makes tools,
for instance: though some chimpanzees have been known to use sticks to get
56
For more on this idea, see Rand, “Definitions,” in Introduction to Objectivist Epistemology (1967/1990),
pp. 40-54.
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ants out of anthills, human beings not only use sticks but knives, plows,
sewing machines and nuclear reactors to alter their environments and
improve their lives in dramatic ways. What makes them be able to do this?
To build a tool, one needs to be able to identify some cause and effect
relationship between a desired end and the factor isolated by the tool. To
make a knife requires one to know that if one wants to kill and eat one’s
prey, for instance, one has to rend apart its flesh. Perhaps early people
observed animals or their own comrades being injured when they scraped up
against a rock, and identified the causal connection between the tearing of
flesh and death. But to do this requires the use of concepts, of “flesh” and
“tear” and “death,” a use which is made possible by the possession of a
rational faculty. Other causal concepts are presupposed by the construction
and use of other tools. So the fact that we are rational animals helps explain
the fact that we use tools.
The same is true for most if not all of the other distinctive traits of
human beings. We use language because we need to be able to express our
use of concepts in physical form, both to communicate our discoveries to
other people, and to be able to deal with abstract reasoning in concrete form.
We have a sense of humor because we are able to detect incongruities and
inconsistencies in the words and actions of others, because we have a sense
of logic. And we get married—though some might not always do this for
rational reasons!—because we are not only able to mate for life, but because
we are able to formulate the idea of a long-range commitment over years and
years, because we have concepts that allow us to project the future.
You should think of a definition as a “handle” that enables us to grab
hold of a great number of other pieces of knowledge about the concept the
definition defines. Definitions do this because of the way in which the trait
cited in the definition—an essential characteristic—helps causally explain
the other distinctive traits. (An essential characteristic is a distinctive
characteristic of the instances of a concept on which many of the other
distinctive characteristics depend.) A diagram like the following is
instructive here:
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Notice that the facts on the left are all explained by our possession of
a rational faculty, but the facts on the right are not. Recall that a definition is
not just a differentia, but also a genus. And there are important facts about
human beings which are, admittedly, not distinctive to them, but which still
follow from their nature as animals, if not from their nature as rational
animals. Human beings are mortal—they’ll die some day. As such they need
things like food and health care if they want to survive. They also need
exercise for their bodies: animals have to move around to get their food, they
don’t just “vegetate” like plants. Etc. Definitions really do condense a vast
array of knowledge.
The definition of “human being” just discussed can, perhaps, be
discussed too exclusively to illustrate this condensing function of definitions
Just to show how this condensing function of definitions applies to many
other concepts, let’s consider the definition of “game” that I proposed in the
section above: a game is a form of recreation deriving from the following of
rules about how to obtain an arbitrarily chosen object. Here is another
diagram summarizing some of the knowledge condensed by this definition
of “game”:
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Every form of recreation is enjoyable for some reason. Parties are
enjoyable because they let us see and communicate with friends. Travel is
enjoyable because it lets us see new people and places we’ve never seen
before. Games are enjoyable because they challenge our bodies or minds to
overcome obstacles and achieve goals without having anything real at stake.
If we lose at a first-person shooter video game, we don’t actually die. We
can just start over and keep playing. Highlighting the importance of having
rules for obtaining an object, then, explains why games are fun, and many
other facts about them. It explains why nobody likes a cheater—not even the
cheater himself, after a while. Cheating at a game may deliver short term
kicks, but once the rules no longer bind one in the achievement of the
game’s goal, all the fun of the game is lost. After all, there is nothing
inherently enjoyable about being able to place tiny plastic flags all over a
board game, or about moving a ball into an end zone. It’s only valuable
insofar as it reflects one’s ability to plan and execute strategies within the
bounds of the rules of the game.
Or: how about the fact that games are “age-appropriate.” Games will
often feature labels designating which age range will be best suited to play
them. Why is this? Because the rules of the game may be easier or harder for
various age groups to learn. If you cannot learn the rules of a game, playing
it will not be any fun. Or: even if you can learn the rules of a game, if you
have to spend hours and hours doing it, because the rules are so intricate and
complicated, this will take the fun out of it, as well. Rules of a game should
be relatively simple compared to the amount of time and effort actually
spent playing the game.
There are some facts about games that also follow from the genus of
this definition. Since a game is a form of recreation, this presupposes a
contrast with forms of work, such as labor or study. If you play games too
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much of the time, to the point where you only engage in forms of recreation
and not in any work or study, you’ll be in trouble. We are only able to
engage in recreation because we engage in creation: we only enjoy the fruits
of our labor because we labor!
By the same token, it would be a mistake to say that “everything is a
game,” as sometimes cynical or non-serious people are inclined, because the
concept of game presupposes a contrast with non-games. If everything is a
game, the concept has no meaning derived from this contrast.
Now that we have gotten to the knowledge-condensing function of
definitions, the function which explains the other two functions of concepts
(we need to interrelate concepts because doing so helps us understand their
meaning), we have actually found the essential characteristic of the concept
of “definition” itself. That means we are in a position to define definition! A
definition is a statement giving the meaning of a concept by identifying its
essential characteristic(s).
Rule 3: Definitions should state essential characteristics
As with the previous two functions of definitions, this third (and most
fundamental) function implies a rule to follow if we want to have a good
definition: definitions should state essential characteristics. What this means,
in practice, is that they should not state superficial, or non-essential
characteristics. A superficial characteristic is a characteristic that, while it
might be possessed by most or even all of the instances of a concept, is one
that only highlights some “surface” feature of these instances, one which
doesn’t explain most of the other distinctive characteristics of these
instances, and which, therefore, does not summarize much of our knowledge
about them.
Here are some examples of definitions in terms of superficial or nonessential characteristics:
Human beings are the animals with a sense of humor.
Human beings are the animals with an opposable thumb.
Human beings are featherless biped
We have already considered the fact that human beings are beings who
distinctively possess a sense of humor. But while humor is explained by the
fact that we are rational animals, the reverse is not true. It neither explains
our being rational, nor explains any (or many) of our other distinctive traits.
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So if we were to pick it as a defining trait, we would be defining by nonessentials.
It is also true that human beings are the only animal with an opposable
thumb. This may or may not be explained by the fact that we are rational
animals. (Perhaps there is an evolutionary argument that would explain it,
but that is very speculative.) But not every distinctive characteristic of a
species needs to be explained by a definition, just most. And what’s clear
here is that this definition does very little to explain any of the other
distinctive traits of human beings. Perhaps this trait would explain our
ability to make tools. But how does it explain our sense of
humor, our use of language, our ability to get married, or
even our ability to play games? It doesn’t.
The last example is a example of a definition that is
said to have been once proposed by ancient Greek
philosophers. They surveyed the animal kingdom and
realized that man was the only being who walked on two
legs, but who (unlike birds) did not have feathers (the
Greeks did not yet know about apes or chimps). Though
this was true of the human beings the Greeks knew about,
there is still a question here about how our walking on two
feet and not having features would explain any of the other
knowledge we have about human beings. It’s not the case
that our mode of ambulation does much to account for our
use of tools or language, and our not having feathers
doesn’t help us get the point of a joke (since it is a negative
trait, it doesn’t positively help us do anything). As it
happens, because the Greeks could get the point of a joke,
one of them plucked a chicken and noted that if man was
the featherless biped, he had just created a man.
Here are just a couple more definitions by nonessentials of other concepts:
Picture credit 155:
The heart is the organ that goes “lub dub.”
http://www.flickr.com/phot
os/estherase/62541029/
Gold is a yellow, malleable metal, soluble in aqua regia.
The heart really does make a distinctive-sounding noise. You’ll find no other
that makes the same. Does that mean that we ought to define the organ by
this sound? The sound it makes does very little to explain many of the other
things we know about hearts. It doesn’t help us explain how, if someone’s
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heart is damaged, or malfunctions or is removed, they will die. It doesn’t
help us explain why exercise increases one’s heart rate. It doesn’t explain
why one’s diet can clog one’s arteries. The essential characteristic that does
help to explain all of these things is that the heart is the organ whose
function is to circulate blood. If we know that blood circulation is necessary
for life, this explains why damage to the heart causes death. If we know that
exercise taxes the body and makes it require more energy and nutrients, and
that blood circulation is what achieves this, this explains why exercise
increases heart rate. And if we know that what one eats is dissolved into
one’s blood stream, which can affect the heart, because the heart circulates
blood, this helps explain why diet can adversely affect the heart.
The last example is an example of definition that would have been
perfectly appropriate for people living in a certain age with a certain amount
of knowledge, but which is not appropriate, given what we know today. This
was the definition of “gold” accepted through the 17th and 18th centuries. At
the time, really all that anyone could do to define this type of metal was to
note its observable properties. (Testing gold by dissolving it in a kind of
acid, “aqua regia,” was the best they could do to distinguish gold from other
look-alike metals.) This definition of “gold” was much like many doctors’
early definitions of diseases in terms of a collection of symptoms (called a
“syndrome”). Until a scientific discovery is made about the cause of this
collection of observable properties, it is the kind of definition we will have
to settle for. In fact, in the 19th and 20th centuries, scientists did make this
advance with respect to gold and every other element. They discovered that
it was the subatomic properties of an element that accounted for its
observable properties. If you know quantum mechanics, the atomic number
of an element (its number of protons), will imply its number of orbital
electrons, and the various properties of those orbital electrons. From that,
you could deduce how the atom would reflect light (and what color it would
be), how it would cohere with other atoms of the same type (and how strong
it would be), and how it would interact with other atoms of different types
(and how chemically reactive it would be).
There are a few rules of definition left over, which do not fall neatly
under any of the functions we have already considered. They might be said
to be necessitated by all of these functions taken together.
Rule 4: Definitions should not be circular
This rule follows most clearly from the fact that definitions serve to state the
meaning of a concept. If a definition is circular—if it defines a concept in
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terms of itself—then it is not composed of concepts that independently help
connect the concept to be defined to its meaning. In this way the error of the
circular definition resembles the error of the circular argument. Here are
some quick examples of circular definitions:
A game is what is played by gamers.
Art is the product produced by artists.
A husband is a man with a wife.
Notice that in each of these definitions,
the term being defined is not repeated
directly in the definition. Rather, another
term is stated, which itself would need to be
defined in terms of the term being defined.
So, for example, what is a “gamer”?
Someone who plays games. That means that
the first definition is really stating: “A game
Picture credit 156:
is what is played by people who play games.”
http://commons.wikimedia.org/wiki/File:Duchamp_F
This definition is obviously not informative!
ountaine.jpg/
The same is true of the definition of “art.”
(We see on the left an example of an artifact by one Marcel Duchamp
considered to be “art” according to this definition.)
What about “a husband is a man with a wife.” Here the circularity is
still present, but not quite as obvious. What term is used in this definition
which might have to be defined in terms of “husband”? Well, if we are to
use the same formula to define “wife,” then it would need to be defined as “a
woman with a husband.” The trouble is that “husband” and “wife” are socalled correlative terms. We should not try to define each in terms of the
other, but to define each in terms of some third, neutral term (like “spouse”).
Rule 5: Definitions should not be needlessly negative
This rule probably also follows from the function that definitions state the
meaning of concepts, but it is also closely connected to their function of
stating essential characteristics that explain much of the rest of our
knowledge about the concept being defined. A definition that states only
what properties are not included under a concept does little to tell us what
properties help explain the other distinctive traits of instances of some
concept.
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Of course sometimes our concepts are negative by their very nature,
and our definitions of them will have to reflect this fact. For instance:
A bachelor is an unmarried male.
Poverty is the absence of wealth.
Freedom is the absence of slavery.
These are all examples of inherently negative concepts, and the definitions
in question reflect this fact appropriately.
But what about these?:
Man is a featherless biped.
A car is a horseless carriage.
“Thinking is the momentary dismissal of irrelevancies” (Buckminster
Fuller)
The first tells us what man does not have: feathers. What does he have? We
need that to understand all of the many other distinctive properties. To
define a car as a horseless carriage is to say what does not power it. But
can’t we and shouldn’t we say something about what does power it, such as
the internal combustion engine? Finally, Fuller’s definition of thinking is not
obviously negative, but if you think about what a dismissal is—it is the nonconsideration of something—you’ll realize that he’s telling us that thinking
is just not thinking about of non-relevant things. But what is thinking? There
may even be circularity in this definition.
Rule 6: Definitions should be clear and literal
Because the purpose of definitions is to state the meaning of our concepts,
and to do so in an economical way that condenses a great amount of
knowledge, this purpose is not served if a definition is not stated clearly or
literally. Here are some examples that violate this requirement (although
some of them violate it on purpose, because they are trying to be funny):
“Home is the place where, when you have to go there, they have to
take you in” (Robert Frost).
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“A conservative is a statesman who is enamored of existing evils, as
distinguished from the liberal, who wants to replace them with others”
(Ambrose Bierce).
“Tickling is an intensely vivid complex of unsteady, ill-localized, and
ill-analyzed sensations, with attention distributed over the immediate
sensory contents and the concomitant sensations reflexively aroused.”
“A definition is the enclosing of a wilderness of ideas within a wall of
words” (Samuel Butler).
What is unclear or misleading about these definitions? How would you
define the same concepts clearly or more literally?
One last note: the last definition may be metaphorical, but it suggests
an idea about definitions that is at odds with the message we have been
pushing in the rest of the chapter above. If a definition encloses a wilderness
of ideas with a wall of words, this suggests that it is artificially confining,
that our ideas would blossom if left unencumbered by needlessly intrusive
definitions. What we hope to have shown is that definitions are not
artificially restrictive boundaries, but tools that help the garden of our ideas
grow and flourish.
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§4: THE ROLE OF MEANING IN LOGIC
Chapter 13:
Settling definitional disputes
Ben Bayer
Drafted August 20, 2010
A puzzle about definitions
In chapter 12, we formulated a series of rules by which to judge the worth of
definitions. The most straightforward rule was that a definition should not be
too wide or too narrow. When we tested definitions using this rule, we used
a fairly straightforward method.
Recall one definition we criticized as too wide: “a table is a piece of
furniture for supporting things.” We can remember why this was too wide by
looking at the following diagram:
We called this definition too wide because “a piece of furniture for
supporting things” would also be true of the examples pictured on the right.
Yet we don’t think that these are tables: we think that these are chairs and
shelves, and “chair” and “shelf” are concepts incompatible with the concept
“table.”
Registering this criticism presupposes that everyone will agree that
the objects pictured on the right are indeed not examples of tables. Usually,
this is not a problem, because everyone demonstrably sane does agree. But
someone intent on stubbornly insisting that the definition of “table” really is
“a piece of furniture for supporting things” could question whether we really
know that these are not tables. This “thing supporter” dogmatist could ask us
to consider why we shouldn’t just think of chairs and desks as special kinds
of tables, such that the concept extends across other sub-types of furniture:
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It is natural to respond to such a critic by insisting that we know that the two
objects on the right are not tables. But how do we know this? Some will say
that these objects are not tables because neither is a piece of furniture with a
flat, level surface intended primarily to support other, smaller objects. The
object in the middle isn’t for supporting smaller objects, and the object on
the right doesn’t have the flat, level surface.
But there’s something logically suspect about this response. In order
to explain why the chair and shelf are not examples of tables, the reply
invokes a definition of table: “a piece of furniture with a flat, level surface
intended primarily to support other, smaller objects.” But how do we know
that this definition of “table” is correct? To determine whether the other
definition is correct, we were testing it by reference to the examples. Now it
seems we are judging the examples as if we have already determined the
correct definition, one which we know is correct only if we already know
that the earlier (“thing supporter”) definition is incorrect. But whether or not
it is incorrect is exactly the question we
are trying to answer. The problem is that
we cannot take for granted that the “flat,
level surface” definition as correct
without begging the question.
This puzzle about how to decide
when we have the right definition is one
that philosophers have grappled with for
ages, going back at least as far as Plato’s
dialogue, the Meno, written around 380
B.C. It is useful to note in broadest
Figure 7:
http://commons.wikimedia.org/wiki/File:Sanzio_01_Socra
outline some of the most popular
tes.jpg
solutions to this problem that
philosophers have proposed. Some solutions attempt to identify an
independent method of knowing when examples are instances of a concept,
apart from using the definition as one’s criterion. Others, lamenting the fact
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that we cannot find this independent method, declare that there can be no
objective judgment of when one definition is better than another. This
second position is what motivates the idea that debating about definitions is
playing an arbitrary “semantic game.”
One attempt to find an independent standard for evaluating definitions
is to claim that we have a special rational “intuition” guiding our evaluation
of examples. According to this view, in just the same way that perceptual
observations are data for our scientific theories, intuitions can be data for our
assessment of the definitions of abstract concepts. To test a definition of
“table,” we need only cogitate from our philosopher’s armchair about
whether a given example seems to us to be a table. These intellectual
“seemings” give us the data against which we test our definitions: if sitting
in our armchair, we can “just know” that a chair is not a table, then a
definition of table as a “thing supporter” is not a good definition. To this
philosopher, chairs and tables and the like do not seem to be tables, so from
this I conclude that the “thing supporter” definition is wrong.
The problem with the intuition approach is that people’s intuitions
will differ. They might not differ with regard to the “thing supporter”
definition of table, but they will with regard to definitions of many other
more abstract concepts. What is an intuition, after all? It is a judgment about
whether or not something falls under a
given concept, made before we formulate
an explicit definition of that concept—it
is a “pre-theoretical judgment.” But
people will have very different opinions
about whether or not an embryo is a fetus,
whether or not a same-sex union is a
marriage, and whether or not intelligent
design theory is science—they will have
these different opinions before they try to
give definitions of the concepts in
question. Armchair “intuitionists” might
respond that intuitions can change, that
they may need to be adjusted by reference
to other intuitions. But if that is true, then
intuitions are not a basic source of
Figure 8:
http://picasaweb.google.com/lh/photo/TIOcrWl9d8WuJrv
evidence for definitions. Some
eL_gMOA
philosophers may be willing to accept
this, but then again, oddly enough, it is not very intuitive to treat our
intuitions as a form of evidence. It would take powerful philosophical
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arguments to convince us that this position is not an unacceptable form of
personal subjectivism.
Another attempt to locate an independent standard for evaluating
definitions is to look beyond an individual’s personal intuitions, to the
judgments of society as a whole. This approach appeals to the verdict of
ordinary language or social convention: what things do most people call
tables? In form this is not very different from the “intuitionist” approach:
rather than consulting one’s own judgments about what is a table, this
approach simply recommends that we take a poll to learn what most people’s
intuitions are about the question. If most people think that chairs and shelves
are not tables, they must not be.
The problems with this approach are analogous to the problems with
the personal “intuitionist”
approach: it is hard to see why
it is not a version of social
subjectivism, not just an
attempt to treat the “hive
mind” as one’s own. Even if it
is true that many people will
agree about what things count
as examples of tables, there
will be greater disagreement
Figure 9:
about more abstract
http://commons.wikimedia.org/wiki/File:Ttitelblatt_1750_Leviathan_Thomas_
concepts—especially
Hobbs.jpg
philosophical ones. What’s
more, for some concepts, there may not even be a single attitude that most
people have about it. On extremely controversial questions (about the
definition of marriage, for instance), popular opinion may split right down
the middle. Perhaps the “social conventionalists” can say that in such cases,
the concept in question simply has no meaning. But here again,
paradoxically enough, this is contrary to social convention: virtually
everybody who debates about the definition of “marriage,” whatever
position they take on the matter, agrees that it has a real meaning—
otherwise they wouldn’t be fighting so much over what it is.
When and if personal intuition and social conventionalism fail to
secure an independent source of data by which definitions can be judged,
many who think about this puzzle throw up their hands and assume that
there is no source of data. They suggest that definitions are arbitrary, and in
cases when people cannot agree on a definition (or even form a majority
view), they are simply speaking different, incommensurable languages.
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Some people might just use “marriage” to refer to same-sex unions, and
others might not.
Of course it is true that people do speak different languages. English
is different from French, which is different from Vietnamese, etc. Notably,
however, even though these different languages use different words, they
use different words for roughly the same stock of concepts. Occasionally
you will find words in one language that have no perfect equivalent in
another, usually because of differences in connotation or shade of meaning.
“Gemütlichkeit” in German is said to have no real equivalent in English. It
suggests a kind of hearty hospitality or coziness, but English has no single
word combining these qualities. English can, however, give a description
characterizing the word using a combination of different concepts—as we
just did. This means that the two languages are not really incommensurable:
we can still understand what the Germans mean by “gemütlichkeit.”
Conceding the point that different languages still seem to be capable
of translation—because every language needs a certain stock of concepts—is
important to resolving the puzzle about definitions, and why speakers of the
same language, in particular, ought to be able to resolve puzzles about
definitions even when they disagree about the examples that a given concept
should apply to. We will explore ways of settling definitional disputes in the
sections that follow.
Settling disputes about definitions of basic-level concepts
Let’s return to our hypothetical controversy about the definition of “table.”
Suppose that a critic disagrees that chairs and a shelves are not examples of
tables. He wants to endorse the definition of “table” as “a piece of furniture
for supporting things.” To see what resources are available for evaluating
this definition, let’s suppose for the sake of argument that he’s right, and that
we should define “table” in his more generic way. What follows?
Notice that even if we start calling each of these items a “table,” there
remains an observable difference among each of them. The table on the left
still looks very different from the “table” on the right, and if we were to
assemble a series of other objects with a flat, level surface intended for
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supporting other smaller objects, they would look similar to the table on the
left, and also differ greatly from the “tables” on the right. There may be
many differences among the many types of objects with a flat, level surface,
but what differences they have are observably smaller and less noticeable
than the bigger differences between them and the objects on the right.
Recall that one of the reasons we need definitions is to condense our
knowledge of the things we conceptualize. We need to condense because the
referents of our concepts have a great many similarities, not all of which are
equally important. Definitions pick out the most important similarities, the
ones that help account for all of the others. So, for instance, there are many
similarities shared by pieces of furniture with a flat level surface. We find
them in homes and offices. We don’t find many of them outside. We find
that they are made within a certain range of sizes: we don’t find real tables
that are three stories tall, or smaller than an inch. Etc. These are all
undeniably real similarities, but we can understand why these similarities
cluster together because of still another similarity they have in their shape
and structure. The essential characteristic of objects of this type is their
function: these objects are intended to support other smaller objects. Because
of this, they are found in places where there are many other smaller objects
worth keeping (inside of homes and offices) and made in a specific range of
sizes (only sizes that scale to the human body, whose needs dictate the need
to support other smaller objects, e.g., food at a dining table or a lamp on an
end table).
