Philosophy of science



Philosophy of science
Philosophy of science
An overview
Main article
Philosophy of science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of particular sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cited texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nature of scientific concepts and statements
Demarcation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ancient Greek science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logical positivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Falsifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Postpositivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Feyerabend and Lakatos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thagard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Some historians’ perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laudan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientific realism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Main features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arguments for and against . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Models of scientific inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Accounts of scientific inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choice of a theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aspects of scientific inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of particular sciences
Philosophy of physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Purpose of physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of space and time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
History of the philosophy of physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reductionism, holism, and vitalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An autonomous philosophy of biology . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientific discovery process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recurrent themes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Major themes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contemporary schools of thought . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aesthetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Foundations of chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophers of chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figures cited in the scholarly literature . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Related disciplines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Philosophy of psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Social accountability
Epistemological anarchism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other proponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Text and image sources, contributors, and licenses
Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 1
Main article
1.1 Philosophy of science
minority of philosophers, and Paul Feyerabend (1924–
1994) in particular, argue that there is no such thing as the
"scientific method", so all approaches to science should
be allowed, including explicitly supernatural ones. Another approach to thinking about science involves studying how knowledge is created from a sociological perspective, an approach represented by scholars like David
Bloor and Barry Barnes. Finally, a tradition in continental
philosophy approaches science from the perspective of a
rigorous analysis of human experience.
This article is about the concept. For the journal, see
Philosophy of Science (journal).
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications
of science. The central questions of this study concern
what qualifies as science, the reliability of scientific theories, and the ultimate purpose of science. This discipline
overlaps with metaphysics, ontology, and epistemology,
for example, when it explores the relationship between
science and truth.
Philosophies of the particular sciences range from questions about the nature of time raised by Einstein’s general
relativity, to the implications of economics for public policy. A central theme is whether one scientific discipline
can be reduced to the terms of another. That is, can
chemistry be reduced to physics, or can sociology be reduced to individual psychology? The general questions of
philosophy of science also arise with greater specificity
in some particular sciences. For instance, the question
of the validity of scientific reasoning is seen in a different guise in the foundations of statistics. The question of
what counts as science and what should be excluded arises
as a life-or-death matter in the philosophy of medicine.
Additionally, the philosophies of biology, of psychology,
and of the social sciences explore whether the scientific
studies of human nature can achieve objectivity or are
inevitably shaped by values and by social relations.
There is no consensus among philosophers about many
of the central problems concerned with the philosophy
of science, including whether science can reveal the truth
about unobservable things and whether scientific reasoning can be justified at all. In addition to these general
questions about science as a whole, philosophers of science consider problems that apply to particular sciences
(such as biology or physics). Some philosophers of science also use contemporary results in science to reach
conclusions about philosophy itself.
While philosophical thought pertaining to science dates
back at least to the time of Aristotle, philosophy of science emerged as a distinct discipline only in the middle of the 20th century in the wake of the logical positivism movement, which aimed to formulate criteria for
ensuring all philosophical statements’ meaningfulness and
objectively assessing them. Thomas Kuhn's landmark
1962 book The Structure of Scientific Revolutions was also
formative, challenging the view of scientific progress as
steady, cumulative acquisition of knowledge based on a
fixed method of systematic experimentation and instead
arguing that any progress is relative to a "paradigm,” the
set of questions, concepts, and practices that define a scientific discipline in a particular historial period.[1]
1.1.1 Introduction
Defining science
Main article: Demarcation problem
Distinguishing between science and non-science is referred to as the demarcation problem. For example,
should psychoanalysis be considered science? How about
so-called creation science, the inflationary multiverse hypothesis, or macroeconomics? Karl Popper called this
the central question in the philosophy of science.[2] However, no unified account of the problem has won acceptance among philosophers, and some regard the problem
as unsolvable or uninteresting.[3][4] Martin Gardner has
argued for the use of a Potter Stewart standard (“I know
it when I see it”) for recognizing pseudoscience.[5]
Subsequently, the coherentist approach to science, in
which a theory is validated if it makes sense of observations as part of a coherent whole, became prominent
due to W. V. Quine and others. Some thinkers such as
Stephen Jay Gould seek to ground science in axiomatic
assumptions, such as the uniformity of nature. A vocal
cessful scientific explanation must deduce the occurrence
of the phenomena in question from a scientific law.[10]
This view has been subjected to substantial criticism, resulting in several widely acknowledged counterexamples
to the theory.[11] It is especially challenging to characterize what is meant by an explanation when the thing to be
explained cannot be deduced from any law because it is
a matter of chance, or otherwise cannot be perfectly predicted from what is known. Wesley Salmon developed a
model in which a good scientific explanation must be statistically relevant to the outcome to be explained.[12][13]
Others have argued that the key to a good explanation
is unifying disparate phenomena or providing a causal
Justifying science
Main article: Problem of induction
Although it is often taken for granted, it is not at all clear
Karl Popper c. 1980s
Early attempts by the logical positivists grounded science
in observation while non-science was non-observational
and hence meaningless.[6] Popper argued that the central
property of science is falsifiability. That is, every genuinely scientific claim is capable of being proven false, at
least in principle.[7]
An area of study or speculation that masquerades as
science in an attempt to claim a legitimacy that it
would not otherwise be able to achieve is referred to as
pseudoscience, fringe science, or junk science.[8] Physicist Richard Feynman coined the term "cargo cult science" for cases in which researchers believe they are doing science because their activities have the outward appearance of it but actually lack the “kind of utter honesty”
that allows their results to be rigorously evaluated.[9]
Scientific explanation
Main article: Scientific explanation
A closely related question is what counts as a good scientific explanation. In addition to providing predictions
about future events, society often takes scientific theories to provide explanations for events that occur regularly
or have already occurred. Philosophers have investigated
the criteria by which a scientific theory can be said to have
successfully explained a phenomenon, as well as what it
means to say a scientific theory has explanatory power.
The expectations chickens might form about farmer behavior illustrate the “problem of induction.”
how one can infer the validity of a general statement from
a number of specific instances or infer the truth of a theory from a series of successful tests.[14] For example, a
chicken observes that each morning the farmer comes and
gives it food, for hundreds of days in a row. The chicken
may therefore use inductive reasoning to infer that the
farmer will bring food every morning. However, one
morning, the farmer comes and kills the chicken. How is
scientific reasoning more trustworthy than the chicken’s
One approach is to acknowledge that induction cannot
achieve certainty, but observing more instances of a general statement can at least make the general statement
more probable. So the chicken would be right to conclude from all those mornings that it is likely the farmer
will come with food again the next morning, even if it
cannot be certain. However, there remain difficult questions about what precise probability any given evidence
One early and influential theory of scientific explanation justifies putting on the general statement. One way out
is the deductive-nomological model. It says that a suc- of these particular difficulties is to declare that all beliefs
about scientific theories are subjective, or personal, and general theory of relativity, observers would have likely
correct reasoning is merely about how evidence should interpreted the image at left as five different objects in
change one’s subjective beliefs over time.[14]
space. In light of that theory, however, astronomers will
Some argue that what scientists do is not inductive rea- tell you that is actually only two objects, one in the center
soning at all but rather abductive reasoning, or inference and four different images of the same object around the
to the best explanation. In this account, science is not sides. Alternatively, if other scientists suspect that someabout generalizing specific instances but rather about hy- thing is wrong with the telescope and only one object is
pothesizing explanations for what is observed. As dis- actually being observed, they are operating under yet another theory. Observations that cannot be separated from
cussed in the previous section, it is not always clear
what is meant by the “best explanation.” Ockham’s ra- theoretical interpretation are said to be theory-laden.
zor, which counsels choosing the simplest available explanation, thus plays an important role in some versions
of this approach. To return to the example of the chicken,
would it be simpler to suppose that the farmer cares
about it and will continue taking care of it indefinitely or
that the farmer is fattening it up for slaughter? Philosophers have tried to make this heuristic principle more precise in terms of theoretical parsimony or other measures.