But if condensing knowledge of
similarities and differences is one of the
most important functions of definitions,
then it follows that whatever we choose to
call the range of objects in the diagram
above, we will still need some concept to
designate the object on the left side of our
diagram (the one we normally call
“table”). If the critic’s point is that we
could call all of these things “table,” he is
of course correct: we can call anything
anything we like. The question is if there
is a good reason to do so. We have a
good reason to conceptualize the object
10:
on the left differently from all of the other Figure
http://commons.wikimedia.org/wiki/File:Humpty_Dumpt
objects. Call all of these objects “tables” y_Tenniel.jpg
if we like, it will remain true that the “tables” that have a flat, level surface,
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etc., are importantly different from the ones that don’t. Call these
“schmables.” There would then be “tables” that are schmables, and then also
non-schmable “tables.”
The basic point here is that no matter what we call things, the
similarities and differences out there in the world are still there, and some of
them are significant enough to warrant conceptualizing. The difference
between furniture with a flat, level surface for supporting other smaller
objects and other kinds of furniture is big and significant enough to warrant
a concept of its own, whether we call it “table,” “schmable” or something
else entirely. The word we choose to designate this group of similar things is
largely arbitrary: there is no special resemblance between words and the
things designated by them in the world (unless the word happens to be
onomatopoeic, like “moo” or “buzz” or “click”). But there is an objective
value in being able to communicate with other people, and so if most of
them choose to use a word to name this group of similar things that we have
independently conceptualized for ourselves, we might as well use the same
word—in this case, “table.” Indeed there is good evidence that this is how
children learn language: they first recognize different categories of similar
objects, and once they figure out that parents are using words to name the
same categories, children’s use of language explodes and they begin to ask
for the name for everything.57
The observations listed above afford us a way of settling controversies
over definitions for concepts like “table,” in a way that avoids the problems
of the earlier solutions we examined. Like the “intuitionist” solution to the
problem, this solution attempts to locate an independent source of evidence
that we can use to identify examples as tables or non-tables, without
presupposing the validity of a given definition. This avoids the problem of
question-begging. Unlike the intuitionist solution, this solution is not
57
See Lois Bloom, The Transition from Infancy to Language, Cambridge University Press, 1993.
267
subjectivist. It does not invoke what merely seems to be true, but perceptual
observations of similarity and difference. Nobody can deny that tables are
more similar to each other than they are to chairs and shelves. Like the
“social conventionalist” solution, this solution takes seriously the ordinary
choice of words in the conceptualization of objects like tables. Unlike the
social conventionalist solution, however, the words of others are not taken as
an independent source of data. We must first observe similarities and
differences of our own, and only then choose the words others use in order
to communicate with them effectively.
There is, however, an important limitation of the solution offered
here: it will only help us settle disputes about the most basic of concepts,
concepts like “table,” for which there is an easily available perceptual
similarity. Not every concept is like this. In fact most of the concepts for
which there are likely to be definitional disputes will fall squarely outside
this category. Precisely because of the fact that there is a perceptual
similarity among their referents, we are unlikely to encounter disagreement
about definitions of perceptual-level concepts except perhaps when we deal
with the psychotic. But for concepts over which controversies rage, there is
no perceptual similarity by reference to which we can designate the (rough)
boundaries of a concept in advance of defining it. There is no perceptual
“look” to a marriage, to a science, or to most of the categories of things
about which there is serious philosophical disagreement. The upshot is that
the method of settling definitional disputes described above may be
successful, but only for the most uninteresting of cases.
In the final section of this chapter, we will endeavor to see whether
the method outlined above for settling definitional disputes for basic
concepts can shed any light on settling disputes about more abstract
concepts. We will work with examples of competing definitions for a single
philosophic concept that is greatly contested by philosophers and by
members of the public, in general: the concept of political freedom. We will
not attempt to actually settle the controversy, but sketch an outline of a
procedure by which it might be settled by philosophers.
Settling disputes over abstract concepts (e.g., in philosophy)
Consider two passages from two famous philosophers who spearheaded
political revolutions, Thomas Jefferson and Karl Marx. In his first inaugural
address in 1801, Jefferson, author of the Declaration of Independence and
then the third president of the United States, wrote:
268
A wise and frugal government which shall
restrain men from injuring one another, which
shall leave them otherwise free to regulate their
own pursuits of industry and improvement, and
shall not take from the mouth of labor the bread
it has earned. This is the sum of good
government.
Writing 44 years later in his treatise, The German Ideology, Karl Marx
expressed a contrasting view:
In communist society, where nobody has one exclusive sphere
of activity but each can become accomplished in any branch he
wishes, society regulates the general
production and thus makes it possible for me
to do one thing today and another tomorrow,
to hunt in the morning, fish; while In
communist society, where nobody has one
exclusive sphere of activity but each can
become accomplished in any branch he
wishes, society regulates the general
production and thus makes it possible for me
to do one thing today and another tomorrow,
to hunt in the morning, fish in the afternoon,
rear cattle in the evening, criticize after dinner, just as I have a
mind, without ever becoming hunter, fisherman, herdsman or
critic.
These philosophers have a basic difference regarding the concept
political freedom. We might summarize the difference—especially as it
bears on the resulting differences in their overall political philosophies—as
follows:
Jeffersonian freedom: Political freedom is the freedom of
human action from physical restraint by other men, including
the government.
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Marxian freedom: Political freedom is the freedom of human
beings to fulfill their desires by the assistance of other men,
including government.
Notice that each of these two definitions does identify a real similarity in the
world. Physical restraint or force really can hinder human action, and
absence of others’ assistance really can contribute to our failure to fulfill our
desires. At the same time, however, each of these definitions of political
freedom picks out a different set of similarities as relevant to the concept,
and the result is that the two embody incompatible views of what policies or
institutions count as embodying respect for political freedom.
Here are three examples of situations or settings which Jefferson
would count as embodying freedom, as opposed to those which embody the
opposite, slavery:
Figure 11: http://commons.wikimedia.org/wiki/File:Auschwitz_gate_in_1945.jpeg
http://commons.wikimedia.org/wiki/File:Marshall%27s_flax-mill,_Holbeck,_Leeds_-_interior_-_c.1800.jpg
http://commons.wikimedia.org/wiki/File:Fishing_Party_New_Rochelle.JPG
On the left is a picture of a Nazi concentration camp. To the right of that we
see a flax mill in England during the beginning of the Industrial Revolution.
Finally, on the right, a pair of men enjoying their day, “fishing in the
afternoon.” Jefferson would identify the concentration camp as a clear
violation of political freedom. Slave labor is the clearest possible example
possible of restraining human action by “[taking] from the mouth of labor
the bread it has earned.” An afternoon spent on the lake enjoying oneself and
catching one’s own food is probably the closest to the opposite we can
approximate: these men are clearly free. As we shall see, the middle case is
more contentious, but Jefferson would probably agree that as long as these
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workers are being paid for the goods they produce, and as long as they are
voluntarily employed, they too are free (they can quit their job anytime they
like).
The middle case of the factory during the Industrial Revolution is
contentious because these workers are probably not enjoying themselves as
much as the fishermen might be. They probably work in dark and grimy
conditions, and if they choose to quit, they will of course lose their wages.
They may even be blacklisted by their employer, and have a difficult time
finding other work. The middle case is contentious enough that Marx would
classify it an entirely different way, as an example of “wage slavery,” not
genuine political freedom:
According to Marx, if the workers want to gain their freedom, they need to
start a revolution against the capitalists and physically force them to
surrender their wealth, which would then be redistributed for the sake of the
workers and the “good of society” as a whole.
How are we to settle the dispute between these very different
definitions of freedom? It is clearly not enough to use the simple
counterexample method. If we tell Marx, “On your view, working in a
factory during the industrial revolution would count as slavery. But
obviously it is not slavery! Therefore your view is wrong.” This would not
be a successful objection, because Marx would not share the “intuition” that
this is not really an example of slavery. The same problem would arise if
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Marx were to attempt the same style of objection in response to Jefferson.
So the question-begging responses are out.
What about appealing to perceptual similarity? There are no obvious
perceptual similarities to use here. Perhaps some factories looked like
concentration camps, but probably many others didn’t. And it would be
conceivable for dictators to construct gleaming white prison camps without
the slightest bit of grime or smoke, while secretly concealing their crimes
inside. By the same token, there are no obvious visual similarities between
factories and fisheries. Perhaps on some days people involved in each have
smiles on their faces, but perhaps some days not. Perhaps at some of each
people will take home rewards of their efforts, but already this would be
hard to see, and we can imagine days on which nobody catches fish, but
workers do bring home wages. We simply cannot settle in favor of one view
or the other on the basis of perceptual similarity.
Is there any alternative? Is there a substitute for perceptual similarity
that will allow us to draw rough boundaries for our concept of political
freedom in advance of giving a formal philosophical definition? Of course
not all similarities are perceptual. Recall our discussion of the definition of
“game”: we urged that the similarity of function shared by games, the
particular way in which they let us have fun by setting out arbitrarily chosen
goals and rules for obtaining them, was not exactly something we could see.
Solitaire looks very different from soccer, which looks very different from a
video game. So we can find non-perceptual similarities to help us formulate
definitions.
But remember that we’ve noted that the competing definitions each
highlight some important non-perceptual similarity. There really are ways of
restraining human action through physical coercion, and there really are
ways of failing to assist people in the fulfillment of their desires. But
remember also that an important use of definitions is to condense our
knowledge of similarities and differences. The way they do this is by
showing how some similarities follow from others. We noted, for example,
how so many different distinctive traits of human beings are accounted for
by human rationality, and how a cluster of facts distinctive to games (like
the fact that cheating stops being fun) were explained by the special way in
which games help us have fun. So it is not enough that a definition highlight
some (perceptual or non-perceptual) similarity: the similarity also has to be
important. It has to be a similarity on which many other similarities depend.
So what are some facts about freedom that a definition of the concept
might help condense for us? If we knew that, perhaps we could find a
definition that would clearly help explain all of these traits. And perhaps
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only one—Marx’s or Jefferson’s—would be the one to do it. Here is a list of
a few points that most people agree on about freedom, regardless of their
political philosophy:
 Protecting political freedom is the job of the government.
 Political freedom is worth fighting for.
 Political freedom is good.
The trouble is that within the philosophic frameworks of Jefferson and
Marx, there are reasons to think that the related definition of freedom
encapsulates a fact that explains each of these additional facts.
Each of the other items on the list depends on the claim that freedom
is good (we only want to fight for and
protect what is good). Why is freedom
good? If we are Jeffersonians, we think that
the need for freedom of human action
depends on the need for freedom of human
thinking. This is an idea born of the
Enlightenment-era conviction that reason is
the distinctive human trait, the use of which
is necessary for science and industry and a
series of other distinctively human modes
of flourishing. Underlying this attitude is
the conviction, eloquently expressed by
Bacon, that nature, to be commanded, must
be obeyed. On this view, it is nature, not
human beings, that is to be manipulated
Figure 12:
and molded—and the only way to
http://www.flickr.com/photos/timbirch/4316651552/
accomplish this goal is to leave human
minds free to think and act.
But if we are Marxists, we are skeptical about the all-important role
assigned to human reason by the Enlightenment. Marx was a materialist who
thought that ideas were mere byproducts of an underlying economic reality,
rationalizations used by members of one class to entrench their power over
another. Thus it is not our ideas but our physical desires that make us who
we are, and Marxists think that more human beings desire to be free from the
need to work for capitalists than think otherwise. In contrast with the attitude
of “nature, to be commanded, must be obeyed,” Marx famous announced in
his Theses on Feuerbach, “The philosophers have only interpreted the
world, in various ways; the point is to change it.”
273
The other traits associated with freedom are also accountable by
Enlightenment and materialist worldviews. Freedom is worth fighting for if
you think life isn’t worth living without freedom. If you accept the
Enlightenment world view, you attach special importance to the values of
the mind. Living life well-fed in prison is, perhaps, a good life for an animal,
but not for a thinking human being. But a Marxist materialist attaches less
importance to values of the mind, and therefore less to the importance of
unimpeded action and thought. To the materialist, it is not our minds but our
bodies that define us, and nothing else matters to a body if it is hungry.
Likewise, we need government to protect freedom according to a
Jeffersonian not only because freedom is good, but because a centralized
body is needed to protect individuals against the main wielders of coercion:
criminals and foreign governments. By contrast, the Marxist needs
government to assist in the fulfillment of human desires because only such a
centralized body can efficiently administer the collective redistribution of
wealth from the capitalists to the people.
So how do we decide between these two competing conceptions of
political freedom? It’s not a question we will answer here. It is a question
whose answer depends on answering some of the more fundamental
questions raised by philosophy. As you should see, basic philosophical
differences between the Enlightenment
and anti-Enlightenment views account
for the resulting differences over the
proper definition of political freedom.
Do we have free intellects, or are we
basically just physical beings, not
essentially different from animals? Do
we survive best as individuals, or as
members of a collective? Does reality
Figure 13:
have an objective nature of its own we
http://www.flickr.com/photos/bunchofpants/4866379452/
must be left free to discover, or is the
idea of objectivity an illusion crafted by capitalists to rationalize their
position in society?
Answering these philosophical questions would help determine
whether a given account of freedom really does explain why freedom is
good, and why it is worth fighting for and protecting. If it turns out that the
power of human reason is far less distinctive and far more limited than
Enlightenment thinkers held, it would follow that political freedom is not
needed to secure the freedom of the mind. It would follow, instead, that the
274
focus of politics would have to be the fulfillment of human desires,
regardless of the needs of the mind.
The picture we have painted of the difference between Enlightenment
and anti-Enlightenment philosophy is, perhaps, oversimplified in a variety of
ways. We have used the example to illustrate that one’s standards of
theoretical importance are what make some similarities appear more
important than others. This could be true even if basic philosophical
premises do not crisply determine views in politics; it is enough that these
premises condition ethical and political attitudes.
And this point about the relevance of standards of importance is not a
point reserved only for assessing philosophical definitions. Any science will
make similar judgments based on its premises. This is in keeping with the
emphasis we have placed in this book on the importance of background
knowledge. Consider, for example, the question of how to define the
element “gold.” Recall that in chapter 12, we discussed how its definition
shifted in time from “gold is a yellow, malleable metal, soluble in aqua
regia,” to “gold is the metal with atomic number 79.” This shift occurred
because of changes in basic background knowledge in physics. Physicists
discovered that differences in atomic number were far more theoretically
important than differences in color or malleability. Atomic number explains
these superficial physical properties along with still others, whereas we can
even envision creating gold in liquid or gaseous form that no longer exhibits
these properties.
We do not think that scientists are wrong when they say that the
definition of gold in terms of atomic number is objectively superior to the
older definition in terms of observable properties. If there is reluctance to
think that we can find objectively superior definitions of abstract
philosophical concepts, it is only because the methods of philosophy are less
well understood than the methods of the scientist. Science has made great
progress over the years, but if you line up a thousand philosophers head to
foot, they are never likely to reach a conclusion. Then again, philosophers
have relied mostly on the method of intuition for settling their philosophic
disputes. It is no wonder there is so much disagreement. Perhaps if
philosophers begin to model their method of defining concepts on the
methods of the sciences, and begin to think about how their definitions relate
to their fundamental philosophic background knowledge, they will begin to
make more progress.
Still, philosophers will not be able to avoid the issues that are
distinctive and fundamental to their discipline: basic questions about the
nature of the mind, the nature of the good life, and the nature of the world,
275
questions that separate the “queen of the sciences” from her loyal subjects in
the specialized sciences. Philosophers still debate about the nature of
philosophical knowledge: is it derived from “pure reason,” or from
observation of the world? How we end up deciding this question may also
determine the view we take of definitions of philosophical concepts. Perhaps
some of them require a form of “intuition” to be tested again. But the matter
is not settled.
If you are interested in learning more about the basic positions
philosophers have taken on these questions, and the methods they use to
answer them, you will need to go beyond an introductory logic class, and
study philosophy. We hope you decide to do so.
276
§5: INDUCTIVE LOGIC
Chapter 14:
Induction and deduction
Ben Bayer
Drafted March 28, 2010
Revised August 21, 2010
Two different functions of inference
From the beginning of this book, we have emphasized that the general
function of logical inference is to help us acquire new knowledge about what
we cannot directly observe on the basis of what we can. We have used
several analogies to bring out this point. Logic is like a telescope: it is a tool
we use to extend the range of our ordinary sensory knowledge. Or, logic is
like a tower: we ascend by a step-by-step method from our basis in the
evidence so that we can know more than what we directly see. Or, logic is
like a tool: with it we use our hands to accomplish what they cannot on their
own.
It turns out that logic can help us acquire knowledge of new
conclusions in one of two importantly different ways.
Here’s a new analogy to bring this out: logical
inference is like bringing luggage on a trip. First you
need to pack it, and then you need to unpack it and do
things with the items you packed. Some kinds of
logical inference help us pick and pack the items in
our journey of knowing. Others kinds help us unpack
our knowledge and know what to do with it. The
remainder of this book will reflect on each of these
two functions of inference and zoom in on what we
know about the rules that govern each of them.
In the present section, we need mainly to
Figure 14:
http://www.flickr.com/photos/geishab clarify the difference between these two functions,
oy500/2580661428/
and we need to go beyond the analogy offered in the
previous paragraph to do so. Let’s first say a word about the “packing”
function of inference. One reason we need logical inference is to help us
gather together our many different observations of the world, and condense
or digest them into some useable form that will inform our future thinking
and acting. The form in which our knowledge serves this purpose is a
general or universal form. Rather than retaining a memory image of every
single table we’ve ever seen, we form a universal concept of “table” that
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helps us identify the facts about tables that are most important, which helps
us make predictions about future tables we will observe and deal with. In our
chapter on definitions, we discussed this knowledge-condensing function of
concepts when we discussed the rule that definitions should state an essential
characteristic (we discusses the example of “human being” and “game”). We
learned, for example, about how identifying human beings as rational
animals enabled us to understand how human beings are also tool-using
animals, language-using animals, animals with a sense of humor, etc.
When we discussed definitions, we tried to show how some
definitions are better than others. There are rules governing definitions,
advice that logic has to give for how to construct them. Since definitions
help us to acquire and retain universal knowledge about the world, and logic
helps guide our formulation of definitions, this was our first example of
logic’s role in helping to “pack” our knowledge into a useful universal form.
But forming a definition presupposes we have already formed the universal
concept we are interested in defining and that we have used this concept in
various generalizations. This “packing” function of logic is referred to as the
process of inductive inference. Induction is the form of inference that
generates conclusions taken to be wider (more universal) in content than the
observations contained in the premises.
Why do we need a logic for induction, a step-by-step method to guide
us in the “packing” together of our
knowledge? Think about why we need a
method in packing things for a trip. We
know we can’t just dump the contents of
our bureau drawer into a suit case, as we
see in movies when people decide they
need to leave right away. It will be too
much for our suitcases to fit, and we’ll
never be able to find anything later. We
need to select the most important items and
Figure 15:
arrange them in an order that will help us
http://www.flickr.com/photos/jeffwerner/2677245039/
retrieve them later as needed. In the same
way, we need a method to help us decide how to pick observations that are
the most relevant and assemble them in a way that allows us to store them in
a form that can be retrieved most easily for later use. We have already seen
how logic offers us advice for the formulating of definitions, which is a big
part of the inductive guidance it gives us. There is more.
But we would suffer from a strange neurosis if we enjoyed packing
our bags as an end in itself—if, when we got to our destination, we refused
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to unpack our bags because we didn’t want to ruin the nice order we’d put
all of our things! We pack our bags before a journey for a reason: to be able
to use our items once we reach our destination. In the same way, we put our
knowledge in universal form to use it. We live in a world of individual
things, not in a world of abstract universal objects. If we want the packing
function of our knowledge to serve a useful purpose, we need a method of
unpacking our knowledge that enables its use. The branch of logic which
guides us in this “unpacking” function is deductive logic. Deduction is the
form of inference in which the conclusion states no more content than that
stated in the premises (and is necessitated by them).
As in induction, we need a deductive logic because we can’t just
unpack our knowledge any way we like. If we unpack our luggage by
dumping its contents onto our hotel bed, we’ll make
a mess and not be able to find items later when we
need them. It helps if we unpack step-by-step, just
as we packed step-by-step. Also: if we unpack our
luggage in a specific, step-by-step way, so that we
have access to all of the different items we brought
with us, we’ll be able to combine and recombine
these items (for instance, items of clothing) in the
most suitable way. In the same way, unpacking our
knowledge in a step-by-step way helps us to see
new relationships among items of knowledge,
relationships we might not have seen otherwise.
Figure 16:
http://www.flickr.com/photos/rutthenut/ This is part of the reason that deductive inference
3172291758/
really is a form of inference: it allows us to see new
things implied by our older knowledge.
In the subsections that form the end of this section, we will briefly
illustrate these distinctive functions of inductive and deductive inference.
This entire chapter serves as an introduction to the topic of induction, so in
order to understand fully just what induction is, we need to contrast it with
deduction. For that reason, we will focus first on some examples of
deduction and then contrast them with induction before ending this section.
In the concluding sections of the chapter, we will say a little more about
what we know about how induction works.
Deductive inference
Consider a simple and famous example of a deductive inference, the
“Socrates syllogism”:
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All human beings are mortal.
Socrates is a human being.
Therefore, Socrates is mortal
A syllogism is just a deductive argument with two and only two premises.
We will study syllogisms in much greater detail at the end of this book. The
above is a classic stock example in many a logic text, but there is a good
reason for its widespread usage. It illustrates the importance of the
“unpacking” function of deductive logic.
Socrates was an amazing philosopher. He would accost citizens of
Athens in the street and engage them in conversation, asking them questions
they had never thought before to ask themselves. His ability to dig into the
deepest questions about the nature of virtue and the soul made him unique
among his fellow Athenians. His philosophical questions made him so
unique that he eventually angered the leaders of Athens enough to cause
them to put him on trial for spreading atheism and corrupting the youth of
Athens. He was sentenced to death. Some of his followers might have
entertained the idea that Socrates’ unique philosophical abilities reflected a
mark of the divine. Perhaps, they might have thought, when Socrates was
administered the poisonous hemlock prescribed by Athens, he might not die.
But however impressive his intellect, Socrates would have been the first to
remind his followers that yes, even he, even great Socrates, was still but a
man, a human being, and because human beings are mortal, he was mortal as
well.
We can see how a deductive syllogism like
this “unpacks” the implication of our previous
knowledge with a simple circle diagram. To say
that all human beings are mortal is to see the
circle of “human beings” as entirely contained
within the circle of “mortals.” To say that
Socrates is a human being is to see his (smaller)
circle as entirely contained within the circle of
human beings. But we cannot see the smaller
circle as contained in the middle circle without seeing it as contained in the
bigger circle! We might have held “All human beings are mortal” and
“Socrates is a human being” as completely separate in our mind. If we had
not put them together in the manner of this syllogism, we might have been
tempted to forget that Socrates, too, must be mortal. Once we put them
together, as represented by this diagram, we see that we cannot avoid seeing
the additional containment relationship: if the smaller circle is contained in
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the medium, and the medium in the bigger, then the smaller is contained in
the bigger, and Socrates will die.
Here is another example of the way deductive arguments bring out
new relationships among our existing items of knowledge.
Aristotle is taller than Plato
Plato is taller than Socrates
Therefore, Aristotle is taller than Socrates.
Adding to this the fairly obvious assumption that being taller than is a
transitive relationship, the relationships represented in the first two premises,
when combined, help us see a new relationship, represented in the
conclusion. We can see this with another diagram. We might have just
focused on the relationship between
Aristotle and Plato, or the separate one
between Plato and Socrates. Without
widening our focus to see how these two
relationships relate, we might not have
noticed that Aristotle is taller than
Socrates. But, as you can see, once all
three are lined up, you cannot see
Aristotle as taller than Plato, and Plato as
taller than Socrates, without seeing Aristotle as taller than Socrates. A
deductive argument has much the same function: it “lines up” knowledge in
our mind for the same purpose of helping us see new relationships among
existing items of knowledge which we might not have seen before.
One feature of deductive argument is that since it is mainly concerned
with unpacking new relationships among existing items of knowledge, it
deals with formal relationships among our knowledge. That is, it deals with
the overall form or “shape” our knowledge, rather than with the material, the
“stuff” of our knowledge. Think about the difference between the shape of a
statue, and what the statue is made of. We can make the same statue, say, of
David, of many different materials—clay, marble, plaster—but as long as it
is the same shape, it has the same form regardless of the material. You can
see how deductive arguments deal with formal relationships by noting that if
we substitute dinosaurs for philosophers, the same kind of deductive
argument still works:
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Dinosaur A is taller than Dinosaur B.
Dinosaur B is taller than Dinosaur C.
Therefore, Dinosaur A is taller than Dinosaur C.
It doesn’t matter what material we are
reasoning about, philosophers or
dinosaurs—or even philosophers who are
dinosaurs—the same kind of argument
applies to each. Deduction helps us unpack
the implications of our knowledge by
finding new relationships among the items
of our knowledge, and it does this by noting
formal relationships among these items.
You might think that if unpacking the implications of our knowledge
is all that deduction does, it doesn’t do much that is very interesting. This
would be true if we restricted ourselves to these very simple two-premise
deductive arguments. But deduction can help us discover even more
complicated relationships among items of our knowledge, relationships we
might not be able to “see” just by lining up everything we know in front of
us. Consider the following riddle:
Brothers and sisters have I none, but this man’s father is my father’s
son.
The challenge of the riddle is to determine who is this man. The riddle
contains all of the information needed to figure out who this man is, but it is
a little challenging. We can stare at the riddle for some time, but unless we
“unpack” the information it contains in a careful, step-by-step way, we will
not be able to figure out who “this man” is.
The content of the riddle effectively provides us with two premises.
We can get everything else we need from these two premises:
1. This man’s father is my father’s son.
2. Brothers and sisters have I none.
Let’s now see what we can get from these two
premises. Who is “my father’s son”? This could
be any number of people, depending upon how
many sons my father has. It could be me, but if I
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have brothers, it could also be one of my brothers. So this gives us a new
premise, deduced from the first, and from our knowledge about what it
means to be a “father’s son”:
3. My father’s son is me or my brothers.
It would be nice if we could whittle this down further. The second premise
lets us do so, because we have been told “brothers and sisters have I none.”
If I have no brothers and sisters, then I have no brothers, and my father’s
only son is me. This gives us an additional premise:
4. My father’s son is me.
If we know #4, it gives us knowledge we can substitute into our original
premise #1, which gives us:
5. This man’s father is me.
Premise #1 used to read “This man’s father is my father’s son.” But we now
know, from premise #4, that “my father’s son” has to be me, so This man’s
father is me. Now let’s just rephrase this into more ordinary language:
6. I am the father of this man.
Remember, our original riddle was: who is this man? Well, which man am I
the father of, if I am the father of any man? The answer can be stated as the
conclusion of this deductive argument:
7. This man is my son.
Here are all of the steps we used to get this
answer:
1.
2.
3.
4.
5.
6.
7.
This man’s father is my father’s son.
Brothers and sisters have I none.
My father’s son is me or my brothers.
My father’s son is me.
This man’s father is me.
I am the father of this man.
This man is my son.
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The point of the preceding example is that when deductive argument
unpacks information in the right step-by-step procedure, it can show us new
relationships among our old items of knowledge which we might not have
been able to see, just by lining up the right items of knowledge in the right
way. This makes deduction exceedingly useful in fields where complex new
relationships can be very important, as in math and science.
There is one last point to make about the use of deductive reasoning.
If you’ve ever heard the term “deduction” before, you’ve probably heard it
in connection with the famous literary figure, Sherlock Holmes, who
famously chided his partner, Dr. Watson, for failing to see various
“elementary deductions” that could be made from various observable facts.
Some philosophers will chide the author, Sir Arthur Conan Doyle, for
characterizing some of Holmes’ logic as deductive when sometimes it
involved other forms of reasoning. But Holmes would routinely use
deductive reasoning, as would any detective who makes the following kind
of argument:
Either the killer was Jones or Smith.
The killer could not have been Jones (he has an alibi) .
Therefore, the killer was Smith.
Using this “process of elimination” (which we examined earlier in chapter 7,
and will examine more in chapter 19) is the hallmark of Holmesian
reasoning. Holmes himself said “When you have
excluded the impossible, whatever remains…. must
be the truth.”58 It is true that in order to establish
the truth of these two premises, more than
deduction is required. And one or the other of the
premises may be uncertain, in which case the
conclusion must be proportionately uncertain, as
well. But the process of unpacking these premises,
regardless of the degree of certainty we assign to
them, is surely a deductive process.
Holmes or any good detective will use
deduction for more than just establishing
Figure 17:
knowledge of specific conclusions. The same
http://commons.wikimedia.org/wiki/File:
Statue_of_Sherlock_Holmes_in_Edinbur “unpacking” function helps us to unpack the
gh.jpg
58
Sir Arthur Conan Doyle, The Sign of the Four (1890), Chap. 6, p. 111.
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implications of things we don’t know—perhaps the implications of
hypotheses whose truth we are merely considering. For instance:
(Suppose:) Smith was the killer
If Smith was the killer, then the killer has escaped. .
Therefore, (on our supposition) the killer has escaped.
Perhaps we do not know that Smith is the killer. But we want to know what
follows deductively if he is the killer. Maybe we need to know this in order
to make some contingency plan. Perhaps we are pretty sure that Jones is the
killer, but we want to know what we should do if it turns out that we are
wrong. We might need to make plans to find the resources to set up a
dragnet in case our other conclusion proves wrong.
Inductive inference
Now that we have a fairly good idea of what it means to unpack and
apply our knowledge using deductive inference, we can begin in earnest the
overall point of this new unit, which is to understand what we can about the
rules of induction.
So far we have compared the function of inductive inference to
packing our luggage: we need some method to condense together many
observations of the world in a retainable, universal form, so that we can use
this knowledge later, applying it deductively to new situations in which our
action must be guided by our knowledge. We have said that this process
involves the formation of universal concepts (like “table” and “human
being”) which help us avoid having to remember every single table or
human being we encounter. But single concepts alone will not give us
knowledge of the world, or at least none that is very useful. To apply our
concepts usefully, we need to be able to know propositions like tables must
be sturdy, or human beings can be friendly. How does induction work to
give us these generalizations about tables or human beings?
The answer to this last question is not completely well understood. In
the concluding sections of this chapter, we will explore some hints that help
us see better how induction works. For the time being, we need to get clear
on just what function induction performs, what it means to generalize.
Consider a key premise in the Socrates syllogism discussed in the
previous section: “All human beings are mortal.” Without this premise, we
could not know that Socrates is still mortal. But what does it mean to know
that all human beings are mortal? We have not seen every human being, let
alone seen them all die? All of the ones we know right now are not dead.
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Most of us, of course, knows of someone
who died. Suppose we know of three people
who have died. We can represent this
knowledge using the same kind of circle
diagrams we used to understand deductive
syllogisms in the previous section. What this
diagram shows is that A, B, and C are human
beings: they are entirely contained in the
circle of human beings. Because they are also entirely contained in the circle
of mortals, the diagram shows that they are (or were) mortal—which we
know because they are now dead. Notice that the diagram also shows one
additional relationship: the circle of human beings is entirely contained in
the circle of mortals. What statement does this translate into?: All human
beings are mortal, the desired premise in the Socrates syllogism.
But there is a problem. The same observations, that A, B and C are
human and that they are mortal, are consistent with a very different diagram.
Consider: Since this shows A, B and C to be entirely contained within both
circles, it is consistent with our observations
that all three were both human and mortal.
But this diagram does not show the truth of
the premise that was required for the Socrates
syllogism. It does not show that all human
beings are mortal. What does it show? That
some human beings are mortal (and these just
happen to include the three we knew), and
that others (whom we’ve never met) are not
mortal—apparently they are immortal and will never die. If we take this
diagram seriously, we have to think that maybe we are one of them and will
never die ourselves.
The problem here is the same regardless of how many additional
people whose death we know about. Even if we know that D, E, F, G, H, I, J,
etc., were each both human and mortal, it might be that they fall in the left
side of the “human being” circle, and there are other human beings we have
not observed who are not mortal. Some philosophers think this means there
is a special problem about whether inductive knowledge is even possible in
the first place. If we have to start with our observations, and our
observations are consistent with two different conclusions, how do we know
which one is correct? How do we know that there aren’t any immortal
human beings?
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Nevertheless, we all assume that death is certain. Some say “death and
taxes” are the only certainties in life. Some find ways to cheat on their taxes,
but nobody seriously thinks they can cheat death. Even if we take it for
granted that there can be no doubt about our inevitable death, the
philosophers’ puzzle about induction has some value. Even if inductive
reasoning does provide us a way of knowing one conclusion rather than the
other, the puzzle helps us see that induction takes us beyond what we
observe, it delivers generalizations. There is a serious and legitimate
question about how induction manages to do this. How does it assemble
evidence in a way that points to one conclusion (that all human beings are
mortal) and not the other (that only some are mortal)?
You might be tempted to say that we could know all human beings
are mortal by deducing it from another premise. For instance:
All animals are mortal.
All human beings are animals.
All human beings are mortal.
In fact it is quite likely that this is how we
know that all human beings are mortal! We
are in fact animals, and we also know that
all animals will die some day.
Remembering our animal nature, another
diagram would clarify why all human beings are mortal. Our mortality is not
something that flows distinctively from our being rational animals.
(Rationality is no special curse, contrary to what some existentialists say!)
The trouble is that deductions like this can only go on for so long. We
still have a question about how we know that all animals are mortal. We can
imagine deducing this from still other
propositions. But we cannot do this
forever! Our premises cannot go back into
infinity! We have to start somewhere.
Eventually, we will have to start with
premises that are connected more closely
to observation, and which are not as wide
in scope as the conclusion we are arguing
for. Here is one example of some
important reasons we might give for the conclusion that all human beings
are mortal:
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We have observed that many people have died in the past.
We know of no one alive today who is older than a particular age.
All living things we know are on a continuum of growth and decay.
Living bodies are delicate mechanisms in which much can go wrong.
Therefore, all human beings are mortal.
We will return to discuss this example in the next section.
Induction and deduction, conclusion
We have defined induction as a form of inference that generates
conclusions taken to be wider (more universal) in content than one’s
observations, and deduction as the other form as a content-preserving form
of inference.
Many philosophers think that deduction and induction should be
defined in terms of the different degrees of certainty they yield. Many say
that induction only yields conclusions with some degree of probability given
the premises, whereas deduction yields conclusions that must be true, given
the premises.
These definitions have some merit to them, but it only goes so far. It is
true that deduction involves a special kind of certainty not found in
induction. We discussed this earlier in chapter 7 when we talked about how
deductive certainty is generated by stated premises alone, whereas what
certainty there may be in other forms of inference is established by the
totality of one’s knowledge, which is not always easily stated. What’s more,
it’s probably true that induction can sometimes be merely probable.
But these definitions are of limited value. To this author, they do not
seem to define the concepts in essential terms. If induction really does yield
probability or a different kind of certainty, then it does so because it delivers
conclusions that are wider in scope than its premises. If only deduction
delivers certainty or that special kind of certainty, then that is because its
conclusions are limited only to the content of the premises.
Second, it is philosophically controversial whether only deduction
yields conclusions with certainty. Everybody thinks that death is a certainty,
but it is a conclusion that has to be induced. Everybody thinks no other
conclusion is possible given our evidence. So philosophers may be relying
on a different definition of certainty and probability than ordinary people do.
If so, there is a serious question about why they think their definition of
these concepts is better.
We will not wade any further into the debate about the relative
certainty of induction and deduction, or how to define these concepts.
288
Instead we will round out the chapter by presenting more positive material
about what induction is and how it works. This will not only help us get a
better idea of the nature of knowledge delivered by induction, but prepare us
for the chapters that follow in this book about popular fallacies of induction.
The “rules” of induction are poorly understood in comparison with
those of deduction. But they are more practical: once we acquire many of
our inductive generalizations, we don’t usually need much knowledge of
deduction to know how to apply them. This is the reason we’ll study
induction first and only conclude with a
discussion of deduction.
We opened this section by drawing
an analogy between logic and “packing”
luggage. We have worn that analogy out!
But here is one last analogy: logic is like
a bridge. Logic helps us build a structure
to take us above our ground in the
Figure 18:
evidence, but we only need to rise above http://www.flickr.com/photos/dkilim/2937395933/
that ground in order to move to new ground. One end of the “bridge” of
logic is the process of induction; the other is deduction.
Basic and advanced forms of induction
We now have a much better idea of what it is to have performed an inductive
inference: it is to have formed a generalization over and above the particular
observations we’ve made. But how do we form such generalizations, and
what kind of evidence do we appeal to? We have already seen that there is a
problem about whether we can ever have enough of the right kind of
evidence to form the generalizations we think are true. (How do we know
that it’s not just some human beings who are mortal?) How we think our
evidence for these generalizations will help move us toward a solution to
this problem, but also help us understand generally what makes for good as
opposed to fallacious induction?
The most basic inductions
We have already seen that it is a mistake to think of the most basic
form of induction as a simple matter of counting instances. It is not enough,
for example, to enumerate people we know who have died, in order to
conclude that all men are mortal. Knowing the fact that some have died in
the past is relevant to coming to this conclusion, but it is far from all of the
relevant evidence. It is easy to illustrate that it is not enough by considering
this example:
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Ryan has taken college classes.
Kelly has taken college classes.
Ben has taken college classes
…
Therefore, all human beings have taken college classes.
We could just as easily enumerate people in a class, notice that they have
taken college classes, and conclude that all people have taken college
classes. But no one would accept this argument; most would realize that
there is nothing about being a human being that makes it necessary to go to
college. (Contrary to the pretensions of many college professors.)
What makes the difference between a conclusion like this—that all
people have taken college classes—and another, more sensible induction?
We assume that there is some sensible induction that leads the conclusion
that all men are mortal. Compare these conclusions:
All human beings are mortal.
All human beings have taken college classes.
There are probably many interesting differences between whatever good
argument has the first as a conclusion, and the bad argument we’ve just
considered that has the second. But there is one interesting difference in type
we can observe just between these two conclusions. In the first, we can see
some connection between the concepts involved in the statement, whereas it
is harder to see any such connection in the second. It is not that the first is
simply a matter of definition, though the definition of “human being” is
informative here. Human beings are rational animals. The fact that they are
animals, a kind of living creature, seems to have something to do with the
fact that they are mortal. (We will say more about this possible connection
later.) In the second example, however, the connection is much looser. It’s
true that being a human being is what makes it possible for us to acquire
conceptual knowledge and gain value from college classes. But of course
there are many different ways to learn, and not all of them involve college,
so the connection between being a human being and having taken a college
class is very weak.
This difference we have just noted between these two conclusions
give us a clue about what kind of evidence counts in favor of good
inductions. It should be the kind of evidence that lets us see connections
between concepts. One form of knowledge that helps us see connections
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between concepts is knowledge of cause and effect. If one type of thing
causes a certain type of event, then our concept of the type of thing will also
have a connection to the concept of the type of effect. Consider the
following examples of generalizations that look to be the products of
induction. There are causal connections that each of these generalizations
help us to identify.
All balls roll.
All knives cut.
All human beings are mortal.
The simplest example on the list is “All balls roll.” (We should read this as
meaning “All balls are capable of rolling”—
nobody would say that they’re rolling all of the
time.) This generalization reflects the fact that
there is something about the nature of a ball
giving it the power to roll. Much the same is
true of the second example. Someone who
Figure 20:
knows that knives cut knows that there is a
http://www.flickr.com/photos/wonderlane/38737
connection between what it is to be a knife—
02464/
i.e., to be an object of a certain size, shape, and structure—and what it is to
rend apart material. The last example is
different from the first two, at least in that it is
harder to see how it is a claim about cause and
effect. But we should still realize that the kind
of connection in this example missing in the
example about all human beings having taken
college classes is something about how the
nature of human beings (as living things) is
responsible for their mortality—and that, too, Figure 19:
http://www.flickr.com/photos/matthijs/311853
is a causal claim. What exactly that is, we’ll
9905/
examine shortly.
The suggestion that inductive generalizations are based on knowledge
of causal connections will only help us to a limited extent. After all, how do
we know of connections between cause and effect? If that knowledge is at
least as challenging to obtain as the inductive generalizations themselves,
then we’re in no better position to understand how induction works. And
indeed, a great deal of our knowledge of cause and effect is of subtle
connections that are not evident to the senses. A great many such
connections require inductive knowledge to be discovered, so they cannot
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explain the origin of inductive knowledge. Some philosophers (such as the
18th century philosophy David Hume) believe in principle that no causal
connections can ever be observed with our senses. Arguments back and forth
on this matter are long and drawn out, and we will not wade into them here.
The author of this text, at least, thinks that there are at least some
fairly simple and obvious causal connections that we might be able to know
about by sheer observation, provided that they are connections between
observations of things and the way they act.59 Consider the first two
generalizations on our list above: “All balls roll” and “All knives cut.” We
said that both of these generalizations might reflect knowledge about the
connection between the nature of balls and rolling, and between the nature of
knives and cutting. But what are these connections, and how can we see
them? It is nothing overly sophisticated. We see a ball’s roundness, and we
see a knife’s sharpness. Furthermore, we cannot see a ball as rolling without
seeing it as round, and we cannot see a knife as
cutting without seeing it as sharp. Try to imagine
a non-round thing rolling. Perhaps you can
imagine a square “wheel” rolling. But then the
wheels will carry the vehicle up and down, up and
down, and it will not be rolling very well. One
might argue that this is not really rolling at all.
Likewise, try to imagine a non-sharp thing
cutting. Perhaps you can imagine a blunt object
rending apart fabric, like a heavy steel beam that
rips apart the threads of a sail as it makes contact.
But once again, this is not really cutting. Cutting
is a precise kind of rending, in which a small
hairline break causes whole parts of a substance
to come apart. We see a connection between the shape of the cutting object
and the cutting itself, in that we see the cutting blade fitting perfectly into the
shape of the tear, and proceeding at the same rate as the tear.
Observing these connections between things and their actions does not
yet establish any general knowledge, of course. The process of forming
concepts like “ball,” “round,” and “roll” is a complicated process which we
cannot describe in detail here. But if we see examples of balls as against
other types of objects (say, cubes), seeing this contrast helps us form the
concept of “ball.” If we take a piece of clay and change its shape from a ball
Figure 21:
http://www.flickr.com/photos/25831992@
N03/2724551187/
59
For more details on the theory that we can directly observe causal connections, see Rom Harre and
Edward Madden, Causal Powers: A Theory of Natural Necessity, Blackwell: 1975, and David Harriman,
The Logical Leap, New American Library: 2010.
292
to a cube, keeping the material the same but changing the form, seeing this
contrast helps us form the concept “round.” Similar comparisons and
contrasts would be involved in forming the concept “roll.” If we can form
these concepts on the basis of observation, we can string together the
concepts into statements like “All balls roll” and “All knives cut” on that
same basis.
Advanced induction building on basic induction
We want induction to give us far more knowledge than just that about
balls and knives, of course. The knowledge that all human beings are mortal
is surely something we can’t just observe. We observe a tiny number of
actual deaths (if we are even so unlucky), and whatever property of human
beings is responsible for their mortality is nothing as simple as their shape,
and therefore not so easy to observe. But with simple observations and the
inductive generalizations they help furnish, we have material we can use to
build more advanced inductions.
Consider some of the simpler observations and generalizations from
them that might be relevant to understanding why all human beings are
mortal. The difference between living beings and non-living (inanimate)
beings is quite observable, for instance. Living things seem to move
themselves, whereas inanimate beings are pushed and pulled around by
external forces. Once we
have focused on living
things and formed the
concept of “alive,” we
can start to think about
what a living things needs
in order to stay alive. We
observe living things
moving towards certain
types of things (“food”)
and away from others (“danger”). We notice that in order for them to move
towards the good things and away from the bad things, their bodies need to
be in the right shape. If they are missing limbs (or other important parts)
they won’t be able to move to the good things and away from the bad ones.
But looking even more carefully at them (and at ourselves), we discover that
there are many different ways in which living bodies can fail to be in the
right working order: they are extremely complicated and intricate
mechanisms, which must be arranged in just the right way for the whole to
function properly. The longer a body exists, the more time there is for things
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to fall apart. Therefore the longer it exists, the chances of its reaching its
survival goals increase. At a certain point, it is simply no longer possible.
All living things are mortal.
The preceding paragraph, however more advanced than the simple
forms of observation we discussed earlier, is still probably an oversimplified
representation of the actual knowledge needed to realize that all living things
die. We have neither discussed all of the necessary observations of
particulars, nor all of the different concepts that would need to be formed for
these types of particulars and their actions and relations to each other, nor
illustrated all of the separate lower-level inductions that form the basis for
the ultimate induction we end with. We have only tried to convey how there
is a difference between simpler and more advanced inductions, and so it is
possible that advanced inductions can have a basis in the simple—this helps
calm worries that such inductions might be circular.
Advanced induction building on advanced induction
Induction can be even more advanced than the examples we’ve just
discussed. In this last section, we will mention three kinds of inductive
inference that build upon already advanced induction, and form the basis of
much of modern science.
Consider the difference between these two inferences60:
Some samples of the element bismuth melt at
271˚C.
Therefore, all samples of the element bismuth
melt at 271˚C.
Some samples of wax melt at 91˚C.
Therefore, all samples of wax melt at 91˚C.
Scientists will find the first compelling, but not the
second. Why? There is an important difference
Figure 22:
http://commons.wikimedia.org/wiki/ between bismuth and the substance wax. Bismuth is a
File:Bi-crystal.jpg
chemical element: it is nothing but atoms of a single
kind (with a single atomic number). Wax, by contrast, is a substance that is
formed from a variety of different, complex organic molecules (it is a lipid,
like fat). Part of what it is to be a chemical element is to have a number of
uniform properties, each of which follows from the fact that this element has
60
I borrow these examples from John Norton, “A Material Theory of Induction,” Philosophy of Science,
70(October 2003), pp. 647-70.