Yet, although various measures of simplicity have been
brought forward as potential candidates, it is generally accepted that there is no such thing as a theory-independent
measure of simplicity. In other words, there appear to be
as many different measures of simplicity as there are theories themselves, and the task of choosing between measures of simplicity appears to be every bit as problematic
as the job of choosing between theories.[15]
Observation inseparable from theory
A celestial object known as the Einstein Cross.
When making observations, scientists look through telescopes, study images on electronic screens, record meter
readings, and so on. Generally, on a basic level, they can
agree on what they see, e.g., the thermometer shows 37.9
degrees C. But, if these scientists have different ideas
about the theories that have been developed to explain
these basic observations, they may disagree about what
they are observing. For example, before Albert Einstein's
All observation involves both perception and cognition.
That is, one does not make an observation passively,
but rather is actively engaged in distinguishing the phenomenon being observed from surrounding sensory data.
Therefore, observations are affected by one’s underlying understanding of the way in which the world functions, and that understanding may influence what is perceived, noticed, or deemed worthy of consideration. In
this sense, it can be argued that all observation is theoryladen.[16]
The purpose of science
See also: Scientific realism and Instrumentalism
Should science aim to determine ultimate truth, or are
there questions that science cannot answer? Scientific realists claim that science aims at truth and that one ought
to regard scientific theories as true, approximately true,
or likely true. Conversely, scientific anti-realists argue
that science does not aim (or at least does not succeed) at
truth, especially truth about unobservables like electrons
or other universes.[17] Instrumentalists argue that scientific theories should only be evaluated on whether they
are useful. In their view, whether theories are true or not
is beside the point, because the purpose of science is to
make predictions and enable effective technology.
Realists often point to the success of recent scientific
theories as evidence for the truth (or near truth) of current theories.[18][19] Antirealists point to either the many
false theories in the history of science,[20][21] epistemic
morals,[22] the success of false modeling assumptions,[23]
or widely termed postmodern criticisms of objectivity
as evidence against scientific realism.[18] Antirealists attempt to explain the success of scientific theories without
reference to truth.[24] Some antirealists claim that scientific theories aim at being accurate only about observable
objects and argue that their success is primarily judged
by that criterion.[22]
Values and science
If it is unclear what counts as science, how the process
of confirming theories works, and what the purpose of
science is, there is considerable scope for values and
other social influences to shape science. Indeed, values
can play a role ranging from determining which research
gets funded to influencing which theories achieve scientific consensus.[25] For example, in the 19th century, cultural values held by scientists about race shaped research
on evolution, and values concerning social class influenced debates on phrenology (considered scientific at the
time).[26] Feminist philosophers of science, sociologists
of science, and others explore how social values affect
See also: History of scientific method, History of science
and History of philosophy
The origins of philosophy of science trace back to Plato
and Aristotle[27] who distinguished the forms of approximate and exact reasoning, set out the threefold scheme
of abductive, deductive, and inductive inference, and
also analyzed reasoning by analogy. The eleventh century Arab polymath Ibn al-Haytham (known in Latin as
Alhazen) conducted his research in optics by way of controlled experimental testing and applied geometry, especially in his investigations into the images resulting from
the reflection and refraction of light. Roger Bacon (1214–
1294), an English thinker and experimenter heavily influenced by al-Haytham, is recognized by many to be the father of modern scientific method.[28] His view that mathematics was essential to a correct understanding of natural
philosophy was considered to be 400 years ahead of its
Francis Bacon’s statue at Gray’s Inn, South Square, London
particular, later in the 18th century, David Hume would
famously articulate skepticism about the ability of science to determine causality and gave a definitive formulation of the problem of induction. The 19th century writings of John Stuart Mill are also considered important
in the formation of current conceptions of the scientific
method, as well as anticipating later accounts of scientific
Logical positivism
Main article: Logical positivism
Francis Bacon (no direct relation to Roger, who lived
300 years earlier) was a seminal figure in philosophy of
science at the time of the Scientific Revolution. In his
work Novum Organum (1620) – a reference to Aristotle’s Organon – Bacon outlined a new system of logic to
improve upon the old philosophical process of syllogism.
Bacon’s method relied on experimental histories to eliminate alternative theories.[30] In 1637, René Descartes
established a new framework for grounding scientific
knowledge in his treatise, Discourse on Method, advocating the central role of reason as opposed to sensory experience. By contrast, in 1713, the 2nd edition of Isaac
Newton's Philosophiae Naturalis Principia Mathematica
argued that "... hypotheses ... have no place in experimental philosophy. In this philosophy[,] propositions are
deduced from the phenomena and rendered general by
induction. "[31] This passage influenced a “later generation of philosophically-inclined readers to pronounce a
ban on causal hypotheses in natural philosophy.” [31] In
Instrumentalism became popular among physicists
around the turn of the 20th century, after which logical
positivism defined the field for several decades. Logical
positivism accepts only testable statements as meaningful, rejects metaphysical interpretations, and embraces
verificationism (a set of theories of knowledge that
combines logicism, empiricism, and linguistics to ground
philosophy on a basis consistent with examples from the
empirical sciences). Seeking to overhaul all of philosophy and convert it to a new scientific philosophy,[33] the
Berlin Circle and the Vienna Circle propounded logical
positivism in the late 1920s.
Interpreting Ludwig Wittgenstein's early philosophy of
language, logical positivists identified a verifiability principle or criterion of cognitive meaningfulness. From
Bertrand Russell's logicism they sought reduction of
mathematics to logic.
They also embraced Rus-
sell’s logical atomism, Ernst Mach's phenomenalism—
whereby the mind knows only actual or potential sensory experience, which is the content of all sciences, whether physics or psychology—and Percy Bridgman's operationalism. Thereby, only the verifiable
was scientific and cognitively meaningful, whereas the
unverifiable was unscientific, cognitively meaningless
“pseudostatements”—metaphysical, emotive, or such—
not worthy of further review by philosophers, who were
newly tasked to organize knowledge rather than develop
new knowledge.
Logical positivism is commonly portrayed as taking the
extreme position that scientific language should never refer to anything unobservable—even the seemingly core
notions of causality, mechanism, and principles—but that
is an exaggeration. Talk of such unobservables could
be allowed as metaphorical—direct observations viewed
in the abstract—or at worst metaphysical or emotional.
Theoretical laws would be reduced to empirical laws,
while theoretical terms would garner meaning from observational terms via correspondence rules. Mathematics
in physics would reduce to symbolic logic via logicism,
while rational reconstruction would convert ordinary language into standardized equivalents, all networked and
united by a logical syntax. A scientific theory would be
stated with its method of verification, whereby a logical
calculus or empirical operation could verify its falsity or
In the late 1930s, logical positivists fled Germany and
Austria for Britain and America. By then, many had
replaced Mach’s phenomenalism with Otto Neurath's
physicalism, and Rudolf Carnap had sought to replace
verification with simply confirmation. With World War
II's close in 1945, logical positivism became milder, logical empiricism, led largely by Carl Hempel, in America, who expounded the covering law model of scientific explanation as a way of identifying the logical form
of explanations without any reference to the suspect notion of “causation”. The logical positivist movement became a major underpinning of analytic philosophy,[34]
and dominated Anglosphere philosophy, including philosophy of science, while influencing sciences, into the
1960s. Yet the movement failed to resolve its central
problems,[35][36][37] and its doctrines were increasingly assaulted. Nevertheless, it brought about the establishment
of philosophy of science as a distinct subdiscipline of philosophy, with Carl Hempel playing a key role.[38]
Thomas Kuhn
For Kuhn, the addition of epicycles in Ptolemaic astronomy was
“normal science” within a paradigm, whereas the Copernican
revolution was a paradigm shift.
its point of view. A paradigm also encompasses the set
of questions and practices that define a scientific discipline. He characterized normal science as the process of
observation and “puzzle solving” which takes place within
a paradigm, whereas revolutionary science occurs when
one paradigm overtakes another in a paradigm shift.[39]
Kuhn denied that it is ever possible to isolate the hypothesis being tested from the influence of the theory in which
the observations are grounded, and he argued that it is
not possible to evaluate competing paradigms independently. More than one logically consistent construct can
paint a usable likeness of the world, but there is no common ground from which to pit two against each other, theory against theory. Each paradigm has its own distinct
questions, aims, and interpretations. Neither provides a
standard by which the other can be judged, so there is no
clear way to measure scientific progress across paradigms.
For Kuhn, the choice of paradigm was sustained by rational processes, but not ultimately determined by them.
The choice between paradigms involves setting two or
more “portraits” against the world and deciding which
likeness is most promising. For Kuhn, acceptance or rejection of a paradigm is a social process as much as a
logical process. Kuhn’s position, however, is not one of
relativism.[40] According to Kuhn, a paradigm shift occurs when a significant number of observational anomalies arise in the old paradigm and a new paradigm makes
sense of them. That is, the choice of a new paradigm
is based on observations, even though those observations
are made against the background of the old paradigm.
Main article: The Structure of Scientific Revolutions
In his landmark 1962 book The Structure of Scientific Revolutions, Thomas Kuhn crystallized the reaction
against logical positivism. He argued that the process of
observation and evaluation takes place within a paradigm.
By paradigm he meant a logically consistent “portrait” of 1.1.3
the world that is consistent with observations made from
Current approaches
Axiomatic assumptions
served, that is likely to occasion an adjustment in the system, a change in some auxiliary assumption, rather than
Some thinkers seek to articulate axiomatic assumptions a rejection of the theoretical system.
on which science may be based, a form of foundational- In fact, according to the Duhem–Quine thesis, after
ism. This is typically the implicit philosophy of working Pierre Duhem and W. V. Quine, it is impossible to test
scientists, that the following basic assumptions that are a theory in isolation.[46] One must always add auxiliary
needed to justify the scientific method: (1) that there is an hypotheses in order to make testable predictions. For exobjective reality shared by all rational observers; (2) that ample, to test Newton’s Law of Gravitation in the solar
this objective reality is governed by natural laws; (3) that system, one needs information about the masses and pothese laws can be discovered by means of systematic ob- sitions of the Sun and all the planets. Famously, the failservation and experimentation.[41] Proponents argue that ure to predict the orbit of Uranus in the 19th century led
these assumptions are reasonable and necessary for prac- not to the rejection of Newton’s Law but rather to the reticing science. For instance, Hugh Gauch argues that jection of the hypothesis that the solar system comprises
science presupposes that “the physical world is orderly only seven planets. The investigations that followed led to
and comprehensible.”[42] Likewise, biologist Stephen Jay the discovery of an eighth planet, Neptune. If a test fails,
Gould cites the constancy of nature’s laws as an assump- something is wrong. But there is a problem in figuring
tion which a scientist should assume before proceeding to out what that something is: a missing planet, badly calido geology.[43] In this view, the uniformity of scientific brated test equipment, an unsuspected curvature of space,
laws is an unprovable postulate which enables scientists or something else.
to extrapolate into the unobservable past. In other words,
the constancy of natural laws must be assumed in order One consequence of the Duhem–Quine thesis is that one
can make any theory compatible with any empirical obto meaningfully study the past.[44]
servation by the addition of a sufficient number of suitable ad hoc hypotheses. Karl Popper accepted this thesis, leading him to reject naïve falsification. Instead, he
favored a “survival of the fittest” view in which the most
falsifiable scientific theories are to be preferred.[47]
Main article: Coherentism
In contrast to the view that science rests on foundational
Anything goes
Main article: Epistemological anarchism
Austrian philosopher of science Paul Feyerabend (1924–
Jeremiah Horrocks makes the first observation of the transit of
Venus in 1639, as imagined by the artist W. R. Lavender in 1903
assumptions, coherentism asserts that statements are justified by being a part of a coherent system. Or, rather,
individual statements cannot be validated on their own:
only coherent systems can be justified.[45] A prediction of
a transit of Venus is justified by its being coherent with
broader beliefs about celestial mechanics and earlier observations. As explained above, observation is a cognitive act. That is, it relies on a pre-existing understanding,
a systematic set of beliefs. An observation of a transit of
Venus requires a huge range of auxiliary beliefs, such as
those that describe the optics of telescopes, the mechanics
of the telescope mount, and an understanding of celestial
mechanics. If the prediction fails and a transit is not ob-
Paul Karl Feyerabend
1994) argued that no description of scientific method
could possibly be broad enough to encompass all the approaches and methods used by scientists. He claimed
there are no useful and exception-free methodological
rules governing the progress of science. Feyerabend objected to prescriptive scientific method on the grounds
that any such method would stifle and cramp scientific
progress. Feyerabend claimed that “the only principle
that does not inhibit progress is: anything goes".[48]
A major development in recent decades has been the
study of the formation, structure, and evolution of scientific communities by sociologists and anthropologists
including David Bloor, Harry Collins, Bruno Latour, and
Anselm Strauss. Concepts and methods (such as rational choice, social choice or game theory) from economics
have also been applied for understanding the efficiency
of scientific communities in the production of knowledge. This interdisciplinary field has come to be known as
science and technology studies.[53] Here the approach to
the philosophy of science is to study how scientific communities actually operate.
Feyerabend felt that science started as a liberating movement, but that over time it had become increasingly dogmatic and rigid, and therefore had become increasingly an
ideology, and, despite its successes, science had started
to attain some oppressive features. He argued it was not
possible to come up with an unambiguous way to distinguish science from religion, magic, or mythology. He saw
the exclusive dominance of science as a means of directing society as authoritarian and ungrounded.[48] Promul- Continental philosophy
gation of this epistemological anarchism earned Feyerabend the title of “the worst enemy of science” from his Philosophers in the continental philosophical tradition are
not traditionally categorized as philosophers of science.