294
a certain atomic number, and therefore a certain orbital electron structure.
There is an entire theory of physics and chemistry behind the first inference:
because we know already know what an
element is, and because bismuth is an element,
it is highly likely that determining the melting
point of a single sample of bismuth will help
us determine the same for all such samples, at
least with a very high degree of probability.
This is not the case for wax. Because there are
many different kinds of wax molecules, and
Figure 23:
because they are molecules (and have more
http://commons.wikimedia.org/wiki/File:Montana_
complicated properties than elements), it is not 10_bg_061905.jpg
as easy to know that the melting point of one sample of wax will tell us
anything more about other samples of wax.
The lesson of the above is that advanced inductive generalizations can
be built on previous advanced inductions (such as general theories in physics
and chemistry). The background knowledge furnished by previous
inductions can be crucial in deciding whether or not a given piece of
evidence is relevant to a conclusion. We will have occasion to see more
examples of the importance of inductive background knowledge in future
chapters on induction. Here are two last examples of how background
knowledge plays this role.
We all know that science works primarily by experimentation.
Experimental reasoning is a form of inductive reasoning we will explore in
more detail in chapter 16. Unlike other forms of induction, experimentation
crucially involves active manipulation of our data. Consider a famous
experiment, first conducted by Louis Pasteur. The evidence of the
experiment and its conclusion might be summarized as follows:
Purified broth sealed from the air shows no growth.
Purified broth exposed to the air shows growth.
Therefore, mere exposure to the air causes growth.
Before Pasteur popularized the results of this experiment, some people
thought that putrescence and decay might be caused by material inherently
present in the putrefying, decaying material. If a rat was found with worms
and the stench of death, it was thought that something inside the rat must
produce such worms and decay. In performing his experiment, Pasteur drew
on two important pieces of background knowledge to come to his conclusion
that this spontaneous generation was impossible. Knowing that something
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had to cause the decay of organic matter, he knew that this something had to
be something in contact with the matter. But that contact could come from
the inside or from the outside. He sought to test whether it could come from
the outside. What’s more, he knew, in the background, that he, the
experimenter, could cause things to happen in the world. If, using samples of
the same vat of broth, he knew that he had exposed one to the air and left the
other sealed, he could reasonably infer that this was the only difference
between the two of them. And so if they began to exhibit a difference later
(one putrefied, and the other did not), then he could reasonably believe that
this was the result of the one difference, exposure or non-exposure to the air.
This second piece of background knowledge, about the experimenter’s
ability to manipulate the data, is relied upon by every piece of experimental
reasoning.
Figure 24: http://commons.wikimedia.org/wiki/File:Experiment_Pasteur.png
There are other forms of non-deductive reasoning that are closely
related to inductive reasoning. One of these is inference to the best
explanation, which we touched on briefly in chapter 7, and will discuss
again in chapter 19.
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§5: INDUCTIVE LOGIC
Chapter 15:
Inductive fallacies
Ben Bayer
Drafted April 4, 2010
Revised August 22, 2010
Inductive fallacies
When we have considered fallacies in the past, we have always classified
them according to which of the three basic requirements of good reasoning
they have most clearly violated. Following in this spirit, now that we have
described the rudimentary basics of what successful inductive generalization
involves, we are now ready to look at some basic and common mistakes
people make in attempts to reason inductively.
Since inductive reasoning begins with observations, there are no
specifically inductive fallacies that violate the first requirement of good
reasoning (that inferences should be based on evidence that is better known
than the conclusion). If an argument does not begin with this, it is hard to
classify it even as a bad inductive argument. Inductive fallacies more
clearly violate the other two requirements. Either they are based on evidence
that is not relevant (or sufficiently relevant) to the conclusion, or they fail to
take account of all of the relevant evidence. Arguably, many of the examples
of ignoring relevant evidence which we discussed in chapter 9 were likewise
inductive fallacies, but presently we’ll focus on their type of mistake from
the perspective of their inductive element.
Hasty generalization
Occasionally you will hear people complain when other people
“generalize”—as if this is an uncontroversially bad thing to do. It would be
odd, however, to hear someone complain about generalizing in the following
way:
You think all human beings are mortal? Come on! That’s just a
generalization!
As we discussed in the last chapter, the claim that all human beings are
mortal is commonly regarded as being as close to certain as anything. Why
then is it a mistake to generalize ? We have general concepts like “human
being,” and we think that some further general concepts can be predicated of
297
human beings. As we discussed when we discussed the “packing” function
of inference, the most important elements of our knowledge come in general
form, and we would be unable to store our past observations for future use
without this general form.
Why then do people sometimes speak as if it is a mistake, even to the
point of regarding it as a moral failing, to
generalize? Probably the reason is that some
generalization is done quite poorly. Some
generalizing is performed too quickly, on the
basis of evidence that is too sparse—as such, it
appeals to insufficient evidence. This is the
fallacy of hasty generalization, the fallacy of
generalizing about an entire class on the basis
of a sample that is insufficient in light of
background knowledge. If induction is like
taking a leap from what we have observed to
what we have not, then hasty generalization is
Picture credit 157:
http://1.bp.blogspot.com/_qxRHzC4mq7M/S6_
like leaping without looking before we leap.
GhJRPeXI/AAAAAAAABBE/t1Iwaho2AWE/s16
00/_MG_9038x2400.jpg
So be careful!: If you conclude that all
generalization is a mistake, simply because some generalization is, this
argument is itself an example of . . . the fallacy of hasty generalization!
The big question about induction is how to know when we have
assembled enough evidence to come to a fully justified conclusion about an
entire class. As we indicated in the last chapter, it is often difficult to know
when, or what kind of evidence is needed for a good inductive inference. But
there are clear cases when we ought to know that inductive arguments are
not based on enough or the right kind of evidence. These are the cases where
we know the fallacy of hasty generalization is being committed.
As suggested earlier, inductive fallacies tend to violate either the
second (relevance) or third (all the relevant evidence) requirements. Either
they lack the background knowledge needed to see observations as relevant
to a general conclusion, or they ignore relevant evidence that shows why
such observations could not be relevant.
For an example of an inductive inference violating the relevance
requirement, consider again the difference between these two inferences
which we examined in chapter 14:
Some samples of the element bismuth melt at 271˚C.
Therefore, all samples of the element bismuth melt at 271˚C
298
Some samples of wax melt at 91˚C.
Therefore, all samples of wax melt at 91˚C.
In the previous chapter, we claimed that the first was a good inference,
whereas the second was not. The second is also an example of hasty
generalization, and the difference between these two inferences helps
illustrate what makes a generalization hasty: it is the difference in amount
and type of background knowledge. In the first case, the reasoner has
background knowledge that chemical elements generally have the same
physical properties, whereas there is no such background knowledge for
more complex chemical molecules like wax.
For an example of the second form of mistake (the wax example was
one of the first), consider the difference between these two inferences:
We have observed many human beings to have died, that they are
living beings with a delicate nature, and that none are older than a
certain age.
Therefore, all human beings are mortal.
I have observed many human beings to have made immoral
choices and have suspicious motives.
Therefore, all human beings are immoral people.
In chapter 14 we spent some time discussing
much of the background knowledge that
supports the conclusion in this first argument:
you can take it as an attempt at an extremely
shorthand summary of the inference described
there in chapter 14. There are important
differences between it and the second argument.
Both of them come to a conclusion about all
human beings, but while the first takes into
account everything we know about human
beings that is possibly relevant to assessing the
extent of their mortality, the second does not do
so with respect to assessing the extent of their
morality. Certainly we know of many people
Picture credit 158:
have made bad choices. Maybe even most
http://commons.wikimedia.org/wiki/File:Lucas
people we know have done some bad things in
_Cranach_d._%C3%84._001.jpg
their lives. But we know more things about these people. We know that the
299
bad things they’ve done are the result of choices. A choice is something that
could, in some sense, go either way, in the direction of wrong or right. Even
if the choices we’ve observed people make have been universally bad, as
long as we understand that they are choices—something we can understand
from our own process of making decisions—we have to know that nothing
obvious in a person’s motives or thinking determines his choices.61 We have
to know that even when we make what we judge to be the wrong choice,
there were motives pulling us in the opposite direction. Given this
background knowledge, the claim that all people are by their nature immoral
is quite a hasty generalization about human nature.
If an inference is simply missing the necessary background
knowledge (as in the case of the wax argument), this makes it hasty
generalization by reason of having premises that are not inductively relevant
to the conclusion (at least, not very). If the inference is contradicting existing
background knowledge (as in the argument about human immorality), this
makes it hasty generalization by reason of having premises that do not
contain all of the relevant evidence.
Here are a few other examples of hasty generalization. Which of the
two requirements do they violate?
All the women I’ve known have been bad drivers.
Therefore all women are bad drivers.
All the men I’ve known have been jerks.
Therefore all men are jerks.
All members of ethnic group X I’ve observed have character
trait Y
Therefore all members of ethnic group X have character trait Y.
Notice that each of these arguments comes to a conclusion that we would
normally regard as a sexual or racial stereotype. Most of us regard racism
and sexism as abhorrent. The root of this abhorrence, we hope you can now
see, is the sheer illogic of the arguments for these stereotypes (when and if
61
There are, of course, philosophers (“determinists”) who insist that ultimately, our choices are determined
by factors we are not necessarily aware of, such as our environment or our genetics. But most of these
philosophers believe that our being determined is compatible with the assignment of moral responsibility
for our actions, roughly on the grounds that we call free those actions which are the products of various
normal motives. And, of course, there is still controversy over whether determinism is true, especially
because it is not clear if determinists can rescue moral responsibility using their “compatibilist” doctrine.
See my essay, “The Elusiveness of Doxastic Compatibilism,” <http://www.benbayer.com/doxasticcompatibilism.pdf>.
300
their advocates deign to give arguments). What background knowledge do
you think is missing in each case? What existing background knowledge do
you think these conclusions contradict? You may notice that they are similar
to the example above about all human beings being immoral. Skills (such as
driving skills) have to be developed by choice. There seems to be no reason
to think that members of a particular sex are simply incapable of choosing to
learn these skills. Likewise, being a jerk is a character trait that has to be
developed by choice, and there is no reason that members of the other sex
can’t choose to develop better traits than this. The same considerations apply
to the inference about ethnic groups.
As mentioned before, it is not usually easy to know when we have a
perfectly good inductive inference, but it is easier to tell when an inference
is hasty. Since we now have a better idea of what makes an inference hasty,
can we tell the difference between hasty inductive inferences, and those
which are at least better than hasty? Which of the following arguments look
hasty to you? Which might be drawing on adequate background knowledge?
I’ve always done poorly on tests in the past.
Therefore I’ll always do poorly on tests in the future.
For thirty years I’ve always unable to reach higher than 7 feet.
Therefore I’ll never be able to reach higher than 7 feet.
Every swan I’ve ever observed has wings.
Therefore, all swans have wings.
Every swan I’ve observed in Europe is white.
Therefore, all swans are white.
Each of the first two examples expresses an individual’s inability to
perform some action. But there is an important difference between the types
of action in question. The first is a type of action, a skill, that can be
cultivated or not by choice. The problem here is similar to the first two
sexual stereotypes described previously. But is there any difference between
the ability to take a test and the ability to reach higher than 7 feet? Try as we
may, we cannot increase our height or the reach of our arms just by doing
stretching exercises. There are real physical limits to what our bodies can do.
We have background knowledge that there is a difference between abilities
that can be cultivated and those which cannot. If we keep this knowledge in
mind, we’ll know why the first argument is hasty, and the second is not.
301
Each of the second two examples
deals with a new subject matter, the
nature of living organisms. We wouldn’t
hesitate to conclude that all swans have
wings. What about a conclusion about
their color? Is there any important
difference between an organism’s basic
bodily appendages and its visual
Picture credit 159:
appearance? We know that there is more
http://commons.wikimedia.org/wiki/File:Cygnus_olor_2_%
28Marek_Szczepanek%29.jpg
variability in the latter. People are
people the world over in spite of differences in color. Could not the same be
true about swans? It is not that color is totally unimportant to an organism in
its environment. A bird’s color is can be a significant form of camouflage,
and environments in different biological niches may necessitate different
colors of camouflage. But if we know this, we will be less confident in
generalizing about an animal’s color because of what we know about the
variability of these niches. As it turns out,
all European swans are white, but there
are black swans in Australia.
So how much evidence is needed to
insure that our inductive inferences are
not hasty? There is no magic number. The
amount, and more importantly, the type
of evidence we need is determined by our
background knowledge, background
knowledge that is obtained itself from
previous, simpler inductions. (If we could Picture credit 160:
http://commons.wikimedia.org/wiki/File:Black_Swans.jp
not build up more advanced inductions
g
from simpler ones closer to perception,
the process could never go very far, and every induction would qualify as
hasty.) Once that background knowledge is in mind, it is not so much the
quantity of evidence that is important, as is the quality and variety of such
evidence.
False cause fallacies
One thing we observed in the previous chapter was that successful inductive
generalizations involve a connection between their component concepts. We
saw this in the following pair of examples:
302
All human beings are mortal.
vs.
All people have taken college classes
In the first, we can see some kind of connection between being human (a
living thing) and being mortal. It is not as easy to see a connection between
being human and taking a college class. This makes it hard to see how any
number of observations of people who’ve taken college classes could ever
justify this generalization.
As we suggested earlier in chapter 14, what we need to see the
conceptual connection in question is knowledge of cause and effect.
All balls roll.
• Something about (the shape of) a ball causes it to roll.
All human beings are mortal.
• Something in the nature of living things causes them to die.
Earlier we suggested that we might just
see the connection between the shape of a
ball and its rolling, and that this is part of
the basis for concluding that balls roll. We
can’t see the connection between being
human and their mortality, but we
described the chain of other observations
(about the difference between living and
Picture credit 161:
non-living things, about the actions
http://www.flickr.com/photos/60319548@N00/98314057/
required by living things, about the
effect of living bodies on these actions, and about their makeup and
ordering) that eventually help us to “see” the connection.
If all of this is true, then if we want to make good inductions from the
ground up, we need to be sure not to have fallacious beliefs about the causal
connections that are needed as their basis. Causal fallacies come in a number
of different forms, each based on different amounts and quantities of
evidence. The first we’ll discuss are the most obviously fallacious, and they
become more plausible as we move on.
303
Post hoc
The simplest causal fallacy is based on a single observation of a pair
of events, one that comes before another. Here are some simple examples of
this simple fallacy:
I wore crystals, and three days later my cold vanished.
Therefore, crystals cause colds to vanish.
I had an awful day after that black cat crossed my path.
Therefore, I had an awful day because of the black cat.
The economy improved after WWII.
Therefore the economy improved because of WWII.
The fallacy here is called post hoc, which is short for the Latin phrase, “post
hoc ergo propter hoc.” This translates as
“after the fact, therefore because of it.” In
each case, a single pair of events is noted,
one that occurs before another. What
makes the argument a fallacy is that this
is all that is noted. The first argument, for
example, does not cite any reason to think
there could be a connection between the
nature, structure, or composition of
crystals and our health. What’s more, we
know that colds typically vanish after
three days on their own accord, anyway,
whether or not we are wearing the crystal.
Many of the same points apply to the
black cat argument: one suspects that
most odd superstitions begin because of
the observation of a chance coincidence
Picture credit 162:
of events, and the drawing post hoc
http://www.flickr.com/photos/hoshiwa/2693336824/
conclusions from these observations.
The final example concerning a connection between World War II and
economic recovery is less obviously fallacious. There is at least a story that
is sometimes told about the connection between the war and the economy.
The government spends money on building munitions for the war effort, this
puts people to work, this puts more money into the economy, etc. A causal
304
story like that does improve the argument and remove it from the realm of
pure post hoc. But the causal story is not always presented. Sometimes
people will present economic arguments like this purely on the basis of post
hoc style reasoning. (“Reagan cut taxes in the 1980s and the economy
improved.” “Clinton raised taxes in the 1990s and the economy improved.”
“Bush cut taxes in the early 2000s and the economy was hurt.” Etc.) And,
we may still ask questions about whether it is a good story: perhaps it
ignores relevant evidence (about the cost and consequences of so much
government spending) as we discussed back in chapter 8.
As in our examples of hasty generalization in the previous example,
post hoc can derive either from an absence of background evidence needed
to establish relevance, or from ignoring relevant evidence. Even if we didn’t
know that colds typically vanish in three days, we would still be committing
post hoc if we only cited the fact that a cold vanishes the day after we wear
crystals. Without at least a background awareness of some mechanism by
which crystals could interact with the body, the argument only cites the
succession of events in time, and this is not evidence of a causal connection.
But if we do know about how colds naturally disappear, and ignore this, we
our post hoc fallacy then violates two requirements of good reasoning.
Likewise, if we are not given an economic explanation of the connection
between war production and economic recovery, this is bad enough. But if
we also know that the return of productive people to an economy can
improve the economy, for instance, it would be an even bigger mistake to
infer that the economy improved after WWII because of WWII; it may have
improved because of the end of WWII.
Confusing correlation with causation
The next fallacy is closely related to post hoc, but it is more plausible
because it appeals to a wider array of evidence. Unlike post hoc, which
appeals to a single observation of a pair of events, one that follows the other,
this next fallacy appeals to a whole series of observations. Whenever the
alleged cause is present, so is the alleged effect; whenever the alleged cause
is absent, so is the alleged effect. Or perhaps the two factors vary in
proportion to each other. This is the fallacy of confusing correlation with
causation, the fallacy of assuming that because one factor varies in
proportion to another, therefore the first factor causes the second. Here are
some examples:
305
Whenever the Times uses more semicolons in its columns, the rate of
famine in India increases.
Therefore, the Times’ use of semicolons causes famine in India.
The stock market varies with women’s hemlines.
Therefore the stock market causes variations in women’s hemlines.
The barometer drops whenever a storm approaches.
Therefore the barometer drops because of the approaching storm.
As before, we can understand the fallacy of confusing correlation with
causation as violating either the relevance requirement or the “all the
relevant evidence” requirement. The first example is a better example of a
violation of the first. If by some strange accident, the quantity of one kind of
punctuation mark in a newspaper varies with the number of famine deaths in
a distant country, we very likely
have no reason to think that
there could be any interaction of
such factors. How does the form
of ink on a page relate to food
supply in a distant land?
Confusing correlation
with causation is compelling
because sometimes we do find
interesting correlations in data
over long periods of time.
Researchers have noticed that as
stock prices rose in the 1920s, so
did women’s hemlines; when the
Picture credit 163:
market crashed at the end of the
http://commons.wikimedia.org/wiki/File:DJIA_historical_graph_to_jan
decade, dresses became longer.62
09_%28log%29.svg
http://commons.wikimedia.org/wiki/File:Hemline_%28skirt_height%29_
Similar correlations were
overview_chart_1805-2005.svg
observed through the 1980s.
Perhaps the correlation has not held in recent years, but even if it had,
speculation about a causal relationship between the stock market and fashion
would remain largely speculative. At best there is a causal story one could
tell according to which prosperity induces immodesty, but this seems largely
62
Tamar Lewin, “The Hemline Index, Updated,” The New York Times, October 19, 2008,
<http://www.nytimes.com/2008/10/19/business/worldbusiness/19iht-19lewin.17068071.html> .
306
unsupported, and one wonders about whether or not any economic
circumstances ever genuinely determine human choices and moral character.
The last example about barometers is especially interesting. It sounds
extremely plausible to say that the storm causes the barometer to change,
and the correlation between the two factors is extremely close. And no one
would argue that the two events are totally unrelated, otherwise we would
not use barometers to determine if storms are approaching. But the storm in
the sky does not radiate signals that somehow affect the barometer. The
storm and the barometer are so well correlated, not because they are causally
connected to each other, but because they are each separately causally
connected to a third, common cause. What causes both is changing pressure.
If we know about this and ignore it, we are still confusing correlation with
causation and committing a fallacy.
Reversing cause and effect
The last causal fallacy is the most plausible of the ones we’ve
considered, because it deals with examples that involve actual causal
connections. The trouble is that the fallacy misidentifies the nature,
specifically the direction of the causal connection. Here are some examples:
Increased sex education is associated with the spread of AIDs
Therefore, sex education must cause the spread of AIDs.
High crime rates are correlated with high poverty rates.
Therefore, poverty must cause crime.
People who are romantically successful have high self-esteem
Therefore, I can build my self-esteem by having flings.
There is something awfully strange about the first example, but we
would be mistaken if we thought there was no causal connection between
AIDs education and the spread of AIDs. Presumably the theory behind the
argument is that AIDs education is usually a part of sex education, and sex
education encourages more students to have sex, which contributes to the
spread of sexually transmitted diseases. One can take apart the pieces of this
theory in any number of ways. But suppose it’s true that there is this
correlation between the rates of education and the spread of the disease. If
we can understand the correlation in a way that doesn’t imply the stated
conclusion, we don’t even need to take apart the theory behind the argument.
307
There is a causal connection between AIDs education and the spread of
AIDs: education programs expanded in response to the spread of the disease
(in the hope of providing a remedy). So if there is a correlation between the
two factors, it might be that the spread of the disease is the cause, not the
effect. This is the fallacy of reversing cause and effect, the fallacy of
observing a real causal connection between two factors, but claiming that
the effect is the cause, and the
cause, the effect. Sometimes
we call this “putting the cart
before the horse.”
The other two examples
can be dealt with along the
same lines, though these are
popular fallacies and it may be
hard to see why the proposed
direction of causality is wrong. Picture credit 164: http://www.flickr.com/photos/learnscope/2594759852/
There often is a correlation between poverty and crime, and there is a
plausible mechanism accounting for it: when a person lacks wealth, he or
she may be more desperate to gain it by taking it from another person. But
there is a plausible mechanism working in the opposite direction: perhaps
crime causes poverty. When criminals terrorize a neighborhood or destroy
property, they destroy wealth and discourage business and commerce. (This
is one of the reasons the “broken window fallacy” we considered in chapter
8 is a fallacy.) And perhaps both of these directions of causality are real.
When it is, we often describe the result as a vicious cycle (or a virtuous
cycle, if we like the effects in question).
The last example is similar to both but hardest to see because
psychological causality can be particularly murky. Most people don’t think
of self-esteem as being the effect of basic choices, they see it as a cause
(which is why so many people are encouraged to praise young students; they
need the self-esteem). But if it is an effect, then the attempt to gain selfesteem through one-night stands and the like involves a logical fallacy.
Unlike the first two causal fallacies we considered, it is harder to see
the fallacy of reversing cause and effect as a fallacy of relevance. There is,
after all, a real causal connection between the covarying factors in question;
the argument only misidentifies the direction of the causality. This means
that the covariation of the factors is not totally irrelevant to a causal
relationship between the two of them. The fallacy, then, will result mainly
from the violation of the “all the relevant evidence” requirement: reversing
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cause and effect ignores relevant evidence by ignoring the possibility of the
reverse direction of the causal connection.