However, they have much to say about science, some of
which has anticipated themes in the analytical tradition.
Sociology of scientific knowledge
For example, Nietzsche advanced the thesis in his “The
Genealogy of Morals” that the motive for search of truth
Main article: Sociology of scientific knowledge
in sciences is a kind of ascetic ideal.[54]
According to Kuhn, science is an inherently communal activity which can only be done as part of a
community.[50] For him, the fundamental difference between science and other disciplines is the way in which
the communities function. Others, especially Feyerabend
and some post-modernist thinkers, have argued that there
is insufficient difference between social practices in science and other disciplines to maintain this distinction.
For them, social factors play an important and direct role
in scientific method, but they do not serve to differentiate
science from other disciplines. On this account, science
is socially constructed, though this does not necessarily
imply the more radical notion that reality itself is a social Hegel with his Berlin students
Sketch by Franz Kugler
However, some such as Quine do maintain that scientific
In general, science in continental philosophy is viewed
reality is a social construct:
from a world-historical perspective. One of the first
philosophers who supported this view was Georg WilPhysical objects are conceptually imported
helm Friedrich Hegel. Philosophers such as Pierre
into the situation as convenient intermediaries
Duhem and Gaston Bachelard also wrote their works with
not by definition in terms of experience, but
this world-historical approach to science, predating Kuhn
simply as irreducible posits comparable, episby a generation or more. All of these approaches involve a
temologically, to the gods of Homer ... For my
historical and sociological turn to science, with a priority
part I do, qua lay physicist, believe in physical
on lived experience (a kind of Husserlian “life-world”),
objects and not in Homer’s gods; and I consider
rather than a progress-based or anti-historical approach
it a scientific error to believe otherwise. But
as done in the analytic tradition. This emphasis can be
in point of epistemological footing, the physitraced through Edmund Husserl's phenomenology, the
cal objects and the gods differ only in degree
late works of Merleau-Ponty (Nature: Course Notes from
and not in kind. Both sorts of entities enter our
the Collège de France, 1956–1960), and Martin Heidegconceptions only as cultural posits.[51]
ger's hermeneutics.[55]
The largest effect on the continental tradition with reThe public backlash of scientists against such views, par- spect to science was Martin Heidegger’s critique of the
ticularly in the 1990s, came to be known as the science theoretical attitude in general which of course includes
the scientific attitude.[56] For this reason the continental
tradition has remained much more skeptical of the importance of science in human life and philosophical inquiry.
Nonetheless, there have been a number of important
works: especially a Kuhnian precursor, Alexandre Koyré.
Another important development was that of Foucault's
analysis of the historical and scientific thought in The
Order of Things and his study of power and corruption
within the “science” of madness. Post-Heideggerian authors contributing to the continental philosophy of science in the second half of the 20th century include
Jürgen Habermas (e.g., “Truth and Justification”, 1998),
Carl Friedrich von Weizsäcker (“The Unity of Nature”,
1980), and Wolfgang Stegmüller (“Probleme und Resultate der Wissenschafttheorie und Analytischen Philosophie”, 1973–1986).
In addition to addressing the general questions regarding
science and induction, many philosophers of science are
occupied by investigating foundational problems in particular sciences. They also examine the implications of
particular sciences for broader philosophical questions.
The late 20th and early 21st century has seen a rise in
the number of practitioners of philosophy of a particular
Philosophy of statistics
Other topics
Analysis is the activity of breaking an observation or theory down into simpler concepts in order to understand it.
Reductionism can refer to one of several philosophical
positions related to this approach. One type of reductionism is the belief that all fields of study are ultimately
amenable to scientific explanation. Perhaps a historical
event might be explained in sociological and psychological terms, which in turn might be described in terms of
human physiology, which in turn might be described in
terms of chemistry and physics.[57] Daniel Dennett distinguishes legitimate reductionism from what he calls greedy
reductionism, which denies real complexities and leaps
too quickly to sweeping generalizations.[58]
cal baggage is taken on board without examination.[60]
— Daniel Dennett, Darwin’s Dangerous
Idea, 1995
Main article: Philosophy of statistics
The problem of induction discussed above is seen in another form in debates over the foundations of statistics.[62]
The standard approach to statistical hypothesis testing
avoids claims about whether evidence supports a hypothesis or makes it more probable. Instead, the typical test
yields a p-value, which is the probability of the evidence
being such as it is, under the assumption that the hypothesis being tested is true. If the p-value is too low, the
hypothesis is rejected, in a way analogous to falsification.
In contrast, Bayesian inference seeks to assign probabilities to hypotheses. Related topics in philosophy of statistics include probability interpretations, overfitting, and
the difference between correlation and causation.
Social accountability
See also: The Mismeasure of Man
A broad issue affecting the neutrality of science concerns
the areas which science chooses to explore, that is, what
part of the world and man is studied by science. Philip
Kitcher in his “Science, Truth, and Democracy”[59] argues that scientific studies that attempt to show one segment of the population as being less intelligent, successful
or emotionally backward compared to others have a political feedback effect which further excludes such groups
from access to science. Thus such studies undermine the
broad consensus required for good science by excluding
certain people, and so proving themselves in the end to
be unscientific.
Philosophy of particular sciences
There is no such thing as philosophy-free
science; there is only science whose philosophi-
A triangle.
Philosophy of mathematics
Main article: Philosophy of mathematics
Philosophy of mathematics is concerned with the philosophical foundations and implications of mathematics.[63]
The central questions are whether numbers, triangles,
and other mathematical entities exist independently of
the human mind and what is the nature of mathematical propositions. Is asking whether “1+1=2” is true fundamentally different from asking whether a ball is red?
Was calculus invented or discovered? A related question
is whether learning mathematics requires experience or
reason alone. What does it mean to prove a mathematical
theorem and how does one know whether a mathematical
proof is correct? Philosophers of mathematics also aim to
clarify the relationships between mathematics and logic,
human capabilities such as intuition, and the material universe.
Philosophy of physics
Main article: Philosophy of physics
phers have also sought to clarify the meaning of chemical
concepts which do not refer to specific physical entities,
such as chemical bonds.
Philosophy of biology
Main article: Philosophy of biology
Philosophy of biology deals with epistemological,
metaphysical, and ethical issues in the biological and
biomedical sciences. Although philosophers of science
and philosophers generally have long been interested
in biology (e.g., Aristotle, Descartes, Leibniz and even
Kant), philosophy of biology only emerged as an independent field of philosophy in the 1960s and 1970s.[66]
Philosophers of science began to pay increasing attention
to developments in biology, from the rise of the modern
synthesis in the 1930s and 1940s to the discovery of
the structure of deoxyribonucleic acid (DNA) in 1953
to more recent advances in genetic engineering. Other
key ideas such as the reduction of all life processes
to biochemical reactions as well as the incorporation
of psychology into a broader neuroscience are also
addressed. Research in current philosophy of biology
includes investigation of the foundations of evolutionary
theory,[67] and the role of viruses as persistent symbionts
in host genomes. As a consequence the evolution of
genetic content order is seen as the result of competent
genome editors in contrast to former narratives in which
error replication events (mutations) dominated.[68]
Philosophy of physics is the study of the fundamental,
philosophical questions underlying modern physics, the
study of matter and energy and how they interact. The
main questions concern the nature of space and time,
atoms and atomism. Also included are the predictions
of cosmology, the interpretation of quantum mechanics, the foundations of statistical mechanics, causality,
determinism, and the nature of physical laws.[64] Classically, several of these questions were studied as part of
metaphysics (for example, those about causality, deterPhilosophy of medicine
minism, and space and time).
Main article: Philosophy of medicine
Philosophy of chemistry
Main article: Philosophy of chemistry
Philosophy of chemistry is the philosophical study of the
methodology and content of the science of chemistry. It
is explored by philosophers, chemists, and philosopherchemist teams. It includes research on general philosophy
of science issues as applied to chemistry. For example,
can all chemical phenomena be explained by quantum
mechanics or is it not possible to reduce chemistry to
physics? For another example, chemists have discussed
the philosophy of how theories are confirmed in the context of confirming reaction mechanisms. Determining reaction mechanisms is difficult because they cannot be observed directly. Chemists can use a number of indirect
measures as evidence to rule out certain mechanisms, but
they are often unsure if the remaining mechanism is correct because there are many other possible mechanisms
that they have not tested or even thought of.[65] Philoso-
Beyond medical ethics and bioethics, the philosophy
of medicine is a branch of philosophy that includes
the epistemology and ontology/metaphysics of medicine.
Within the epistemology of medicine, evidence-based
medicine (EBM) (or evidence-based practice (EBP))
has attracted attention, most notably the roles of
randomisation,[69][70][71] blinding and placebo controls.
Related to these areas of investigation, ontologies of
specific interest to the philosophy of medicine include Cartesian dualism, the monogenetic conception of
disease[72] and the conceptualization of 'placebos’ and
'placebo effects’.[73][74][75][76] There is also a growing interest in the metaphysics of medicine,[77] particularly the
idea of causation. Philosophers of medicine might not
only be interested in how medical knowledge is generated, but also in the nature of such phenomena. Causation is of interest because the purpose of much medical research is to establish causal relationships, e.g. what
causes disease, or what causes people to get better.[78]
reports of feelings and beliefs may not be reliable because, even in cases in which there is no apparent incentive for subjects to intentionally deceive in their answers,
self-deception or selective memory may affect their responses. Then even in the case of accurate self-reports,
how can responses be compared across individuals? Even
if two individuals respond with the same answer on a
Likert scale, they may be experiencing very different
Other issues in philosophy of psychology are philosophical questions about the nature of mind, brain, and cognition, and are perhaps more commonly thought of as part
of cognitive science, or philosophy of mind. For example, are humans rational creatures?[79] Is there any sense
in which they have free will, and how does that relate to
the experience of making choices? Philosophy of psychology also closely monitors contemporary work conducted in cognitive neuroscience, evolutionary psychology, and artificial intelligence, questioning what they can
and cannot explain in psychology.
A fragment of the Hippocratic Oath from the third century.
Philosophy of psychology
Main article: Philosophy of psychology
Philosophy of psychology refers to issues at the theoret-
Philosophy of psychology is a relatively young field, because psychology only became a discipline of its own in
the late 1800s. In particular, neurophilosophy has just
recently become its own field with the works of Paul
Churchland and Patricia Churchland.[61] Philosophy of
mind, by contrast, has been a well-established discipline
since before psychology was a field of study at all. It is
concerned with questions about the very nature of mind,
the qualities of experience, and particular issues like the
debate between dualism and monism. Another related
field is philosophy of language.
Philosophy of economics
Main article: Philosophy and economics
Wilhelm Wundt (seated) with colleagues in his psychological laboratory, the first of its kind.
ical foundations of modern psychology. Some of these
issues are epistemological concerns about the methodology of psychological investigation. For example, is the
best method for studying psychology to focus only on the
response of behavior to external stimuli or should psychologists focus on mental perception and thought processes?[79] If the latter, an important question is how the
internal experiences of others can be measured. Self-
Philosophy of economics is the branch of philosophy
which studies philosophical issues relating to economics.
It can also be defined as the branch of economics which
studies its own foundations and morality. It can be categorized into three central topics.[81] The first concerns the
definition and scope of economics and by what methods
it should be studied and whether these methods rise to
the level of epistemic reliability associated with the other
special sciences. For example, is it possible to research
economics in such a way that it is value-free, establishing facts that are independent of the normative views of
the researcher? The second topic is the meaning and implications of rationality. For example, can buying lottery
tickets (increasing the riskiness of your income) at the
same time as buying insurance (decreasing the riskiness
of your income) be rational? The third topic is the normative evaluation of economic policies and outcomes. What
criteria should be used to determine whether a given public policy is beneficial for society?
its quest for the truth according to a general 'law of three
stages'. These are (1) the theological, (2) the metaphysical, and (3) the positive.[84]
Comte’s positivism established the initial philosophical
foundations for formal sociology and social research.
Durkheim, Marx, and Weber are more typically cited
as the fathers of contemporary social science. In
psychology, a positivistic approach has historically been
favoured in behaviourism. Positivism has also been espoused by 'technocrats' who believe in the inevitability of
social progress through science and technology.[85]
The positivist perspective has been associated with
'scientism'; the view that the methods of the natural sciences may be applied to all areas of investigation, be
it philosophical, social scientific, or otherwise. Among
most social scientists and historians, orthodox positivism
has long since lost popular support. Today, practitioners of both social and physical sciences instead take
into account the distorting effect of observer bias and
structural limitations. This scepticism has been facilitated by a general weakening of deductivist accounts
of science by philosophers such as Thomas Kuhn, and
new philosophical movements such as critical realism
and neopragmatism. The philosopher-sociologist Jürgen
Habermas has critiqued pure instrumental rationality as
meaning that scientific-thinking becomes something akin
to ideology itself.[86]
Amartya Sen was awarded the Nobel Prize in Economics for
“combining tools from economics and philosophy.”[80]
1.1.6 See also
1.1.7 References
Philosophy of social science
Main article: Philosophy of social science
The philosophy of social science is the study of the logic
and method of the social sciences, such as sociology,
anthropology, and political science.[82] Philosophers of
social science are concerned with the differences and
similarities between the social and the natural sciences,
causal relationships between social phenomena, the possible existence of social laws, and the ontological significance of structure and agency.
The French philosopher, Auguste Comte (1798–1857),
established the epistemological perspective of positivism
in The Course in Positivist Philosophy, a series of texts
published between 1830 and 1842. The first three volumes of the Course dealt chiefly with the physical sciences
already in existence (mathematics, astronomy, physics,
chemistry, biology), whereas the latter two emphasised
the inevitable coming of social science: "sociologie".[83]
For Comte, the physical sciences had necessarily to arrive
first, before humanity could adequately channel its efforts
into the most challenging and complex “Queen science”
of human society itself. Comte offers an evolutionary
system proposing that society undergoes three phases in
[1] Encyclopaedia Britannica: Thomas S. Kuhn. “Instead, he
argued that the paradigm determines the kinds of experiments scientists perform, the types of questions they ask,
and the problems they consider important.”
[2] Thornton, Stephen (2006). “Karl Popper”. Stanford Encyclopedia of Philosophy. Retrieved 2007-12-01.