Here are some final examples of causal fallacies. Can you tell which
of the three types of fallacy listed above is committed by each?
Whenever there is thunder and lightning, there is rain.
Therefore, thunder and lighting cause it to rain.
Everywhere there is a lush green forest, it rains.
Therefore, lush green forest causes rain.
Homer: “Not a bear in sight. The Bear Patrol is working like a
charm!”
Lisa: “That’s specious reasoning, dad. . . By your logic, I could claim
that this rock keeps tigers away.”
Homer: “Hmm; how does it work?”
Lisa: “It doesn’t work; it’s just a stupid rock!”
Homer: “Uh-huh.”
Lisa: “… but I don’t see any tigers around, do you?”
Homer: “Lisa, I want to buy your rock…”
Statistical generalization and associated fallacies
Our last set of inductive fallacies relates to a sort of induction we have not
previously commented on. Induction seeks to generalize about every
member of a class: it seeks to claim of all Xs that some predicate Y holds of
them. Sometimes we are not in a position to make a sweeping of a claim
about every member of a class, and not for a lack of evidence. We may
observe the following, for instance:
15% of smokers develop lung cancer.
Although this is not as interesting as being able to say that 100% of smokers
develop lung cancer, it is still very useful knowledge to have. Knowing such
a percentage can provide important clues for discovering genuine inductive
generalizations, and at the very least show that some aspect of smoking may
be a “risk factor” in the development of the disease. It may be that smoking
causes lung cancer under specific circumstances which we have not yet
identified. Perhaps smoking under condition Z causes lung cancer, because
this condition operates in conjunction with a complex combination of
additional environmental and genetic factors to bring about the effect in
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question. When we gather statistical correlations like this at first, whether we
get cancer from smoking may look like the luck of the draw, but in fact there
are unseen factors operating which end up making the difference.
Since discovering what is true of a
mere percentage of a class is still useful
in the process of induction, it is
important to demarcate the conditions
under which it is useful and reliable.
There are fallacies we can commit while
making statistical generalizations just as
there are in making straightforward
inductive generalizations. This is
because even in order to make a claim
about a percentage of a class (like about
20% of smokers), we need to generalize
that percentage to the entire population,
which may be much wider than the
original set of observations. The original
set, therefore, states describes a fraction
Picture credit 165:
of a fraction. For instance, we don’t have
http://www.flickr.com/photos/marcemarc/2292588450/
access to all smokers, and so our claim
that 20% develop lung cancer is based on a statistical sampling of smokers.
Because we have to rely on this sampling, we need to know that our sample
is representative of the total class we are trying to generalize (on a fractional
basis) about. How do we know when it is?
The answer here is the usual answer that helps guide us in more
advanced induction: we think of a sample as representative because we have
background knowledge to that effect. Here is a standard example of
statistical sampling:
I’ve drawn 100 white balls from this urn: 90 were white, 10
were black.
Therefore, 90% of the balls in the urn are white.
There is a fair amount of background knowledge we can have about urns and
balls in them that helps lead us to this conclusion. Since we know that both
the urn and the balls are man-made, we suppose they are manufactured for a
reason, and on that assumption we usually expect manufactured items to
have a certain kind of uniformity. Placing our hand into the urn, we feel that
the balls are mixed up with each other, and so there are no pockets of balls
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separated from others which would detract from the randomizing of the
mixture of balls. Hence the balls we draw at random are likely to be
representative of the total population of balls, even if we do not draw every
one. If any of these conditions failed to hold, we could not be as confident
that the conclusion here would follow.
As with previous fallacies, fallacies of statistical sampling can result
from missing or ignored background knowledge, knowledge which we need
to determine whether or not the sample is representative. In what remains,
we will list examples of different forms of background knowledge that can
be missed or ignored, specifically knowledge about the objects being
sampled, and about the methods of sampling used to pick them out.
Sometimes we simply do not know enough about the objects sampled
or method of sampling them. This will sometimes occur when we hear the
results of a survey without knowing
much about the facts of the survey
itself. Consider a claim made by
many a toothpaste advertisement:
3 out of 4 dentists recommend
brushing with Brand X.
Therefore, 3/4 of dentists
recommend brushing with
Brand X
The important question here is: how
big is the original sample? Is it 2/3 of
a sample of 100 or 1,000 dentists? Or
were there literally only 3 dentists
sampled? And how were these
Picture credit 166:
particular dentists chosen? If they
http://commons.wikimedia.org/wiki/File:Older_barber-dentist.jpg
http://commons.wikimedia.org/wiki/File:The_London_Dentist_by_R
werer paid by the toothpaste
obert_Dighton.jpg
company to contribute their opinion http://commons.wikimedia.org/wiki/File:%27Dentist_by_Candlelight
%27,_oil_on_oak_panel_painting_by_Gerrit_Dou.jpg
and picked because they were
http://www.flickr.com/photos/herry/424274849/
already known to be favorable to the
company, there is reason to think the sample is not representative.
Merely missing knowledge about a sampling procedure is unlikely to
happen if we have done the sampling ourselves, so the first problem really
only applies to reasoning about statistical surveys that have been reported to
us. (See also chapter 5’s advice about assessing the reliability of testimony.)
The rest of the statistical fallacies we’ll consider are fallacies that can be
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committed by the actual conductors of a statistical survey when they draw
conclusions from known samples.
It is important not to ignore facts about the particular objects sampled,
especially if there is reason to think them different from the rest of the
population being generalized about. Consider this argument:
Surveys by psychologists show 80% of people feel unsure
about their future.
Therefore, 80% of people are unsure about their future.
As it happens, many psychological studies are conducted by university
psychology researchers, on college freshmen or sophomores who are taking
psychology classes (usually they will get credit for performing as
experimental subjects). If this is true, these researchers must be careful to
ensure that student populations can be seen as representative of the
population as a whole, and be on guard against attributing characteristics
distinctive of college students to the population as a whole. Yet in this
example, the trait noted of the experimental subjects is one we would expect
to be distinctive of students: students are young and often undecided about
their future. It is natural that many of them will feel unsure. This does not
mean it is natural to expect it of the population as a whole.
Statistical samplers can also ignore facts about the method of
sampling they have used, specifically facts about the method that can cause
the population sampled to be unrepresentative. Consider these two
examples:
More cases of polio were counted in 1952 than ever before.
Therefore, there were more cases of polio in 1952 than ever
before
Border officials made 1 million apprehensions in one year .
Therefore, border officials apprehended 1 million distinct
border-crossers.
Each example above involves a problem concerning the effectiveness of our
counting. Absent more specific information, it is possible that we counted
the greatest number of polio cases in 1952 because that is the year that polio
has reached its largest number of victims. But it is also possible that we
counted the greatest number that year because our method of diagnosing and
reporting cases of polio have improved. The opposite kind of problem is
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involved in the second case. In this case, it is a deficiency in the counting
process that could account for the fallacy. Perhaps border officials have
indeed made 1 million apprehensions of border-crossers. But what if, once
someone has been apprehended and sent back across the border, he tries to
cross again, and is apprehended a second time. If the border officials aren’t
keeping track of repeated crossings, they will double-count border-crossers
and the number of attempted border-crossers will look higher than it actually
is. Obviously one of the best examples of double counting would have been
counting the ballots of those who voted “early and often” in the corrupt
elections of the past in Chicago.
Some methods of sampling may permit perfectly good identification
and counting, but attract specific kinds of data to the sampling process,
which make the sample unrepresentative. Take these examples on for size:
70% of eligible voters surveyed by telephone in 1936
favored Republican Alf Landon over FDR for president
Therefore, Republican Alf Landon will beat FDR.
An alumni association mail survey reveals that the average
salary of a University of Illinois graduate is $68,997
Therefore, a U of I student is likely to make that much money.
At the time of the 1936 survey, only the wealthy
were able to afford telephones of their own. This
meant that the sampling was biased towards the
political opinions of the wealthy, and since, at the
time, the wealthy were likely to favor
Republicans, the sample suggested that
Republicans would win. In fact, the Democratic
candidate Franklin Roosevelt won the election,
contrary to the prediction of the statistical survey.
A similar problem is found in the second
example. Remember that it takes some
convincing to get someone to fill out a mail-in
Picture credit 167:
survey; these surveys are easily tossed out as junk
http://www.flickr.com/photos/leebennett/261
9096448/
mail. Who is more likely to be convinced to fill
out the survey? Someone who is or is not doing well with his post-college
career? Those doing well are more likely to have something to brag about,
less likely to be ashamed about their socioeconomic position. So the most
likely people to respond are the ones doing well, which would have the
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effect of pushing the average salary of university graduates higher than it
would be if everyone were to respond to the survey.
One last method of sampling not only attracts a specific kind of
sampling data, but actively modifies that data: this is the method of sampling
by surveying people’s own self-reports about facts about themselves.
Consider:
The percentage of sexually active young women rose
from 13 percent in 1943 to 47 percent in 1999
Therefore, the number of sexually active women increased
during the second half of the 20th century.
This example is similar to the polio example stated earlier, except that we
have not become better counters of women’s self-reports about sex since
1943. Instead, there is reason to think that since 1943, women may have
acquired different reasons to answer the survey differently. In an earlier
time, they may have been more reluctant to report accurately about their sex
lives, perhaps because of Victorian-style reasons of modesty. More recently,
they might have become not only less reluctant to self-report, but even more
likely to lie while self-reporting, perhaps because of a desire to brag about
sexual prowess. There is of course a decent possibility that the level of
sexual activity has increased in this time. But can we conclude that it has
increased this much, when self-reporting is relatively unreliable? If we
ignore the complications of self-reporting, we might come to the conclusion
above, but it might not be completely justified. Here again, considerations
from chapter 5 on the reliability of testimony are important to consider.
One last point to consider about the reliability of statistical reasoning
is less a matter of how to form statistical generalizations, and more a matter
of how to apply them, deductively, once we acquire them in a reliable
manner. As such, this last is not really an inductive fallacy, but since it is
closely related to the factors that make statistical generalizations reliable, it
is worth mentioning here to round out our discussion.
Suppose it is true that 40% of men have extramarital affairs. Would
the following argument from this premise be logically acceptable?
40% of men have extramarital affairs.
Therefore, there is a 40% chance that my husband is having an affair.
Remember that when we reason from a sample, we generalize to the
population as a whole, to the extent that we judge our sample to be
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representative of the population as a whole. There is a point to keep in mind
that works in the opposite direction, a sense in which the population must be
“representative” of the individual the statistic is being applied to, if the
statistic is to be applied. What happens if the particular husband in question
is never known to have cheated, has an upstanding moral character in every
other aspect of his life—he even refuses to download pirated MP3s! Also,
his spouse has no known him for decades, they have been raising children
together for years, and their lives are intimately connected. None of this
makes it impossible that he would ever stray. But it does reduce the chances.
It would be nonsensical to say that there is a 40% chance that he is going to
cheat—probably the chance is much lower.
The lesson here is that statistical generalizations can be applied
deductively to individuals only when we know nothing about them in
particular. To say that there is a 40% chance that a given individual will
cheat means that there is a 40% chance that a random individual will. Once
we know a great deal about the individual, all bets are off (quite literally).
This is the reason health insurance companies who acquire knowledge of a
pre-existing condition in a prospective customer will charge higher
premiums or even refuse coverage: statistics about the general population no
longer apply to him: his chances
of developing some disease or
condition may actually be
higher.
Similar considerations
also applying to the controversy
about racial profiling. The
premise behind arguments for
profiling prospective criminals
or terrorists is that those
Picture credit 168: http://www.flickr.com/photos/ngorung/4695438204/
involved in crime or terrorism
are sometimes disproportionately members of certain ethnic or religious
groups. However you decide the controversy about whether it is just or
moral to use statistics to prevent crime or terrorism, one thing is for sure: the
more we know an individual member of an ethnic or religious group, the less
relevant those statistics become. If we have known the individual for years,
see that he is educated and productive, a real asset to society, then regardless
of his ethnic or religious ties, we have less or no reason to suspect he is
involved in illicit activities.
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§5: INDUCTIVE LOGIC
Chapter 16:
Causal analysis
Ben Bayer
Drafted April 10, 2010
Revised August 22, 2010
Introduction: types of causal conditions
In chapter 14, we briefly discussed some basic methods of establishing
causal knowledge, before we moved on to chapter 15 where we discussed
fallacious attempts to do the same. But there are methods of both identifying
and eliminating causes that go beyond the fairly simply types of
observations and generalizations we’ve discussed. In the present chapter,
we’ll present the most basic rudiments of a more advanced method of
identifying causes, the scientific method, which in the last 400 years, has
played a crucial role in the greatest achievements of human knowledge.
Since we will only examine the rudiments of this topic, you will
probably not learn how to be a scientist from this chapter. But the methods
that work for science at its most advanced stages have precursors in
everyday knowledge. By taking only a brief glimpse at the scientific method,
you can at the very least become a better reasoner in everyday life.
The methods we will discuss below are methods of identifying and
eliminating cause and effect relationships. Since we will discuss methods of
both identifying and eliminating possible causes, the present subject (and
title of this chapter) is causal analysis. But if we want to know how to
perform methods of causal analysis, we will need a better idea of what
causal relations are. What is a cause?
There are many different senses of the word “cause.” In chapter 14, in
order to show how causal knowledge could provide a basis for inductive
generalization, we spoke primarily about how facts about the nature of
things cause their distinctive types of action. The cause of a ball’s rolling,
for instance, was said to be something in the nature of the ball’s shape. The
author of this text believes this kind of causal knowledge is the most basic
kind, and the corresponding sense of the word “cause” is the most basic
sense of the word.
But words can have a basic sense, while also having derivative senses.
Consider how we speak of various kinds of food as “healthy.” Is food really
the kind of thing that can be healthy or unhealthy? Yes, but only in a
derivative sense. The primary thing we call healthy or unhealthy is a living
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organism. But we call food (or exercise or psychological habits) “healthy” or
not insofar as they contribute to an organism’s being healthy or not. In the
same way, we can call things “causes” insofar as they reflect in some way
the basic facts about the nature of things that we say are responsible for how
they act.
For example: we easily talk about how one kind of event or happening
involving some entity causes another type of event of happening. We say,
for instance, that pushing the ball causes it to roll. Usually when we describe
causal relations as holding between one
happening and another, there is a special
reason: instead of trying to explain a ball’s
general ability to act in a certain way(the
ability to roll), we instead want to explain
why a ball exercises its ability on a
particular occasion. The difference is a
matter of emphasis and contrast: are we
Picture credit 169:
trying to explain why it rolls rather than
http://commons.wikimedia.org/wiki/File:Billard.JPG
slides, or why it rolls now vs. rolls later? It
rolls now rather than later because of something that happens to it just prior
to now. It also rolls in a specific way rather than another because of the kind
of thing that happens to it (for example, it was pushed, as opposed to moving
because the surface suddenly inclines).
The examples of cause and effect relationships we’ll now study help
us to establish causes in both senses: they help us discover general facts
about objects that explain how they act, and also how various events or
happenings are explained by other events or conditions. Thinking about
cause and effect as a relationship among happenings can be very useful,
precisely because of the specificity it allows. We are, after all, only
interested in knowing about the general abilities of entities because we want
sometimes to know how to predict when and under what circumstances they
will exercise these abilities. Just keep in mind that event-event causal
relations are derivative from the more basic kind: without understanding
how an action depends on the thing that acts, we cannot understand how it
will act in a given circumstance. We know that billiard balls can cause the
motion of other billiard balls only because of their shape, size, and density.
(A triangular group of cubic objects would not “break” in the distinctive way
that such a group of spheres does at the beginning of a game of pool.)
Even causality considered as a relationship among events divides into
several sub-types. Sometimes we speak of things as “causes” that are
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sufficient conditions. Here are some ordinary examples of causal statements
describing sufficient conditions:
A stab to the heart causes death
A spark causes a fire.
The assassination of Franz Ferdinand caused WWI.
We call X a sufficient condition for Y just
in case whenever X occurs, Y must also
occur, i.e., just in case “If X, then Y” is
true. We call such a factor a sufficient
condition because it suffices to bring about
some other event; it is enough to bring it
about (in a specific circumstance). So, for
instance, a stab to the heart is enough to
cause death. Once the mortal wound has
Picture credit 170:
been dealt, nothing further may be
http://www.flickr.com/photos/matthewvenn/469764055
required; nature will take its course. Simply
exposing a spark to dry underbrush on the right kind of day can be enough to
set an entire forest ablaze. Some have compared
geopolitical conflagrations as occurring because
of “sparks” that set afire regional tinderboxes.
This is often how the beginning of World War I
has been described: the 1914 assassination of
Archduke Franz Ferdinand of the AustroHungarian empire by a Serbian nationalist in
Sarajevo, Bosnia was the spark that inflamed
already tense relations between the Austrians
and Serbians, leading to military conflict
between them, which eventually brought their
allies into conflict with each other, as well.
Part of what distinguishes a sufficient
Picture credit 171:
http://commons.wikimedia.org/wiki/File:WW
condition from other causal conditions is that
I-Causes.jpg
while it may be enough to bring about an effect,
it is not necessarily the only way to bring it about. As you well know, a stab
to the heart is enough to cause death, but there are (unfortunately) many
other ways to bring about the same result. The same goes for the fire. A
spark can do the job under a given circumstance, but so can a magnifying
318
glass or certain chemical reactions. A spark is sufficient, but it is not
necessary. There may have been other ways to “raise the temperature”
between Austria and Serbia in 1914. If the assassination had not come off,
some other international incident may have provoked the same response.
Keep in mind that when we speak of causes as sufficient conditions
they are usually only sufficient to bring about some effect under specific
circumstances. Stabbing the heart doesn’t cause death unless it is the heart of
an already living thing, for instance. It has to be a working heart in a body
that needs the blood it circulates. It has to be normal heart that will be
damaged irreparably by a stab wound, as opposed to some cybernetic heart
that automatically seals any wounds. By the same token, a spark in a vacuum
doesn’t start a fire. There needs to be some form of carbon fuel (like wood
or paper), fuel that is not too wet, and of course, oxygen. Those who have
compared the beginning of World War I have given long lists of conditions
that had brought continental Europe to the brink of war, only to be pushed
over the edge by the assassination of Franz Ferdinand. There were
preexisting tensions between rival powers, entangling alliances that arrayed
series of such powers against each other, arms races giving their militaries
itchy trigger fingers, etc. In each case, an array of conditions has lined up,
and only one more is needed to bring about a new effect. A sufficient
condition is just the last missing necessary condition.
Philosophers will also describe as a sufficient condition the total set of
conditions necessary to bring about some effect. This often comes up in the
context of giving a definition. Supposing our earlier definition of “human
being” is correct, to be a rational animal is sufficient to be a human being.
But this is the use of “sufficient condition” that is appropriate for describing
general conditions sufficing to bring about very general states of affairs. So,
for instance, if we want to describe what is sufficient to bring about
combustion in general, it will not do to put it in terms of something as
specific as a spark. We would either have to list either a spark or a
magnifying glass or various chemical reactions, or simply state more
generally a source of heat. But when we speak at such a level of generality,
as opposed to what is sufficient in a given circumstance, it is no longer
meaningful to say that the heat alone is sufficient. It is only sufficient in
combination with all of the other necessary conditions.
This brings us to the sense of “cause” as a necessary condition, the
other major conceptualization of the causal relationship between specific
events. We call X a necessary condition for Y just in case it’s true that
without X, Y does not occur, or there must be an X for Y to occur; i.e. it must
be true that“If Y, then X,” or “If not X, then not Y”). We call this a
319
“necessary condition” because it is a factor needed to bring about some
effect. But a necessary condition is not (usually) a sufficient condition; it
may be one thing needed to bring about an effect, but it will not bring it
about on its own. Here are some examples of ordinary statements describing
necessary causal conditions:
A virus causes a flu.
Flaws in bridges cause them to collapse.
The cause of the recession was the bursting of the real
estate bubble.
In each case, the cause is an important condition
required to bring about some effect. Ordinarily,
unless a number of other necessary conditions
are fulfilled, the condition in question is not
sufficient. As mentioned above, what we call
“sufficient conditions” are often just the last
needed condition, i.e., the final necessary
condition. It follows that when we speak of
necessary conditions that are not sufficient, we
often refer to ones that may come earlier in a
causal sequence, but which are important
enough to isolate for special attention. A virus
causes a flu, but a long chain of physiological
conditions must obtain before the infection
occurs. Just to state one example, the body does Picture credit 172:
http://www.flickr.com/photos/pmarkham/1299
not become infected until protease enzymes split 963592/
apart viruses, thereby causing them to replicate and spread throughout the
body. Likewise a crack that appears in bridge will not cause it to collapse
unless a truck with enough weight drives over it or the wind begins to blow
hard enough. The recent housing bubble did not cause a general economic
recession until losses in the housing market cascaded through other
industries (such as insurance and banking).
If a necessary condition does not bring about an effect until other
necessary conditions “pile up” to bring it about, why do we bother to single
it out from among those other necessary conditions as “the cause”? Why do
we say that a virus is the cause of a flu, rather than the protease enzyme that
helps transmit infection through the body? The answer has something to do
320
with something of special interest about this particular necessary condition.
The presence of the protease enzymes is a normal condition for the body.
But the virus is a unique intruder, not the normal condition. A crack in the
bridge is not only abnormal, but undesirable and avoidable. The bridge could
have been better constructed, or could still be fixed, in order to eliminate the
problem. But we do not presume that
adverse environmental conditions or
heavy loads are avoidable: they are
inherent in what it is to be a bridge.
Likewise the other conditions that
enabled the housing collapse to affect
the rest of the economy were also
normal, and normally useful.
Insurance companies and banks serve
Picture credit 173:
a vital function in an economy; the
http://en.wikipedia.org/wiki/File:Subprime_Crisis_Diagram_fact that they magnified the effects of
_X1.png
the collapse actually shows their
overall importance (if they are hurt, the rest of us are hurt). It was the
housing collapse that was abnormal, not predicted by most, and (many think)
avoidable.
We’ve said that a sufficient condition is often the last in a series of
necessary conditions, and that a necessary condition that is not sufficient is
earlier in the series. But it is also possible to think of all of the necessary
conditions taken together as a sufficient condition. We will often describe
them as individually necessary but jointly sufficient. We can speak of either
combinations of necessary general conditions as jointly sufficient for some
general phenomenon, or of combinations of necessary specific conditions in
a given context as sufficient for bringing about a specific event.
Here are some examples of causal claims that refer either to primarily
necessary or sufficient conditions. Which are which? It is not always
obvious. Do any of them seem odd to identify as causes?
Gasoline causes cars to move.
Pressing the key of a well-built piano causes a note to sound.
Oxygen was the cause of World War I.
The recent recession was caused when banks called for the payment
of loans that people could not afford.
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As we shall see in the next few sections, there are different methods
that allow us to discover different types of causal
conditions. These methods have been used by
thinkers for millennia, but they were first categorized
and named by the British philosopher and logician
John Stuart Mill (1806-1874). Accordingly the
methods are known most
widely as Mill’s Methods.
As we move through Mill’s
list of methods of identifying
necessary and sufficient
Picture credit 174:
conditions, we’ll discover
http://commons.wikimedia.org/wiki/F
that each method also carries ile:JohnStuartMill.jpg
with it a method of eliminating possible causes, as
well. The identifying function of the method we’ll
call the positive method; the eliminating function, we’ll call the negative
method.
The Method of Agreement
To learn the first and simplest of Mill’s methods, consider the following list
of sick people and the things they ate:
Subject Food
Effect?
1
Turkey
Cream
Beer
Apples
Sick
2
Ham
Cream
Mead
Apples
Sick
3
Ham
Cream
Beer
Carrots
Sick
If each person, 1, 2 and 3 got sick, but there is no kind of meat, fruit, or
drink that each eats beforehand, we cannot blame the meat, fruit or drink for
the sickness. But notice that each had the cream. It is the one known factor
on our list that is common to every case in which the effect occurs. The
natural and logical conclusion to come to is that the cream was the cause of
the sickness.
322
Examples like this utilize what Mill called the Method of Agreement.
We will call it the positive Method of Agreement, because it is concerned
with identifying rather than eliminating a possible cause. The positive
Method of Agreement identifies the probable cause as the
one condition (X) present in all cases where the effect is present. A
schematic representation of this rule is seen in the following:
A X C E  Y
B X D E  Y
B X C F  Y
Suppose in the example at the beginning of the section, 1, 2 and 3 are
the only people who got sick at a given feast.
Why are we only considering the list of foods
they ate? Conceivably we could also list as
possible causes the animals or people they
came into contact with that day, the places
they visited, their genetic history, and so on.
The list above, of course, is presented in
abbreviated form only to simplify the example.
Whatever possible factors will go on our
ultimate list will depend on our background
judgments of relevance: we have some general
background theory about what kinds of things
can cause the transmission of disease (they
usually involve the sorts of activities that
involve inhaling or ingesting foreign
Picture credit 175:
http://commons.wikimedia.org/wiki/File:Glutao.j
substances).
pg
Sometimes logicians and philosophers
complain that Mill’s methods cannot help us discover or justify causal
claims because the methods presuppose a background of causal knowledge
that conditions our background knowledge of the potentially relevant
factors. The allegation is that using the methods to justify new causal
knowledge would beg the question. But this is not a serious objection as
long as the causal knowledge presupposed by judgments of relevance is
distinct and simpler causal knowledge, knowledge that is closer to direct
observation.
Of course we can sometimes be mistaken about what general factors
are relevant. As a result, we might neglect to list relevant factors when
looking to see which is common to all cases in which the effect is present.
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We might, therefore, not be able to find any single factor common to all of
these cases (the real one might have been left off the list). For this reason, it
is best to say that a given application of the Method of Agreement only helps
to discover what is probably the cause of some observed effect. Before we
reach a considered judgment on the cause, we will need to have very good
reason to think that no other causally relevant factors are possibly present.
Applying the additional methods we are about to learn will help give us
more reason to think this.
In some cases, we might know all of the relevant factors, and still
have trouble seeing the one factor common to all
cases of the effect. Our inability to discover the
common factor may not be because it is hiding,
but because we are not conceptualizing the
possible causes and effects at the right level of
generality. Consider this list of possible physical
Picture credit 176:
factors and the corresponding outcomes:
http://commons.wikimedia.org/wiki/File:Ice
BlockNearJoekullsarlon.jpg
Subject
Effect?
1
Water
2
Silicon
solution
Limestone
solution
3
Cold
Room
pressure
Room Room
temp. pressure
Heat High
Pressure
Ice
Quartz
Marble
Ice, quartz, and marble are each distinct types of
solid substance. So at first it might not even look like
we’ve assembled a list of three cases of the same
effect. But there is something common to ice, quartz,
and marble: they are all forms of crystal. Our
question here is really a question about what causes
crystals in general, not a question about the cause of
a specific event in a specific Picture credit 177:
http://commons.wikimedia.org/wiki/
circumstance. This means
File:Quartz.jpg
we should look for a more
general common factor in the columns on the left.
As presently formulated, we see no single factor on
the list is present in all three cases. This is only a
problem if we are looking for the most fine-grained
Picture credit 178:
http://commons.wikimedia.org/wiki/Fil
e:MarbleUSGOV.jpg
324
type. If we think about a more general category each belongs to, we’ll notice
that water, silicon solution, and limestone solution are all liquids. Under the
right temperature and pressure, each of these liquids can, apparently, turn
into a crystal. So there is something common to all cases of crystal
formation, after all, even if temperatures and pressures vary across the
board: the factor common to all cases of crystal formation is the slow
solidification of some physical substance under an appropriate pressure.
The example of the Method of Agreement we’ve just examined is a
method for identifying the cause of some observed set of effects. But even
when the method does not yield conclusive results—even when we can find
no single common factor present in all cases of the effect, for example—
examining the possible relevant factors present in each case of the effect still
has an additional use. It can be also used to rule out factors as possible
causes. This is the aspect of the method we call the negative Method of
Agreement. Look again at the data concerning the cases of food poisoning:
Subject Food
Effect?
1
Turkey
Cream
Beer
Apples
Sick
2
Ham
Cream
Mead
Apples
Sick
3
Ham
Cream
Beer
Carrots
Sick
Suppose for the moment that we did not know to consider the cream as a
possible cause, or suppose that none of these people had actually consumed
any cream. The data about the other food they consumed is still helpful in
eliminating possible causes. We know that turkey, for example, is not likely
the cause: while it is present in case 1, it is not present in cases 2 and 3, even
though the effect (sickness) still occurred (the same can be said about ham,
which is missing in case 1). Likewise we know that the mead is not likely
the cause, as it is absent in cases 1 and 3, where the effect is nonetheless
present (the same applies to beer, missing in case 2). A similar story can be
told about both apples and carrots.
The negative Method of Agreement, the rule corresponding to the
positive method that allows us to eliminate possible cause, rules out as
possible causes those factors that are absent when the effect is present. Here
is a schematic representation of this rule is as follows:
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A X C E  Y
B X D E  Y
B X C F  Y
Here we can rule out as causes all of the factors apart from X, because Y is
present on some cases where each of A, B, C, D, and E are absent. Notice
that while the positive Method of Agreement is used to identify sufficient
conditions, the corresponding negative method only helps to eliminate
necessary conditions. To say that a factor is absent when the effect is present
shows that this factor is not needed to bring about the effect. This does not
mean it could not count as some kind of sufficient condition under the right
circumstance. The fact that B is not present when the effect Y is present
shows that it is not needed to bring about Y in the presence of X, C, and E.
But perhaps the special combination of X, D and E provide the special
circumstances needed to bring about Y when B is finally added, leaving
open the possibility that B would suffice for Y. Perhaps B is even necessary
given the specific combination of X, D and E, but not generally necessary.
The negative Method of Agreement is commonly used to refute
general causal claims. It gives us a recipe for finding counterexamples to
these claims. Here are some contentious causal claims. Can you use the
negative Method of Agreement to supply counterexamples to them?:
The necessary condition for succeeding in life is graduating from
college.
Poverty and ignorance cause people to commit acts of terrorism.
A country’s possession of natural resources makes it prosperous.
In each case, the way to use the negative method to supply counterexamples
is to try to find cases in which the effect is present though the alleged cause
is absent. Can you think of cases of people who have succeeded in life
without graduating from college? Or people who have committed (or
planned) acts of terrorism without being poor or uneducated? And are there
examples of countries who have achieved economic prosperity in spite of
lacking significant natural resources?
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The Method of Difference
The Method of Agreement is a fairly limited method of identifying causes. It
is always possible that we may not find a single factor common to all cases
where the effect is present: perhaps we do not know all of the relevant
factors to consider, or some known relevant factors may be hiding from us.
We may find a common factor which is only there coincidentally, while the
real common factor is hidden from us. Perhaps one type of factor varies
from case to case because it combines with other types of factors in different
circumstances to bring about the effect (as B above may work in conjunction
with X, D and E to bring about Y, whereas A might work with X, C and E.)
There are other possibilities.
Because of the uncertainty of the Method of Agreement, we need a
method that takes into account a broader variety of evidence. Consider this
example of the same kind of food poisoning discussed in the previous
section:
Subject
Food
1
Turkey
2
Turkey
Effect?
Cream
Beer
Apples
Sick
Beer
Apples
Not sick
In this data, we actually only consider two subjects, 1 and 1. But instead of
looking at all of the cases in which the effect is
present, we are now examining cases in which the
effect is present, and similar cases in which it is
absent. The key to the success of examining this
data is the similarity of the cases: all known
relevant factors are held constant: both subjects ate
the turkey, beer, and apples, but only one got sick.
But the subjects are not exactly the same. If we
have considered all of the possibly relevant factors,
they differ in one and only one respect: one ate
cream, the other did not. The natural conclusion
credit 179:
here is that this is the one difference that has made Picture
http://commons.wikimedia.org/wiki/File:
a difference between the subject who gets sick, and FressendNarr-1568.png
the one who does not.
This example illustrates a simple use of the positive Method of
Difference, which identifies the probable cause as the only condition (X)
327
that differs between cases in which the effect (Y) is present and in which it is
absent. A schematic representation of the method is as follows:
X
X
B C D  Y
B C D  Y
B C D  no Y
Applying this method can involve many of the uncertainties of the Method
of Difference. Its successful use presupposes that we have identified all of
the possibly relevant factors, and that we know that cases in which the effect
is present and in which it is absent differ in only one respect. Any two cases
could differ in numerous ways we are unacquainted with, however, so it is
exceedingly hard to know that only one potentially relevant difference is
there. But supposing that we have identified all of the relevant factors, the
method of difference helps us identify a necessary condition for the effect in
question.
It is possible to use both the Method of Difference and something
approximating the Method of Agreement to determine that a factor is both
necessary, and possibly sufficient. Notice that the first two lines of the
diagram show that X as present in both cases where the effect is present. But
so are B, C, and D. Thus we do not have a perfect application of the Method
of Agreement, because there is not only one factor in common among all
cases of the effect. So we can perform a test: remove one of each of these
factors, and see what happens. If we remove B, leaving everything the same,
and the effect is present, we know it is not the cause. But if we remove X,
leaving everything else the same, and the effect does disappear, X is the
likely cause we should take seriously. In the data above, it is of course
possible that B, C, and D are other necessary conditions that X needs to
bring about Y, but this can only be determined by further applications of the
Method of Difference.
Notice that in the previous paragraph, we spoke of applying the
Method of Difference by consciously removing a single factor to see what
would happen. Learning ways to remove just one factor is the essence of the
experimental method. In our first example of the Method of Difference, we
simply surveyed the existing cases: only one relevant difference held
between the two cases, so we assumed that the presence or absence of that
factor made the difference. It is one thing to look for similarities and
differences; it is another matter to go out and actively create them. Playing a
role in creating them, which is the strategy of the experimental method, can
328
help us know that the differing factor is the only one. If we begin with a
single sample, and make only one known alteration to it, this can deliver
more certainty than looking for differences between two samples. Even
better is to create two samples from the same stock of originally uniform
material, and make a change in one while leaving the other (the control
group) the same.
This method was used by Louis Pasteur in a famous experiment in the
1860s which helped demonstrate that putrefaction is not “spontaneously
generated” by the putrefying subject. This discovery was instrumental in
justifying the germ theory of disease. Here are the essential observations that
Pasteur made:
Case
A
Possible
causes
Broth
Effect
Air
Growth
B
Broth
No air
No growth
Pasteur took a single stock of broth, which he had boiled to kill any possible
preexisting sources of infection, and split it between two apparently identical
swan-necked flasks. In case A, Pasteur broke the neck of the flask and
exposed it to the air. In case B, he plugged the neck of the flask to keep it
hermetically sealed from the outside. What he observed after time had
passed was that only the flask that had been exposed to the outside air began
to exhibit putrefaction. Here Pasteur had reasonable confidence that the only
relevant difference between the two samples was their exposure to the
outside air. As a result, he concluded that the broth was infected not by
something originally contained within it, but by some external agent in the
air. This helped him develop, with others, the germ theory of disease.
As with the Method of Agreement, there is a negative method that
corresponds to the Method of Difference, one that helps us rule out causes
even if we cannot rule any “in.” Look again at the data from our original,
simpler example of the Method of Difference:
329
Subject
Food
1
Turkey
2
Turkey
Effect?
Cream
Beer
Apples
Sick
Beer
Apples
Not sick
Even if we did not know about the difference in cream consumption between
1 and 2, we would still know that the turkey, beer, and apples are present in
case 2, when the effect is absent. As a result, we know that none of these
factors is individually sufficient to bring about the sickness, nor are all three
of them together jointly sufficient to cause it.
The negative Method of Difference, then, rules out as possible causes
those factors that are present when the effect is absent. As with the negative
Method of Agreement he schematic is the same as the corresponding
positive method:
X
X
B
B
B
C D  Y
C D  Y
C D  no Y
But the focus of the negative method is on the factors still present (B, C, and
D), when the effect is absent. Just as the positive Method of Agreement
helps identify sufficient conditions, while its corresponding negative method
rules out necessary conditions, the positive Method of Difference helps
identify necessary conditions, and rule out sufficient conditions. Of course
being a sufficient condition can depend on circumstances. The results here
show that B, C, and D are not individually or jointly sufficient to bring about
Y. But they might be sufficient in a different circumstance. Suppose only X
is present, but not B, C and D. Then suppose we add B, C, and D.
Presumably the effect Y would return. Then their introduction would suffice
to bring about the effect, but they are not sufficient on their own.
Like the negative Method of Agreement, the Negative Method of
Difference can be used to refute contentious causal claims. In the last
section, you were presented with three such claims and asked to use the first
method to generate counterexamples. We can list the same claims here, and
apply the second method:
A sufficient condition for succeeding at life is graduating college.
330
Poverty and ignorance cause people to commit acts of terrorism.
A country’s possession of natural resources makes it prosperous.
Last time you were asked to think of examples in which the alleged cause
was missing while the effect was present. This helped show that the alleged
causes were not necessary to bring about the effect. Now you can do the
opposite. Can you think of cases in which the alleged cause is present, but
the effect absent, to show that it is also not even a sufficient condition for the
effect? Can you think of people who have graduated from college but who
have not been successful in life? Can you think of poor, uneducated people
who do not commit acts of terrorism? Can you think of countries with
plentiful natural resources who nonetheless fail to achieve economic
prosperity?
Here is a summary of the difference between the two most important
of Mill’s methods we’ll learn: what they identify, what they eliminate, and
how in each case. You may find this useful to memorize.
Method
Works by…
Identifies… Negative method
works by…
Agreement Identifying factors
Sufficient Finding an alleged
common to all cases
condition cause absent when
sharing the same effect
effect present.
Difference Identifying only factor Necessary Finding an alleged
different between cases condition cause present when
differing in effect
effect absent.
Eliminates…
Necessary
condition
Sufficient
condition
The joint method
Earlier we noted that the Method of Difference provides conclusions with a
higher degree of confidence than the Method of Agreement. Usually this is a
result of the carefully controlled conditions that experimentation makes
possible. Sometimes, however, we want more confidence than the Method of
Agreement, but controlled experimentation is still not possible. It is useful to
observe that there is an intermediate method identified by Mill which
provides more certainty than Agreement, but not as much as Difference.
Usefully, it can be used even when controlled experimentation is not
possible, even when nothing like a controlled experiment is possible
(nothing involving the comparison of two cases that differ in only one
respect).
Consider this data from another hypothetical food-poisoning case:
331
Subject
Turkey
Apples? Beer?
Cream?
Effect?
1
No
Yes
Yes
Yes
Sick
2
Yes
Yes
No
Yes
Sick
3
Yes
No
No
No
Not sick
4
No
Yes
No
No
Not sick
Notice that the Method of Agreement will take us only so far here. We see
two factors that are common in both cases of the effect: the cream and the
apples. It would be nice if we could perform a controlled experiment, in
which we held all factors common and removed each of these possible
causes, only to see what would follow. But perhaps this is historical data and
we cannot recreate the exact circumstances of the poisoning. Notice also that
we cannot hold the other factors constant; they vary: the turkey is present in
one case, but not the other; likewise for the beer. Is there anything else we
can do to see which, the apples or the cream, is the more likely cause? We
can look at cases where the effect is absent, even if there is no way to hold
constant factors besides the two possible causes. Notice that this is what we
have above in cases 3 and 4. So looking at the cases of the missing effect
does not count as an application of the Method of Difference, but it is still
relevant data. And look what we find when we look for the presence or
absence of the apples and the beer. The apples are missing in case 3, but not
in 4, whereas the cream is missing in both cases where the effect is missing.
This increases our confidence that cream is the cause, even if we are not as
confident as we would be if we could perform a genuine Method of
Difference controlled experiment.
The above is an illustration of Mill’s “joint method,” also called the
Method of Double Agreement. According to this method, the probable
cause is the one condition (X) that is always present when the effect is
present, and always absent when the effect is absent. Illustrated
schematically, it looks like this:
X A C D  Y
X A D E  Y
B D F  no Y
A D E  no Y
332
Interestingly, we now have three methods which we can arrange in the
order in which they provide us with increasingly certain conclusions. These
three methods correspond to the stages of the “scientific method” you are
often taught in high school science classes:
1. The Method of agreement: helps form a hypothesis
2. The second step of the Joint Method: helps confirming
predictions of the hypothesis.
3. The Method of difference: helps perform a controlled
experiment
A last step of the scientific method we are often taught concerns putting the
results of our experiments in quantitative form, perhaps by formulating an
equation that describes the pattern of the numbers. The next method we’ll
examine briefly is what helps us do that.
The method of concomitant variations
First, an obligatory but simple example. Suppose we
observe a single person drinking more and more of
an alcoholic beverage. (If we wanted to make this a
truly controlled experiment, we could find a pair of
twins in the same state of health, and give one
alcohol, while having the other drink water.) As we
observe the person imbibing more of the stuff, we
Picture credit 180:
observe the following change in his behavior:
http://commons.wikimedia.org/wiki/F
ile:Jan_Vermeer_van_Delft_018.jpg
1
2
3
No alcohol
No
intoxication
A little alcohol A little tipsy
A lot of
alcohol
Smashed
At stage 1, he is normal and sober. At stage 2, he
is a little tipsy—volunteering more information
than usual, laughing more, gesticulating more
wildly. At stage 3, he is now obviously
completely smashed. He is yelling at the top of
his voice, getting violently angry at the smallest
slights to his dignity (of which he possesses very
Picture credit 181:
http://commons.wikimedia.org/wiki/File:M
olenaer,_Jan_Miense_333
_The_King_Drinks.jpg
little at this point). His face is red and he can no longer walk in a straight
line. The natural conclusion to reach here is that it is the increasing amount
of alcohol that has made him increasingly drunk. We may observe his twin,
who has been drinking only water, and observe that his behavior has not
changed in any significant way.
Unlike a more straightforward application of the Method of
Difference, in this use of the experimental method we are looking not only
for the presence or absence of the effect, but for the degree of intensity of
these present or absent factors. If, as we increase a relevant factor, the effect
increases (or decreases) in the same proportion, we have good reason to
think they are closely linked, causally. The method illustrated here is known
as the method of concomitant variations, which identifies the probable cause
as the one factor which, when altered gradually, changes in proportion to
the alleged effect. (Something “concomitant” is something that accompanies
something else. A concomitant variation is one that accompanies another
variation.) Here is the method represented schematically:
X+
X
X-
B
B
B
C
C
C



Y+
Y
Y-
X+
X
X-
B
B
B
C
C
C



YY
Y+
We include two sets of cases here in order to allow for the possibility that
factors can relate causally in both directly proportional and inversely
proportional ways. The example already considered, the relationship
between alcohol consumption and drunkenness, is a straightforward direct
proportionality. As a factor (X) is increased, the effect (Y) is increased in
step.
An example of an inverse proportionality can be seen in the following
more advanced scientific example, an experiment that permitted the
experimenter (Robert Boyle, in 1662) to derive a physical equation. Boyle
took a curved tube, shaped like a “J” like the one below, and poured liquid
mercury into it. A bubble of air remained at the end of the tube. As more and
more inches of mercury were poured into the tube, increasing the pressure
on the air bubble, the volume of the air bubble decreased.
334
Volume
Pressure
48
29 inches mercury
38
37 inches mercury
22
64 inches mercury
12
117 inches mercury
This is a perfect example of an inversely proportional
causal relationship: as the amount of pressure on the
gas increases, its volume decreases. Boyle used this
data to formulate the equation, Pressure x Volume =
constant. Or, Volume = constant/Pressure. By the logic
of the mathematics, as the pressure increases, the
volume decreases (since the constant is being divided
by a bigger and bigger number). Boyle’s law was the
basis of much of our current understanding of the
physics of liquids and gases. Every respectable
scientific equation will have observations of
proportionalities like this (direct or inverse) at its basis.
The method of residues
One last method concerns leftover effects. The previous methods we’ve
considered have relied on background knowledge of possibly relevant
factors to discover new cause and effect relations. Our last method relies on
the all of these previous methods, because it supposes that we already know
the actual causes of many different effects. It even presupposes that we are
able to know how much of an effect can be attributed to a given cause. But it
uses this knowledge to point to the existence of a cause that is not yet
known.
Here is a simple example. Suppose we pick up our luggage at the
airport, and it seems heavier than it used to be. By chance we have a list of
the items we know we packed, which we carefully weighed before packing
them. Without yet opening the luggage, we weigh it as a whole and make the
following list:
335
Clothes
Luggage itself
??
10 lbs
5 lbs
5 lbs
Total
20 lbs
We know that we had 10 pounds of clothes, and that the luggage itself
weighs 5 pounds. But the whole package weighs 20 lbs. This tells us there is
something else in the luggage—something that accounts for the extra 5
pounds—that must have been placed there without our knowledge. Maybe it
is a bomb—or a present!
This leftover method concerns leftover effects: here, it concerns the
leftover or “residual” 5 pounds that we cannot account for with known
causes. This example illustrates Mill’s Method of Residues, which identifies
the cause as the factor that remains unaccounted for after some portion of
the effects are accounted for by known causes. We can represent it
schematically like this:
C1 + C2 + ??  E1+ E2 + E3
C1  E1
C2  E2
??  E3
Supposing that we already know how to account for the portion of the effect
E1 by reference to cause C1, and for E2 by reference to C2, portion E3
remains unaccounted for, and must be due to some new, unidentified cause.
An interesting example from the history of science in which this
method revealed a new, previously unknown cause was the discovery of the
planet Neptune by Urbain LeVerrier in
1846. LeVerrier observed that the orbit of
Uranus did not follow the precise path that
was predicted by Newton’s theory of
universal gravitation. It followed that path
for the most part, but was deflected from it
slightly in certain parts of the sky.