[3] “Science and Pseudo-science” (2008) in Stanford Encyclopedia of Philosophy
[4] Laudan, Larry (1983). “The Demise of the Demarcation
Problem”. In Adolf Grünbaum, Robert Sonné Cohen,
Larry Laudan. Physics, Philosophy, and Psychoanalysis:
Essays in Honor of Adolf Grünbaum. Springer. ISBN 90277-1533-5.
[5] Gordin, Michael D. (2012). The Pseudoscience Wars: Immanuel Velikovsky and the Birth of the Modern Fringe.
University of Chicago Press. pp. 12–13. ISBN
[6] Uebel, Thomas (2006). “Vienna Circle”. Stanford Encyclopedia of Philosophy. Retrieved 2007-12-01.
[7] Popper, Karl (2004). The logic of scientific discovery
(reprint ed.). London & New York: Routledge Classics.
ISBN 0-415-27844-9 First published 1959 by Hutchinson
& Co.
[8] "Pseudoscientific – pretending to be scientific, falsely represented as being scientific", from the Oxford American Dictionary, published by the Oxford English Dictionary; Hansson, Sven Ove (1996)."Defining Pseudoscience”, Philosophia Naturalis, 33: 169–176, as cited
in “Science and Pseudo-science” (2008) in Stanford Encyclopedia of Philosophy. The Stanford article states:
“Many writers on pseudoscience have emphasized that
pseudoscience is non-science posing as science. The foremost modern classic on the subject (Gardner 1957) bears
the title Fads and Fallacies in the Name of Science. According to Brian Baigrie (1988, 438), "[w]hat is objectionable about these beliefs is that they masquerade as genuinely scientific ones.” These and many other authors assume that to be pseudoscientific, an activity or a teaching
has to satisfy the following two criteria (Hansson 1996):
(1) it is not scientific, and (2) its major proponents try to
create the impression that it is scientific”.
• For example, Hewitt et al. Conceptual Physical Science Addison Wesley; 3 edition (July 18, 2003)
ISBN 0-321-05173-4, Bennett et al. The Cosmic
Perspective 3e Addison Wesley; 3 edition (July 25,
2003) ISBN 0-8053-8738-2; See also, e.g., Gauch
HG Jr. Scientific Method in Practice (2003).
• A 2006 National Science Foundation report on Science and engineering indicators quoted Michael
Shermer's (1997) definition of pseudoscience:
'"claims presented so that they appear [to be] scientific even though they lack supporting evidence
and plausibility"(p. 33). In contrast, science is “a
set of methods designed to describe and interpret
observed and inferred phenomena, past or present,
and aimed at building a testable body of knowledge
open to rejection or confirmation"(p. 17)'.Shermer M. (1997). Why People Believe Weird Things:
Pseudoscience, Superstition, and Other Confusions
of Our Time. New York: W. H. Freeman and Company. ISBN 0-7167-3090-1. as cited by National
Science Foundation; Division of Science Resources
Statistics (2006). “Science and Technology: Public Attitudes and Understanding”. Science and engineering indicators 2006.
• “A pretended or spurious science; a collection of
related beliefs about the world mistakenly regarded
as being based on scientific method or as having
the status that scientific truths now have,” from the
Oxford English Dictionary, second edition 1989.
[9] Cargo Cult Science by Feynman, Richard. Retrieved
[10] Hempel, Carl G.; Paul Oppenheim (1948). “Studies in
the Logic of Explanation”. Philosophy of Science 15 (2):
135–175. doi:10.1086/286983.
[11] Salmon, Merrilee; John Earman, Clark Glymour, James
G. Lenno, Peter Machamer, J.E. McGuire, John D. Norton, Wesley C. Salmon, Kenneth F. Schaffner (1992). Introduction to the Philosophy of Science. Prentice-Hall.
ISBN 0-13-663345-5.
[12] Salmon, Wesley (1971). Statistical Explanation and Statistical Relevance. Pittsburgh: University of Pittsburgh
[13] Woodward, James (2003). “Scientific Explanation”. Stanford Encyclopedia of Philosophy. Retrieved 2007-12-07.
[14] Vickers, John (2013). “The Problem of Induction”. Stanford Encyclopedia of Philosophy. Retrieved 2014-02-25.
[15] Baker, Alan (2013). “Simplicity”. Stanford Encyclopedia
of Philosophy. Retrieved 2014-02-25.
[16] Bogen, Jim (2013). “Theory and Observation in Science”.
Stanford Encyclopedia of Philosophy. Retrieved 2014-0225.
[17] Levin, Michael (1984). “What Kind of Explanation is
Truth?". In Jarrett Leplin. Scientific Realism. Berkeley:
University of California Press. pp. 124–1139. ISBN 0520-05155-6.
[18] Boyd, Richard (2002). “Scientific Realism”. Stanford Encyclopedia of Philosophy. Retrieved 2007-12-01.
[19] Specific examples include:
• Popper, Karl (2002). Conjectures and Refutations.
London & New York: Routledge Classics. ISBN
0-415-28594-1 First published 1963 by Routledge
and Kegan Paul
• Smart, J. J. C. (1968). Between Science and Philosophy. New York: Random House.
• Putnam, Hilary (1975). Mathematics, Matter and
Method (Philosophical Papers, Vol. I). London:
Cambridge University Press.
• Putnam, Hilary (1978). Meaning and the Moral Sciences. London: Routledge and Kegan Paul.
• Boyd, Richard (1984). “The Current Status of Scientific Realism”. In Jarrett Leplin. Scientific Realism. Berkeley: University of California Press. pp.
41–82. ISBN 0-520-05155-6.
[20] Stanford, P. Kyle (2006). Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives. Oxford University Press. ISBN 978-0-19-5174083.
[21] Laudan, Larry (1981). “A Confutation of Convergent Realism”. Philosophy of Science 48: 218–249.
[22] van Fraassen, Bas (1980). The Scientific Image. Oxford:
The Clarendon Press. ISBN 0-19-824424-X.
[23] Winsberg, Eric (September 2006). “Models of Success
Versus the Success of Models: Reliability without Truth”.
Synthese 152: 1–19. doi:10.1007/s11229-004-5404-6.
[24] Stanford, P. Kyle (June 2000). “An Antirealist Explanation of the Success of Science”. Philosophy of Science 67
(2): 266–284. doi:10.1086/392775.
[25] Longino, Helen (2013). “The Social Dimensions of Scientific Knowledge”. Stanford Encyclopedia of Philosophy.
Retrieved 2014-03-06.
[26] Douglas Allchin, “Values in Science and in Science Education,” in International Handbook of Science Education,
B.J. Fraser and K.G. Tobin (eds.), 2:1083–1092, Kluwer
Academic Publishers (1988).
[27] Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp.
181–531 in Aristotle, Volume 1, Loeb Classical Library,
William Heinemann, London, UK, 1938.
[28] Lindberg, David C. (1980). Science in the Middle Ages.
University of Chicago Press. pp. 350–351. ISBN 978-0226-48233-0.
[29] Clegg, Brian. “The First Scientist: A Life of Roger Bacon”. Carroll and Graf Publishers, NY, 2003, p. 2.
[30] Bacon, Francis Novum Organum (The New Organon),
1620. Bacon’s work described many of the accepted principles, underscoring the importance of empirical results,
data gathering and experiment. Encyclopædia Britannica
(1911), "Bacon, Francis" states: [In Novum Organum, we
] “proceed to apply what is perhaps the most valuable part
of the Baconian method, the process of exclusion or rejection. This elimination of the non-essential, ... , is the most
important of Bacon’s contributions to the logic of induction, and that in which, as he repeatedly says, his method
differs from all previous philosophies.”
[31] McMullin, Ernan. “The Impact of Newton’s Principia on
the Philosophy of Science”. Pari
Center for New Learning. Retrieved 29 October 2015.
[32] “John Stuart Mill (Stanford Encyclopedia of Philosophy)". Retrieved 2009-07-31.
[33] Michael Friedman, Reconsidering Logical Positivism (New
York: Cambridge University Press, 1999), p xiv.
[34] See “Vienna Circle” in Stanford Encyclopedia of Philosophy.
[35] Smith, L.D. (1986). Behaviorism and Logical Positivism:
A Reassessment of the Alliance. Stanford University Press.
p. 314. ISBN 978-0-8047-1301-6. LCCN 85030366.
The secondary and historical literature on logical positivism affords substantial grounds for concluding that logical positivism failed to solve many of the central problems
it generated for itself. Prominent among the unsolved
problems was the failure to find an acceptable statement
of the verifiability (later confirmability) criterion of meaningfulness. Until a competing tradition emerged (about
the late 1950’s), the problems of logical positivism continued to be attacked from within that tradition. But as
the new tradition in the philosophy of science began to
demonstrate its effectiveness—by dissolving and rephrasing old problems as well as by generating new ones—
philosophers began to shift allegiances to the new tradition, even though that tradition has yet to receive a canonical formulation.
[36] Bunge, M.A. (1996). Finding Philosophy in Social Science. Yale University Press. p. 317. ISBN 978-0300-06606-7. LCCN lc96004399. To conclude, logical positivism was progressive compared with the classical positivism of Ptolemy, Hume, d'Alembert, Compte,
John Stuart Mill, and Ernst Mach. It was even more
so by comparison with its contemporary rivals—neoThomisism, neo-Kantianism, intuitionism, dialectical materialism, phenomenology, and existentialism. However,
neo-positivism failed dismally to give a faithful account
of science, whether natural or social. It failed because it
remained anchored to sense-data and to a phenomenalist metaphysics, overrated the power of induction and underrated that of hypothesis, and denounced realism and
materialism as metaphysical nonsense. Although it has
never been practiced consistently in the advanced natural
sciences and has been criticized by many philosophers,
notably Popper (1959 [1935], 1963), logical positivism
remains the tacit philosophy of many scientists. Regrettably, the anti-positivism fashionable in the metatheory of
social science is often nothing but an excuse for sloppiness
and wild speculation.
[37] “Popper, Falsifiability, and the Failure of Positivism”.
7 August 2000. Retrieved 7 January 2014. The upshot is that the positivists seem caught between insisting
on the V.C. [Verifiability Criterion]—but for no defensible reason—or admitting that the V.C. requires a background language, etc., which opens the door to relativism,
etc. In light of this dilemma, many folk—especially
following Popper’s “last-ditch” effort to “save” empiricism/positivism/realism with the falsifiability criterion—
have agreed that positivism is a dead-end.
[38] Friedman, Reconsidering Logical Positivism (Cambridge
U P, 1999), p xii.
[39] Bird, Alexander (2013). Zalta, Edward N., ed. “Thomas
Kuhn”. Stanford Encyclopedia of Philosophy. Retrieved
[40] T. S. Kuhn, The Structure of Scientific Revolutions, 2nd.
ed., Chicago: Univ. of Chicago Pr., 1970, p. 206. ISBN
[41] Heilbron 2003, p. vii
[42] Gauch 2002, p. 154, “Expressed as a single grand statement, science presupposes that the physical world is orderly and comprehensible. The most obvious components
of this comprehensive presupposition are that the physical
world exists and that our sense perceptions are generally
[43] Gould 1987, p. 120, “You cannot go to a rocky outcrop and observe either the constancy of nature’s laws or
the working of known processes. It works the other way
around.” You first assume these propositions and “then
you go to the outcrop of rock.”
[44] Simpson 1963, pp. 24–48, “Uniformity is an unprovable
postulate justified, or indeed required, on two grounds.
First, nothing in our incomplete but extensive knowledge
of history disagrees with it. Second, only with this postulate is a rational interpretation of history possible and we
are justified in seeking—as scientists we must seek—such
a rational interpretation.”
[45] Olsson, Erik (2014). Zalta, Edward N., ed. “Coherentist
Theories of Epistemic Justification”. Stanford Encyclopedia of Philosophy. Retrieved 2015-10-26.
[46] Sandra Harding (1976). Can theories be refuted?: essays
on the Dunhem–Quine thesis. Springer Science & Business
Media. pp. 9–. ISBN 978-90-277-0630-0.
[47] Popper, Karl (2005). The Logic of Scientific Discovery
(Taylor & Francis e-Library ed.). London and New York:
Routledge / Taylor & Francis e-Library. chapters 3–4.
ISBN 0-203-99462-0.
[48] Paul Feyerabend, Against Method: Outline of an Anarchistic Theory of Knowledge (1975), ISBN 0-391-00381X, ISBN 0-86091-222-1, ISBN 0-86091-481-X, ISBN
0-86091-646-4, ISBN 0-86091-934-X, ISBN 0-90230891-2
[49] Paul Feyerabend entry by John Preston in the Stanford
Encyclopedia of Philosophy, 2007-02-15
[50] Kuhn, T. S. (1996). "[Postscript]". The Structure of Scientific Revolutions, 3rd. ed. [Univ. of Chicago Pr]. p. 176.
ISBN 0-226-45808-3. A paradigm is what the members
of a community of scientists share, and, conversely, a scientific community consists of men who share a paradigm.
[51] Quine, Willard Van Orman (1980). “Two Dogmas of Empiricism”. From a Logical Point of View. Harvard University Press. ISBN 0-674-32351-3.
[52] Ashman, Keith M.; Barringer, Philip S., eds. (2001).
After the Science Wars. London, UK: Routledge. ISBN
0-415-21209-X. Retrieved 29 October 2015. The “war”
is between scientists who believe that science and its methods are objective, and an increasing number of social scientists, historians, philosophers, and others gathered under the umbrella of Science Studies.
[53] Woodhouse, Edward. Science Technology and Society.
Spring 2015 ed. N.p.: U Readers, 2014. Print.
[54] Hatab, Lawrence J. (2008). “How Does the Ascetic Ideal
Function in Nietzsche’s Genealogy?". The Journal of Nietzsche Studies (35/36): 107.
[55] Gutting, Gary (2004), Continental Philosophy of Science,
Blackwell Publishers, Cambridge, MA.
[56] Wheeler, Michael (2015). “Martin Heidegger”. Stanford
Encyclopedia of Philosophy. Retrieved 2015-10-29.
[57] Cat, Jordi (2013). “The Unity of Science”. Stanford Encyclopedia of Philosophy. Retrieved 2014-03-01.
[58] Levine, George (2008). Darwin Loves You: Natural Selection and the Re-enchantment of the World. Princeton
University Press. p. 104. ISBN 978-0-691-13639-4. Retrieved 28 October 2015.
[59] Kitcher, P. Science, Truth, and Democracy, Oxford: Oxford University Press, 2001
[60] Dennett, Daniel (1995). Darwin’s Dangerous Idea: Evolution and the Meanings of Life. Simon and Schuster. p.