LeVerrier reasoned that some previously
unknown massive body must be influencing
Picture credit
the path of Uranus, and proposed that if
182:http://www.flickr.com/photos/three_french_hens/
4395278810/
astronomers were to look in the right part of
336
the sky, they might observe it. Within days of his prediction, astronomers
discovered the new planet in the part of the sky he had indicated. We now
call this planet Neptune.
337
§6: DEDUCTIVE LOGIC
Chapter 17:
Deductive validity and invalidity
Ben Bayer
Drafted April 25, 2010
Revised August 23, 2010
Deduction vs. induction reviewed
In chapter 14, we spent a fair amount of time introducing the distinction
between inductive and deductive reasoning. To explain the distinction, we
made an analogy to the difference between the packing and unpacking of
luggage. Induction is the process by which we “pack” together observations
in a retainable cognitive form that is usable in the future. Deduction is the
process of “unpacking” that knowledge, of using it in application to specific
situations.
Previously, we contrasted induction from deduction in order to focus
on induction, the source of generalization and scientific knowledge. Now
that we have already dwelled on that contrast, we will briefly dwell on some
very basic principles of deductive reasoning in this, the last section of our
book.
We will discuss only the most basic principles of deduction, because
many logicians have written a great deal explaining these principles
elsewhere. From ancient Greece, where geometers perfected the first formal
deductive systems and where Aristotle first reflected on the principles that
governed these systems and
human reasoning more
generally—to the Middle
Ages, when philosophers
extended and perfected
Aristotle’s logic—to the late
19th and early 20th century,
when mathematicians and
philosophers developed a new system that supplemented, and in some cases,
may have highlighted limitations of Aristotle’s system—we can see that
logicians understand the rules of deductive logic with far greater
systematicity and precision than they do the rules of inductive logic. If you
want to learn more about the rules of deductive logic, there are whole other
texts and courses available on this subject alone.
338
Recall that induction is defined as the form of inference that generates
conclusions taken to be wider (more universal) in content than the
observations contained in the premises, whereas deduction is the form of
inference in which the conclusion states no more content than that stated in
the premises (and is necessitated by them). Part of the reason deduction is
understood so well is that it is confined to “unpacking” the content of the
stated premises. Deduction works with a finite number of premises which
contain a finite amount of information; as a consequence, there are only so
many implications one can derive from them. The rules of deductive
reasoning help to delimit precisely which implications one can derive, and
how. This is in contrast to inductive inference, which works with an entire
body of observations and background knowledge as its starting point, not all
of which can easily be summarized in the form of stated premises. This
makes it much harder to know what conclusions follow from the starting
points of induction: it is, after all, very hard even to specify these starting
points.
None of this should be taken as disparaging the usefulness of
deduction. The fact that its rules are well-understood does not mean that they
are always easy to apply or that the conclusions of deductive arguments are
obvious. Neither is true. Recall, for example, the deduction we used to solve
the riddle in chapter 14 (“Brothers and sisters have I none, but this man’s
father is my father’s son”). And though we cannot possible study the content
or even all of the method used to perform them, we should mention just a
few examples of sophisticated deductive argumentation that have helped
scientists uncover surprising new facts about the world. Induction may be
the indispensible fuel of human reasoning power, but deduction is where the
rubber hits the road.
Way back in chapter 1 when we were discussing the ancient evidence
for the conclusion that the Earth is a sphere, we mentioned that the Greeks
were even able to infer the size of the Earth from (literally) mundane
observations to within a small margin of error of the correct conclusion.
Their argument was deductive, beginning with premises taken from
trigonometry and
observations of
measured quantities.
Here is Eratosthenes
proof of the Earth’s
circumference:
339
1.
2.
3.
4.
5.
6.
7.
8.
The angle of the shadow at noon at Alexandria is 7.2˚
Alternating interior angles are equal.
Therefore, the angle between Alexandria and Syene is 7.2˚
The distance from Alexandria to Syene is 500 miles.
But (Circumference of earth/500 miles)=360˚/7.2˚
Therefore Circumference of earth = 25,000 miles.
But Circumference/π = Diameter, 25,000/3.14 = 8,000 miles.
Therefore, the diameter of earth is 8,000 miles.
Using knowledge of the size of the Earth, and a
related argument for the size of the moon, the Greeks
were even able to determine the distance to the sun:
1. The angle between the sun and the moon
during a half moon is 87˚
2. Cos 87˚ = moon distance/sun distance
3. Sun distance/moon distance = 1/cos 87˚ =
19
4. Therefore, the sun’s distance from the earth
is 19 times its distance to the moon.
Through mere connections of deductive logic, the
Greeks were able to travel millions of miles with their minds.
A final example of the amazing power of deductive reasoning is so
complicated that we cannot even represent the argument in symbolic terms
here that the reader is likely to understand. Using fundamental laws of
electricity and magnetism that he himself had formulated, James Clerk
Maxwell, famously constructed a proof in 1864 showing that a change in a
electrical field would induce a corresponding change in the magnetic field.
But it was already known that the reverse was true, that a changing magnetic
field would cause a change in the electrical field. It followed logically that
the first would cause the second, which would in turn cause the first, and
then the second, etc. Maxwell was predicting the existence of what we now
call electromagnetic waves. He even predicted their speed, which
corresponded closely to the known speed of light: Maxwell had shown that
light was an electromagnetic wave. His discovery was the basis of countless
innovations in 20th century electronics.
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We cannot
hope even to begin
to teach you how to
be an Eratosthenes
or a Maxwell. The
deductions you will
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learn to perform
will be comparable simple. But you have to walk with simple syllogisms
before you can run with whole chains of sophisticated deduction.
Two requirements of reasoning in general, and of deduction in particular
Before we describe some basic rules of deductive reasoning and methods of
evaluating the quality of deductive argument, it is worth reviewing the most
general requirements of reasoning of any kind. Recall our three basic rules:
1. The premises of the argument must be known and known better than
the conclusion (they must be well-evidenced).
2. The premises must be relevant to the conclusion (they must be likely
to establish the conclusion as true).
3. The argument’s premises must contain all of the known relevant
evidence.
The first requirement applies to deductive arguments no differently
than it applies to inductive ones. Premises can be shown to be wellevidenced if they are either derived from some form of direct awareness, or
from some further premises that are themselves derived from a form of
direct awareness. Either way, the premises must be ultimately derived from
some form of direct knowledge, like sensory observation. We discussed this
requirement in more detail in chapter 3.
Regarding the second requirement, in good non-deductive arguments
premises are relevant to their conclusion when they are such that if they are
true, the conclusion is at the very least highly likely to be true. (Some might
suggest that inductive arguments can still establish conclusions that are
made necessary not only by stated premises, but by the totality of unstated
background knowledge.) The relevance relationship between the premises
and conclusion of a good deductive argument, on the other hand, is of such a
special type of relevance that if these premises are true, the conclusion
absolutely must be true, and this follows from nothing more than its
premises. We will explore this special type of relevance in the next section:
it is called validity.
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Back in chapter 7, we also discussed how the third requirement
applies differently to inductive and deductive reasoning. The whole function
of deductive inference is just to unpack the implications of some stated
premises. If a given conclusion is not an implication of these premises, the
argument containing the conclusion is simply not valid. If the conclusion is
an implication of these premises, the argument containing it is valid, and no
assessment of other relevant evidence is needed to see this: those premises
are all the relevant evidence there is. This is not the case in inductive
inference, which can establish conclusions as at least somewhat probable
independently of other considerations, and the probability of an inductive
conclusion can change for better or worse as more evidence is brought in.
All of this, however, is dependent on understanding the nature of the
difference between deductive and inductive relevance. We will now focus
exclusively on the topic of deductive relevance, i.e., validity.
As a preliminary introduction to the uniqueness of deductive
relevance, consider the following two arguments. Which one is inductive,
and which is deductive? Is there any difference between the kinds of
relevance you see in each?
All rain is from condensed cloud vapor.
Rain is falling in New Orleans.
Therefore, cloud vapor is condensing in New Orleans.
We know that water evaporates when it is hot.
We know that water condenses on cool surfaces.
We see clouds present whenever it rains.
All rain is from condensed cloud vapor.
Deductive validity, soundness, and invalidity
The name given to deductive relevance is “validity.” An argument is said to
be deductively valid if its conclusion cannot be false if its premises are
assumed to be true; i.e., it is such that if its premises are true, its conclusion
must be true. A key part of this definition is that validity is a fact about
arguments conditioned on the assumption that their premises are true. It is
purely an assessment of the relevance of these premises, independent of
whether or not they are really true. Judging validity involves a kind of
pretense: we pretend that the premises are true, and see what follows—even
if we know they are not.
Validity, then, is distinct from soundness: an argument is said to be
deductively sound just in case its conclusion follows validly from premises,
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when all these premises are known to be true. Every sound argument is
valid, but not every valid argument is sound. An
argument can be valid even if its premises are known
to be false: what makes it valid is that it is such that if
the premises were true, they conclusion would be true.
We need examples to bring out this distinction.
Our favorite stock example of a deductively valid
argument is also an example of a deductively sound
argument:
All men are mortal.
Socrates was a man.
Therefore, Socrates was mortal
As we demonstrated in chapter 14 through the use of simple circle diagrams,
if these premises are true, the conclusion has to be true. What makes this
argument sound in addition to valid is that the relationship between the
premises and conclusion is not merely hypothetical: we do accept that these
premises are true, and hence that the conclusion is, as well.
Contrast the Socrates argument with the following pair of valid but
unsound arguments:
All men are immortal.
Fido is a man.
Therefore, Fido is immortal.
All dogs are philosophers.
Socrates is a dog.
Therefore, Socrates is a philosopher.
And surely this instinct of the dog is very
charming;—your dog is a true philosopher.
Why?
Why, because he distinguishes the face of a
friend and of an enemy only by the criterion of
knowing and not knowing. And must not an
animal be a lover of learning who determines
what he likes and dislikes by the test of
knowledge and ignorance?
Most assuredly.
And is not the love of learning the love of
wisdom, which is philosophy?
--Plato, Republic, Book II
Suppose that Fido, per his name, really is a dog. In that case, the first
argument scores a trifecta of unsoundness: each and every statement, both
premises and the conclusion, is false. But the argument is valid. If all men
were immortal and Fido were a man, he would be immortal. The same can
be said for the second example, though in this case, we have two false
premises in effect cancelling each other out and yielding a true conclusion.
You should think of deductive validity as a testing a purely
hypothetical relationship between premises and conclusion. When we
evaluate validity, we are, in a way, performing a test in our imagination. But
it is a test in the imagination that is constrained rigorously by our premises
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and our understanding of the meaning of any statements of the form “S is
P”: if All S is P, and Fido is an S, then Fido must also be a P. Deductive
validity involves a special kind of relevance because its relevance is based
strictly on the form of its premises and conclusion. We will say more about
what this means shortly.
If you really understand the concept of deductive relevance, i.e. of
validity, you will appreciate why the following is a fairly clear example of
an invalid argument:
All men are mortal.
All mice are mortal.
Therefore, all mice are men.
We know both of the premises to be true. But the conclusion is quite
obviously false. Recall: a valid argument is one whose conclusion cannot be
false if its premises are assumed to be true. In this case, not only can we
assume the premises to be true, we know they are! So we know that the truth
of this conclusion could not follow from assuming the truth of these
premises, because we know the conclusion is false, even as we know that the
premises are true. Examples like this, in which we know the premises are
true but the conclusion false, are case studies of invalid arguments. Knowing
that these are the most obvious case studies proves to be useful for
evaluating arguments as invalid even when we do not know whether their
premises and conclusion are true or false.
If you really, really understand the concept of validity, you will even
be able to discern why the following are examples of invalid arguments:
All people are animals.
All animals move.
Therefore, all philosophers are people.
Picture credit 184:
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2RKpV2ORjZwhttp://picasaweb.google.com/lh/photo/zXenfB_2
m42RKpV2ORj-Zw
This example is tricky to someone who is
new to the rules of validity, because each
premise is true—and so is the conclusion. Yet
it is invalid. The premises “All people are
animals” and “All animals move” says
something about animals, and we might think
this is a common factor that could yield some
new conclusion. But the conclusion, “All
philosophers are people,” is one which,
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though we know to be true, seems to have nothing at all to do with the
premises. The premises, after all, said nothing about philosophers. If you
understand the concept of deductive validity, you should now clearly see
why validity is entirely a matter of the relationship of relevance between the
premises and the conclusion. In this argument, all of the premises are true, as
is the conclusion, but the premises do not make the conclusion true. Nothing
links the premises to the conclusion.
As a final test of your understanding of validity, consider a second
example:
All human beings are mortal
All philosophers are mortal.
Therefore, all philosophers are human beings
Unlike the previous example, there is no new concept that appears in the
conclusion that makes it obviously irrelevant to draw. The conclusion
mentions something about philosophers and their relationship to people, and
both were mentioned in the premises. Making things trickier still is the fact
that both premises are true, as is the conclusion. But if you remember that
not every set of true premises is related to every true conclusion, you should
remember that these true premises do not necessarily make this true
conclusion true. We could imagine a situation in which, though the premises
are true, the conclusion is false. Suppose that all people are mortal, as are all
philosophers. But it turns out that some philosophers are mortal Martians. In
this case, it would not follow that all philosophers are people. Even though
the present conclusion is true given the facts we know about philosophers,
we would not be averse to changing it if we discovered new kinds of
philosophers in the universe, even if we continued to accept the premises as
true.
If, in order for an argument to be sound, it must be both valid and in
possession of true premises, it follows that every invalid argument is also
unsound (though some unsound arguments are valid). All of the possible
combinations are summarized on the following table:
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As you can see, no special combination of premise types (true or false) will
make an argument valid. Any of the four possible combinations in the first
column can be invalid. Of the valid arguments, only one possibility allows
the argument to be sound: the case in which the argument has true premises
and a true conclusion. Of course there are examples of valid arguments
where this does not hold: valid arguments can have false premises with a
true conclusion, or false premises with a false conclusion. What makes them
valid is that if their premises were true, their conclusion would be as well.
And all of the invalid arguments are of course also unsound: to be sound an
argument must be valid as well.
With these distinctions in mind, can you tell which if any of the
following arguments are valid? And which of the valid ones are also sound?
All U.S. senators are federal representatives.
All federal representatives work in Washington, DC.
Therefore, all U.S. senators work in Washington, DC
Some politicians are promise-makers.
Some promise-makers are sincere.
Therefore, some politicians are ambitious.
Some politicians are liars.
Some liars are killers.
Some politicians are killers.
Some politicians are truth-tellers.
Some truth-tellers are fools.
Therefore, some politicians are fools.
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The counterexample method of testing validity
How easy was it for you to tell that any of the above arguments were
invalid? It is particularly hard to tell in cases where you think that the
premises and the conclusion are true. How can you tell whether or not the
true premises make the conclusion true?
In the last section, we mentioned a way of evaluating this by trying to
think of a situation in which the premises could be true but the conclusion
false. If we think of the way in which true premises make conclusions true as
analogous to a kind of cause and effect relationship, then when are looking
for an example in which the premises might be true but the conclusion false,
we are doing something like applying Mill’s negative method of difference
for refuting causal claims. We’re looking for a case in which the alleged
cause (the truth of the premises) is present, but the effect (the truth of the
conclusion) is absent. Any time we find an argument with true premises and
a false conclusion, we know it cannot be valid for this reason. This is
reflected by the one block missing examples in our table of different
possible argument types:
What if we simply can’t think of a situation in which the given
premises are true, but the conclusion false? What if we don’t even know
when the premises of a given argument are true and its conclusion false? It
can be difficult to know how to do either, and our failure to do either doesn’t
show that the argument is valid; we might simply lack imagination. We need
a more systematic method of finding counterexamples, so that if we fail even
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after applying this method, it is at least more likely that what we have in the
end is a valid argument. We need a method that helps us transform
arguments into equivalents for which counterexamples are easier to find.
There is such a method that works with some understanding of what it
is it about a set of premises that makes a conclusion true. Consider a case
where true premises obviously do make the conclusion true.
All men are mortal
All mortals are living
All men are living.
What makes these premises guarantee the truth of the conclusion? It is
something about the abstract pattern of the argument. Notice in this case that
there are terms in the premises that also appear in the conclusion (“men . . . .
living”). A third term (“mortal”) is common to both premises, but missing
from the conclusion. And there is something about the order in which these
terms appear that is important. After all, the following argument with the
exact same terms would clearly not be valid:
All men are mortal
All living things are mortal.
All living things are men.
The only difference between this argument and the previous is that the terms
in the second premise and the conclusion have been reversed. The second
premise is still true, but the conclusion is false.
So there is something about the abstract pattern of the terms in the
premises and conclusion that makes one argument valid and the other
invalid. So what happens when we turn to an entirely different argument,
composed of different terms, but possessing the same abstract pattern, the
same form? An argument of exactly the same form would also have the same
deductive validity—and, we presume, because it has the same form. For
example:
All vampires are immortal.
All immortals are undead.
All vampires are undead.
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What exactly do we mean by the “form” of an
argument? The form of a statue, for example, is its
shape, as opposed to its matter or stuff. We can make
copies of a statue using many different materials—
marble, bronze, plaster, etc.—but they are copies of
that statue as long as they are of the same shape. When
we speak of the form of an argument, we mean the
“shape” of the statements composing it, the order in
which various terms appear in premises, and the order
of the same terms in the conclusion.
Picture credit 185:
If it is the form of an argument that allows its
http://www.flickr.com/photos/blon
davenger/2455815329/sizes/m/in/
premises to determine the truth of its conclusion of a
photostream/
deductive argument, perhaps
having the wrong form could account for the invalidity
of deductive arguments. Let’s look at an example of an
argument that we can agree is obviously invalid, with
premises that are obviously true and a conclusion that
is obviously false:
All men are mortal.
All mice are mortal.
All mice are men.
Picture credit 186:
http://www.flickr.com/photos/sulin/266340072/
If it is an argument’s form that
allows the truth of the premises
to guarantee the truth of its conclusion, what is the
form of the argument above? We represent it this way:
All A are B.
All C are B.
All C are A.
We know that an argument of this form can include
true premises and a false conclusion, because the “All
mice or men” argument is of this form. So if any other
argument has this same form, we know that nothing
about its form guarantees that true premises must be
accompanied by true conclusions. And since form is
the source of deductive validity, missing the right form
means the argument cannot be valid.
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y7171/15315121/
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Suppose, for example, that we were asked to evaluate the validity of
these arguments:
All whales are cetaceans.
All dolphins are cetaceans.
All dolphins are whales.
All derivatives are options.
All futures are options.
All futures are derivatives.
All naiads are fairies.
All dryads are fairies.
All dryads are naiads.
Notice that each of these arguments has the same “bad form” as the “All
mice are men” argument. If the abstract form of that argument is consistent
with having true premises and a false conclusion, we know that nothing
about the form of these arguments will guarantee a true conclusion. So even
if we don’t know what a cetacean is, what the difference between a
derivative and an option is, or the meaning of any of the terms in the last
argument, we can still know—without knowing whether any of these
statements are true or false—that these arguments simply lack the necessary
form to be valid. They lack the necessary form, because they are all
instances of the form “All A are B, All C are B; Therefore all C are A.”
These observations help give us a recipe for finding counterexamples
that prove the invalidity of many arguments. We know that if an argument
has true premises and a false conclusion, it cannot be valid. But if the form
of another argument would permit the substitution of the obviously invalid
argument, we know that that the other argument itself does not have the
form that it needs to be valid. Here, then, are the steps by which this
counterexample method works.
1. First, we break the argument down into premises and conclusions.
Suppose we want to test the following argument for validity:
Some traders are not brokers.
All buyers are traders.
Some buyers are not brokers.
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2. Next, we find the abstract form of the argument, as follows:
Some A are not B.
All C are A.
Some C are not B.
3. Finally, we find substitution instances for each of these abstract
variables that amount to an argument in which the premises are
obviously true, and the conclusion obviously false. Here is one such
example:
Some animals are not mammals.
All dogs are animals.
Some dogs are not mammals.
It is useful, for the purposes of the counterexamples involved in this method,
to work with concepts like animals, mammals, and dogs, for which we
already have clear knowledge of the category relationships in question. We
know that it is obviously true that animals are not mammals if we know of
fish and birds. We know it is true that all dogs are animals (none are plants).
And yet, we know that the conclusion here is false: it’s false that some dogs
are not mammals. Does someone think they are reptiles or amphibians?
Since the argument about traders, brokers, and buyers has the form that
permits this obviously invalid argument, nothing about the form of the
traders/brokers/buyers argument supports its validity. We can conclude it is
invalid.
This three-step method helps clarify the concept of validity for us,
especially insofar as it may have been difficult to detect when arguments
containing actually true premises and actually true conclusions could still
fail to be valid. Here we return to the example of this type of argument
mentioned before:
Some politicians are truth-tellers.
Some truth-tellers are fools.
Therefore, some politicians are fools.
The abstract form of this argument is as follows:
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Some As are Bs.
Some Bs are Cs.
Therefore, some As are Cs.
But there are fairly straightforward counterexamples (and probably many
more) to any argument utilizing this pattern:
Some friends are unhappy people.
Some unhappy people are enemies.
Therefore, some friends are enemies.
Consider a final analogy to help explain how an argument’s form
helps determine its validity. Arguments are not the only things that have a
form. Anything with a physical shape also has a form (as our earlier example
of statues brought out). Sometimes in matters outside of logic, the physical
form or shape of a thing can also determine whether or not it has a relevant
property or power to get something done. To take a somewhat curious
example, the shape of a thing can determine what kinds of spaces it can fit
through. Suppose we have a triangular hole of a specific size cut into a wall.
Non-triangular objects greater than a specific surface area could not fit
through the hole, because of its shape. Suppose we use a bundt cake mold to
create circular objects of a larger size. Well then the circular form of the
cake mold does not make objects of the right size to fit through this
triangular hole:
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But suppose that we can fill that cake mold with many different substances.
We can fill it with water and freeze it, or with concrete mix, or with Jello.
Many of these substances will yield “cakes” that will be too solid to fit
through the hole. Using Jello, the size and shape will still be wrong to fit
easily through the hole, but perhaps the right kind of squeezing can still
accomplish the task. The Jello example is analogous to the examples above
in which argument’s form is invalid even if the premises and conclusion are
true. In these cases, there is nothing about the form of the argument that
transmits truth from the premises to the conclusion. Still, the conclusion is
true, but it’s true as a matter of luck. Likewise, in this example, it’s not the
form of the cake as supplied by the bundt that allows it to pass through the
triangular hole. All things being equal it wouldn’t have so passed. But by
chance, the material in this case is squishy enough that it can pass through
after all, just like a conclusion might have been true by chance.
Sadly, this doesn’t mean that testing validity is always a piece of
cake…. Here, then, for final practice, is another example of an argument that
may be tested for validity using this counterexample method:
Some philosophers are not poets, for some singers are not poets (P)
and some poets (P) that are not singers (S) are philosophers.
Which of the following best captures the form of this argument?
1. Some S are not P.
Some P are F.
Some F are not P.
2. Some P that are not S are F.
Some P are not F.
Some S are not P.
3. Some S are not P.
Some P that are not S are F.
Some F are not P.
4. Some F are not P.
Some S are not P.
Some P that are not S are F.
5. Some F are not P.
Some S are not P.
All P that are not S are F.
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If you look carefully, you will see that it has to be 3. So which of the
following substitutions gives us a counterexample, a case in which we have
two true premises and a false conclusion which shows that the argument as
presented is not valid?:
1.
2.
3.
4.
5.
P = mammals, S = animals, F = dogs.
P = cats, S = trees, F = animals.
P = mammals, S = cats, F = animals.
P = animals, S = trees, F = cats.
P = fish, S = dogs, F = mammals.
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§6: DEDUCTIVE LOGIC
Chapter 18:
Categorical syllogisms
Ben Bayer
Drafted May 2, 2010
Revised August 24, 2010
Categorical syllogisms defined
In chapter 17, we observed that if an argument has all true premises but a
false conclusion, we don’t need any special method for judging its validity:
we know it is invalid. A valid argument is one that is such that if its premises
are true, its conclusion must be true, i.e., its conclusion cannot be false. So if
we have an argument whose premises are true while its conclusion is false,
we know that it is not one for which the truth of the premises forces the truth
of the conclusion. The conclusion is not true, so its premises did not have
that power.
But we don’t always know if the premises of an argument are true and
its conclusion false. Sometimes we don’t know enough about the subject
matter to know the truth or falsehood of any of the statements in the
argument. When this happens, we need a systematic method for determining
whether an argument is invalid. We examined a fairly systematic method in
the last chapter: the counterexample method. To use this method, we took an
argument of unknown validity and identified its abstract form. For example,
this argument
All philosophers are mortal.
All dogs are mortal.
Therefore, all philosophers are dogs
has the following abstract form:
All A is B
All C is B
Therefore, All A is C.
We took this abstract form and looked to see if we could identify examples
to substitute into the abstract variables, which would yield an argument with
all true premises and a false conclusion. For instance, the following
substitution yields the desired result, proving that the argument is invalid:
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All men are living.
All insects are living.
Therefore, all men are insects.
(T)
(T)
(F)
This method of finding counterexamples through substitution into the
abstract form is very effective, but it has at least two limitations. First, it
depends in part on the power of your imagination, or at least on your
patience for the repeated use of trial and error, in order to find substitution
instances that finally yield the desired T, T, F combination. Second, it is only
a method of demonstrating that the argument is invalid. We do not have a
comparable method for demonstrating that an argument is valid. You might
point out that if we try and try, and simply can’t find a counterexample
demonstrating the invalidity of a method, this is good enough to show that
an argument is valid. And it is often good enough for us to assume that
provisionally. But it is not a definitive proof. Perhaps our imagination or
patience are simply in short supply, and we haven’t tried hard enough.
The question of how we prove the validity of an argument—proving
whether or not it is a proof!—is a bigger question than we can answer in
what remains of this book. There are many forms of deductive reasoning and
proof that we will not examine here, and questions about logical “metatheory” (the theory of how we prove that something is proven or provable),
are especially complicated. From the beginning, it has only been our goal to
examine the most basic principles of the most basic forms of deductive
reasoning, and we will continue to confine ourselves to this goal in this
chapter. We’ll be interested in just one method of showing that just one kind
of deductive argument is valid: the Venn diagramming method of
demonstrating the validity of categorical
syllogisms.
What is a categorical syllogism? It is
the type of deductive argument that is
implicit in much of the flesh of everyday
thinking that concerns relationships among
categories. Consider these two separate
arguments:
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4/
Saints cultivate some excellence. After all, saints are virtuous.
Yes, even the divine Socrates must be mortal. Alas, he is a man.
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If these arguments make sense to you, it’s because they rely implicitly on a
slightly more elaborate structure, which looks as follows:
All saints are virtuous people.
All virtuous people are cultivators of excellence.
Therefore, all saints are cultivators of excellence.
All men are mortal beings.
Socrates is a man.
Therefore, Socrates is a mortal being.
By now you are all too familiar with arguments of this type (especially the
second). They are examples of categorical syllogisms. Not every deductively
valid argument is a categorical syllogism. Here are some other arguments
widely given as exemplary deductive arguments, but which are not
categorical syllogisms:
If Edison was a hero, he overcame great obstacles in the pursuit of a
goal.
Edison was a hero.
Therefore, he overcame great obstacles in the pursuit of a goal.
Any inventor is either inspired or hard working.
Some inventor is not hard working.
Therefore, some inventor is inspired.
These arguments draw on forms of deductive logic that we will not examine
in this chapter, only because they are more advanced and better suited for a
longer discussion of their own. Notice that the first involves the use of a
premise involving an “if-then” statement. This makes it a form of
hypothetical syllogism (in particular, it is a “mixed hypothetical syllogism”).
The second also makes use of an “either-or” premise, as well as the
relationship between a premise using the quantifier “any” and another with
the quantifier “some.” It is a form of disjunctive syllogism, and one that is
said to involve a special logic of logic of quantified predicates.
Our focus will be categorical syllogisms. Since we’ve called all three
of these types of reasoning “syllogisms,” it is worth briefly defining that
term. A syllogism is a deductive argument from two premises. There are
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other deductive arguments that are not syllogisms. Consider, for instance,
this three premise argument:
If someone is an inventor, then everyone is helped by his creation.
If someone is an artist, then someone or other is inspired by her work.
Edison was an inventor, and Austen was an artist.
Therefore, everyone is helped by his creation, and someone is inspired
by her work.
So we know that a categorical syllogism is one kind of two-premise
deductive argument. But what sets it apart from the other kinds of syllogisms
briefly mentioned above? The difference stems from the type of judgment
used in the premises and the conclusion. Here are examples of the type of
judgment used:
All saints are virtuous people.
Some saints are heroes.
No heroes are villains.
These are the type of judgments that describe relationships among
categories. Categories are just the classes or kinds into which we divide up
the world. They’re anything we mean when we use a general concept.
The first statement represents a relationship between categories also
shown using this circle diagram:
You can see that this shows the same relationship between saints and
virtuous people as “All saints are virtuous people,” because the circle of
“saints” is entirely contained within the circle of “virtuous people”; none of
the “saints” circle is outside of the circle of “virtuous people.” The second
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statement states a different kind of category relationship, this time as
represented by the following circle diagram:
We see that this diagram represents “Some saints are heroes” because only
part of the circle of “saints” overlaps the circle of “heroes.” The last
statement, “No heroes are villains,” separates these categories even further:
In fact these categories are entirely separate: hence, “No heroes are villains.”
These types of judgments are called categorical judgments, which are
judgments that relate a subject and predicate concept, each of which is
taken to stand for a class or category of objects. That means that a
categorical syllogism is just a syllogism whose premises and conclusions are
composed of categorical judgments. (In grammar as well as in categorical
logic, the subject term of a sentence is the one that refers to what one is
talking about; the predicate term is the one describing what one says of the
subject.)
Because a categorical syllogism has two categorical premises, and
each premise has two terms, we can expand its description as follows. A
categorical syllogism consists of
a) Three categorical propositions (two premises and one conclusion)
b) A total of three and only three terms, each of which appears twice
in distinct propositions.
With only this many terms in this many propositions, one of the three terms
must appear in a way that links the two premises but drops out in the
conclusion. This term is known as the middle term. In the following
argument, “saint” is the middle term:
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Some saints are not heroes.
All perfectionists are saints.
Therefore, some perfectionists are not heroes.
The other two terms also appear twice: once in a premise, and once in the
conclusion.
Categorical judgment types
Each categorical judgment has three important components that we’ll
need to be able to identify when evaluating categorical syllogisms in the
future. First, each such judgment contains quantifiers. Here are two (but not
the only) examples of quantifiers, “all” and “some”:
All heroes are saints.
Some saints are not heroes.
Using the same examples, we can also see the second important component
of categorical judgments, the subject and predicate terms:
All heroes are saints.
Some saints are not heroes.
“Heroes” is the subject term in the first example, and “saints” is in the
second. The other highlighted terms are predicate terms. The subject is the
thing or set of things a judgment is judging about, whereas the predicate is
what is judged about those thing or things. In grammar classes, you may
have learned to classify everything that isn’t the noun or noun phrase of a
sentence as the predicate. In logic, we are considering as the predicate only
the noun or noun phrase that comes after the third major component of a
categorical judgment, the copula:
All heroes are saints.
Some saints are not heroes.
The copula is just the form of the verb “to be” (or its negative counterpart)
which links the subject and predicate concepts.
Recall that the valid categorical syllogisms we’ve considered so far
have been valid because of their form, because of the abstract pattern among
the terms involved in categorical judgments, not because of anything special
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about the meaning of the terms themselves. As a result, it is instructive to
hold fixed the “matter” of a categorical judgment—the subject and predicate
concepts—and vary the form—the types of quantifier and copula. If we
know all of the ways in which these aspects of the form can differ, we will
be able to know how a difference in form can make a difference in whether
an argument is valid or not. Holding our subject and predicate concepts
fixed, here are the four types of categorical judgments—the four types of
categorical form—that are possible:
The convention here is to name these four categorical judgment types with
the letters A, E, I and O (which you may remember as the first four vowels).
There are four types because there are four possible combinations of
the two kinds of quantity (as represented by choice of quantifier) and two
kinds of quality (as represented by choice of copula). A universally
quantified judgment is one that says something about every member of a
category. Notice that even “No heroes are saints” does this: it says of all
heroes that they are not saints. A judgment with a particular quantity is one
that does not say something about every member of the category, but does
say something about at least one such member. The representative of an
affirmative quality indicates that a predicate is affirmed of a subject, i.e., the
predicate is said to be true of the subject. A judgment possesses a negative
quality when it claims that a predicate is not true of a subject.
Notice, of course, that since we are keeping the same “S” and “P”
terms through these four examples, it is impossible for all four of these
statements to be true at the same time. (In particular, if the first statement,
named “A,” is true, then at the very least the statement named “O” cannot be
true. Ordinarily, you would think that if “A” is true, “E” could not be true,
either.)
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If you understand the ways in which these four judgment types differ,
in terms of both quantity and quality, you should be able to take any
particular judgment and change just one of the dimensions without the other.
Consider the following examples:
1.
2.
3.
4.
Some orcs are not urukai.
No dwarves are men.
All urukai are orcs.
Some hobbits are reliable hobbitses.
What do you get when you change the quality of each, but not the quantity?
Or when you change the quantity, but not the quality?
Diagramming categorical judgments
Earlier, we used intersecting circle diagrams to represent various kinds of
categorical judgments. These are called Euler diagrams, after the
mathematician who popularized their use. Although these Euler diagrams
are straightforward when it comes to representing single judgments, it turns
out that it is not always easy to use them to represent the relationship
between two separate judgments in the way we need to represent syllogisms.
For this reason, we will adopt a slightly more complicated form of circle
diagram which, while it is slightly less intuitive, will turn out to be easier to
use to represent syllogisms. Here are the simpler Euler diagrams:
We will now learn about the slightly more counterintuitive kind of
diagram, called a Venn diagrams (again, named after their originator). (Note:
among teachers and business professionals, the phrase “Venn diagram” is
sometimes used to refer to any intersecting circle diagram. This is
inaccurate; only the kind of intersecting circle diagram we’re about to learn
is properly a Venn.) Every Venn diagram we’ll use begins with a simple
template, which otherwise looks like the diagram of “Some S is P” above.
But it does not mean “Some S is P”: as a mere template, it doesn’t actually
mean anything yet:
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Because we’re treating this as a template, it doesn’t acquire any meaning
until we do something to fill it in.
Here is how we will represent the “All S is P” categorical judgment:
When you see the left portion of the “S” circle filled in, you tend to think of
it as a form of marking territory, as a way of highlighting something that is
present. But you should really think of this filling in as a blackening out.
When this portion is blackened out, the diagram is, in effect, lopping off this
portion of the original “S” circle. All that is now left of “S” is what is still
white, what is inside “P.” Do you now see how this is equivalent to the
original Euler “All S is P” diagram? In the Euler diagram, the “S” circle is
entirely contained within the “P” circle. Here, all that remains of the “S”
circle is entirely contained within the “P” circle. The idea and the topology
is the same.
You can see the same logic at work in the Venn diagram for “No S is
P”:
Again, don’t think of the middle portion as filled in or as an overlap between
the two classes; instead, think of it as a blackened-out deletion. This diagram
is now saying that there is no overlap between the “S” circle and “P” circle.
(Think of the diagram as two kissing Pac-Men.) In the same way, the
original Euler diagram simply shows the “S” and “P” circles as entirely
separate, i.e., as not overlapping.
For “Some S is P” and “Some S is not P,” we introduce a new
symbolic element, the asterisk. Here is “Some S is P”:
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This diagram says that there is at least one S that is also P, i.e., “Some S is
P.” By the same token, the following says there is at least one S that is not
also P (“Some S is not P”):
We have now encountered three distinct symbolic elements of Venn
diagrams: black space, which means nothing is in the area designated, the
asterisk, which means something is present, and white space. What is the
white space, if not something or nothing? It is ignorance. It indicates that
there may or may not be something present in the area designated, that the
premise in question simply does not tell us.
At this point, you might be wondering why we include an asterisk in
“Some S is P,” but not in “All S is P.” The absence of the asterisk in “All S
is P” suggests that we do not know if there is at least one S that is also P. But
doesn’t “All S is P” imply that “Some S is P”? When we say that all heroes
are virtuous, aren’t we implying that there are some heroes?
The answer is somewhat controversial among logicians. The logicians
who defend the Venn diagram of “All S is P” without the asterisk argue for
what is called the Boolean interpretation of “All S is P” (after the logician
who originated the idea). According to this interpretation, we should not
suppose that “All S is P” implies the existence of any S, because there are
seemingly straightforward examples of universal affirmative categorical
judgments which we accept as true without supposing that they refer to any
real S, such as “All unicorns have horns,” or “All urukai are orcs.” The
Boolean interpretation says we should just assume that all “All S is P”
statements are the same way; with this assumption, we will never draw any
mistaken implications of existence. Here, then, are the original Euler
diagrams, paired with their Boolean Venn counterparts:
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Other logicians—who defend what is called an Aristotelian
interpretation, after the great Greek philosopher and logician—will argue
that the common sense is right, and that “All S is P” does imply “Some S is
P.” In this case, “All S is P” implies the existence of at least one S. They will
point out that of course “All unicorns have horns” does not imply the
existence of any unicorns, but that the sense in which we take this statement
to be true is not the same in which we take “All heroes are virtuous” to be
true. When we use statements taken from fiction, we are speaking in a
different voice than when we speak literalities. Accordingly, provided that
we know that we are speaking in a literal voice, we presuppose that the
subject term in question really exists, and it is fine if we place an “asterisk”
in the diagrams of universal categorical statements:
Diagramming to test simple arguments for validity
To show how these diagrams can be used to test the validity of categorical
syllogisms, we should first illustrate how they can be used to test the validity
of arguments even simpler than syllogisms: one-premise arguments called
immediate inferences..
Consider the following examples of an immediate inference:
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All saints are producers
Therefore, some saints are producers.
You’ll notice that this is an example of an implication from an “All S is P”
judgment to a “Some S is P” judgment. We know this implication holds only
on Aristotelian assumptions, and we can show this if we use an Aristotelian
diagram of both the premise and the conclusion:
Recall that an argument is valid if it is such that its conclusion cannot
be true if its premises are assumed to be true. In the same way, you can see
that this pair of diagrams is such that the second diagram contains no more
information than that contained in the diagram of the premise. The first has a
blackened left portion, and an asterisk; the second is missing the blackened
portion, but it has the asterisk. Remember that missing black space, i.e.
white space, represents nothing but ignorance: i.e., the lack of information.
So there is no information in the conclusion that is not in the premise (the
white space on the left is not information; it’s the lack of information). This
tells us that the argument is valid.
Now, consider an example of an invalid argument, demonstrated
using the same kind of method:
All urukai are orcs.
Therefore, some urukai are orcs.
This time we are speaking about things we know not to exist—the mythical
race of the urukai, the “men crossed with orcs” from The Lord of the Rings.
Since we are speaking of fictional items, we have to be sure to use Boolean
Venn diagrams to make sure we don’t infer unwarranted conclusions:
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Given the Boolean presumption against inferring “Some S is P” from “All S
is P,” we can see how this conclusion does in fact contain more information
than the premise. Right there in the middle, we see an asterisk that does not
originally appear in the premise. This is new information, not implied by the
premise. So the argument is invalid.
We could have realized in advance that the first argument was valid,
and the second invalid. We didn’t need diagrams to understand it. But now
that we know how to construct diagrams to reveal validity or invalidity, we
can use this technique to test arguments whose validity or invalidity is not as
obvious.
Diagramming to test syllogisms for validity
We now have all of the pieces we need to use Venn diagrams to test validity
of full-fledged syllogisms, i.e. two premise deductive arguments composed
of categorical judgments. To illustrate, let’s test the validity of the following
argument:
No heroes are villains.
All perfectionists are heroes.
No perfectionists are villains.
There are three steps in the method:
1. Construct a diagram with three interlocking circles, each representing
one of the terms of the syllogism.
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2. Fill in the diagrams for each of the premises.
To perform this second step, it is important to be able to focus
selectively on one pair of circles at a time. To diagram the first premise, “No
heroes are villains,” we focus exclusively on the relationship between the
“H” and “V” circles. Just for the sake of simplicity, we’ll start by using only
Boolean diagrams. The Boolean Venn diagram for a “No S is P” judgment
blackens out the overlap between the two circles, so that is what we do here.
Then, to diagram the second premise, “All perfectionists are heroes,” we
focus just on the relationship between the “P” and “H” circles, and
reproduce the Boolean Venn diagram of an “All S is P” judgment only
between these two circles:
3. See if you can “read off” the desired conclusion from the diagram of
the premises.
Just for the sake of reference, it is useful to know what the diagram of
the conclusion would look like, were it true. Here, the conclusion is “No
perfectionists are villains,” so we should focus just on the relationship
between the “P” and “V” circles, and use the appropriate Boolean Venn:
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This is just the conclusion that we would like to find in the diagram of the
premises, if we like valid arguments. So do we find it? In this case, we do.
Notice that the darker shading between the “H” and the “V,” together with
the (here) lighter shading between “P” and “H” together fully shade the
overlap between “P” and “V.” This means there is no overlap between “P”
and “V” possible, which, when translated, means that the diagram of our
premise implies “No perfectionists are villains.” This is a valid argument.
Now for a quick example of an invalid argument:
All moralists are ideologues.
No pragmatists are moralists.
No pragmatists are ideologues.
Here is our diagram of the premises:
Here is the diagram of the conclusion:
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The question is: do we see the conclusion already contained in the
premises? As you see, the question concerns the overlap between the “P”
and the “I” circle. It is filled in entirely in the diagram of the conclusion, but
not in the diagram of the premises. The premises only fill in half of that
overlap. That means this conclusion contains more information—the ruling
out of any overlap between “P” and “I”—than the premises. This argument
is invalid.
Now for a third example, but this time a syllogism using a particular
categorical judgment—not just universal judgments:
Some people are thinkers.
All thinkers are focusers.
Some people are focusers.
The usual tendency when diagramming an argument like this is to
diagram the first premise first, the second, second. But what happens when
you try doing this? If you focus on the relationship between the “P” and “T”
circles, you’ll notice that the intersection between these two circles divides
between an area that is in the “F” circle and an area that is not. Where are we
to put the asterisk? Inside “F” or not? We simply don’t know. The first
premise doesn’t tell us whether the people who are thinkers are focusers or
not. So we would have to make the asterisk “straddle” the line between “F”
and not “F”:
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These “straddling” asterisks can be a source of consternation, since they do
not reveal as much information as they would if the asterisk were on one
side of the line or the other. It would be far better if we could force a
decision. If we avoid the temptation to diagram the first premise first, we can
do that. The second premise above is a universal premise that eliminates the
possibility that the asterisk falls on one side. If we diagram the second
premise first, diagramming the first premise will be easier:
With this diagram of the premises in hand, let’s compare it to the
diagram of the conclusion, “Some people are focusers”:
Here you need to be careful. What does the diagram of the conclusion mean?
Here again we see the straddling asterisk. But this time it is not a source of
consternation, but of liberation. The straddle says that these people who are
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focusers may be either thinkers, or not. Our diagram of the premises has an
asterisk in the “T” part of the overlap, so it affirms the existence of people
who are focusers who are thinkers. This is one of the two options allowed by
the conclusion. As a result, the conclusion contains no more information
than the premises. If it had definitively affirmed that the star was on the
south side of the “T”/non-“T” divide, then it would be saying something that
the premises do not say. But since it straddles, it makes no commitment and
claims nothing that the premises do not claim. Hence, its information is
already contained in the premises, and this argument is valid.
Let’s rehearse one last example, this time one involving particular
categorical judgments, but one which turns out to be invalid.
Some dreamers are angels.
All people are dreamers.
Therefore, some people are angels.
Here is our diagram of the premises:
And here is our diagram of the conclusion, “Some people are angels”:
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As before, our conclusion contains a “straddling” asterisk. But does
the uncertainty of this asterisk help us or hurt us when it comes to
determining validity? This time, it hurts, because you’ll notice that the
asterisk in the diagram of the premises also straddles. Suppose that the
asterisk in the premises were right in the middle of the three circles, in the
intersection of “P,” “A,” and “D.” If it were there, the premises would be
giving us a definite statement about where to find existing dreamers who are
angels. But it does not. As a result, we cannot say that these premises imply
a claim that is consistent with the claim of the conclusion. If it turns out that
the asterisk in the premises straddles only because there are dreaming angels
who are not people, then the conclusion, that there are people who are
angels, does not follow. This argument is invalid.
We have now gone through most of the nuances of using Venn
diagrams to determine validity, but we have only used Boolean Venn
diagrams, not Aristotelian diagrams. Because Aristotelian diagrams for
universal judgments contain more information than Boolean diagrams for
universal judgments, the Aristotelian interpretation yields more valid
arguments than the Boolean. But because these diagrams are slightly more
complicated, we will not go into them here, and will leave their use as an
exercise for the student. Here are some syllogisms for which the Aristotelian
interpretation will sometimes deliver the same answers as the Boolean, and
sometimes not:
1. Some saints are not heroes.
All truth-tellers are saints.
Some truth-tellers are not heroes
2. All people are choosers.
All people are valuers .
All valuers are choosers.
3. All heroes are saints.
Some villains are evaders.
All evaders are heroes.
4. All good people are truth-tellers.
All truth-tellers are focusers.
Some focusers are good people.
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5. All Dryads are Tree spirits.
All Tree spirits are magical creatures.
Some magical creatures are Dryads
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