21. ISBN 978-1-4391-2629-5.
[61] Bickle, John, Mandik, Peter and Landreth, Anthony, “The
Philosophy of Neuroscience”, The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), Edward N.
Zalta (ed.), URL = <
[62] Romeijn, Jan-Willem (2014). Zalta, Edward N., ed.
“Philosophy of Statistics”. Stanford Encyclopedia of Philosophy. Retrieved 2015-10-29.
[63] Horsten, Leon (2015). Zalta, Edward N., ed. “Philosophy
of Mathematics”. Stanford Encyclopedia of Philosophy.
Retrieved 2015-10-29.
[64] Ismael, Jenann (2015). Zalta, Edward N., ed. “Quantum
Mechanics”. Stanford Encyclopedia of Philosophy. Retrieved 2015-10-29.
[65] Weisberg, Michael; Needham, Paul; Hendry, Robin
(2011). “Philosophy of Chemistry”. Stanford Encyclopedia of Philosophy. Retrieved 2014-02-14.
[66] Hull D. (1969), What philosophy of biology is not, Journal
of the History of Biology, 2, p. 241–268.
[67] Recent examples include Okasha S. (2006), Evolution and
the Levels of Selection. Oxford: Oxford University Press,
and Godfrey-Smith P. (2009), Darwinian Populations and
Natural Selection. Oxford: Oxford University Press.
[68] Witzany G. (2010). “Biocommunication and Natural
Genome Editing”. Dortrecht: Springer Sciences and
Business Media.
[69] Papineau, D., 1994. The Virtues of Randomization.
British Journal for the Philosophy of Science, 45(2), pp.
[70] Jstor, Worrall, J., 2002. What Evidence in EvidenceBased Medicine? Philosophy of Science, 69(3), p.S316S330.
[71] Worrall, J., 2007. Why there’s no cause to randomize.
British Journal for the Philosophy of Science, 58, pp.
[72] Lee, K., 2012. The Philosophical Foundations of Modern
Medicine, London/New York, Palgrave/Macmillan.
[73] Grünbaum, A., 1981. The Placebo Concept. Behavioural
Research & Therapy, 19(2), pp. 157–167.
[74] Gøtzsche, P.C., 1994. Is there logic in the placebo?
Lancet, 344(8927), pp. 925–926.
[75] Nunn, R., 2009. It’s time to put the placebo out of our
misery. British Medical Journal, 338, b1568.
[76] Springer Turner, A., 2012. “Placebos” and the logic of
placebo comparison. Biology & Philosophy, 27(3), pp.
[77] PubMed, Worrall, J., 2011. Causality in medicine: Getting back to the Hill top. Preventive Medicine, 53(4–5),
pp. 235–238.
[78] Springer, Cartwright, N., 2009. What are randomised
controlled trials good for? Philosophical Studies, 147(1),
pp. 59–70.
[79] Mason, Kelby; Sripada, Chandra Sekhar; Stich, Stephen
(2010). “Philosophy of Psychology” (PDF). In Moral,
Dermot. Routledge Companion to Twentieth-Century Philosophy. London: Routledge.
[81] Hausman, Daniel (Dec 18, 2012). “Philosophy of Economics”. Stanford Encyclopedia of Philosophy. Stanford
University. Retrieved 20 February 2014.
• Papineau, David (2005) Science, problems of the philosophy of. Oxford Companion to Philosophy. Oxford.
• Hollis, Martin (1994). The Philosophy of Social Science: An Introduction. Cambridge. ISBN 0-52144780-1.
• Salmon, Merrilee; John Earman, Clark Glymour,
James G. Lenno, Peter Machamer, J.E. McGuire,
John D. Norton, Wesley C. Salmon, Kenneth F.
Schaffner (1992). Introduction to the Philosophy of
Science. Prentice-Hall. ISBN 0-13-663345-5.
[83] Stanford Encyclopaedia: Auguste Comte
[84] Giddens, Positivism and Sociology, 1
[85] Schunk, Learning Theories: An Educational Perspective,
5th, 315
• Popper, Karl, (1963) Conjectures and Refutations:
The Growth of Scientific Knowledge, ISBN 0-41504318-2
[86] Outhwaite, William, 1988 Habermas: Key Contemporary
Thinkers, Polity Press (Second Edition 2009), ISBN 9780-7456-4328-1 p.68
• van Fraassen, Bas (1980). The Scientific Image. Oxford: The Clarendon Press. ISBN 0-19-824424-X.
Cited texts
• Ziman, John (2000). Real Science: what it is, and
what it means. Cambridge, Uk: Cambridge University Press.
• Gauch, Hugh G. (2002). Scientific Method in Practice. Cambridge University Press.
• Heilbron, J. L. (editor-in-chief) (2003). The Oxford Companion to the History of Modern Science.
New York: Oxford University Press. ISBN 0-19511229-6.
• Kneale, William; Martha Kneale (1962). The Development of Logic. London: Oxford University
Press. p. 243. ISBN 0-19-824183-6.
• Simpson, G. G. (1963). “Historical science”. In
Albritton, Jr., C. C. Fabric of geology. Stanford,
California: Freeman, Cooper, and Company. pp.
• Gould, Stephen J (1987). Time’s Arrow, Time’s Cycle: Myth and Metaphor in the Discovery of Geological Time. Cambridge, MA: Harvard University
Press. p. 120. ISBN 0-674-89199-6.
• Whitehead, A.N. (1997) [1920]. Science and the
Modern World. Lowell Lectures. Free Press. p.
135. ISBN 978-0-684-83639-3. LCCN 67002244.
Further reading
• Bovens, L. and Hartmann, S. (2003), Bayesian Epistemology, Oxford University Press, Oxford.
• Gutting, Gary (2004), Continental Philosophy of Science, Blackwell Publishers, Cambridge, MA.
• Kuhn, T. S. (1970). The Structure of Scientific Revolutions, 2nd. ed. [Univ. of Chicago Pr]. ISBN
• Losee, J. (1998), A Historical Introduction to the
Philosophy of Science, Oxford University Press, Oxford, UK.
External links
• Philosophy of science at PhilPapers
• Philosophy of science at the Indiana Philosophy Ontology Project
• Philosophy of science entry in the Internet Encyclopedia of Philosophy
Chapter 2
Nature of scientific concepts and
2.1 Demarcation problem
alytics.[9] One element of this polemic for science was an
insistence on a clear and unequivocal presentation of arguments, rejecting the imagery, analogy, and myth of the
old wisdom.[10] Some of their claimed naturalistic explanations of phenomena have been found to be quite fanciful, with little reliance on actual observations.[11]
The demarcation problem in the philosophy of science is about how to distinguish between science and
nonscience,[1] including between science, pseudoscience,
and other products of human activity, like art and
literature, and beliefs.[2][3] The debate continues after
over a century of dialogue among philosophers of science
and scientists in various fields, and despite broad agree- 2.1.2 Logical positivism
ment on the basics of scientific method.[4][5]
Logical positivism held that only statements about matters of fact or logical relations between concepts are
meaningful. All other statements lack sense and are la2.1.1 Ancient Greek science
belled 'metaphysics' (see the verifiability theory of meanAn early attempt at demarcation can be seen in the efforts ing also known as verificationism). This distinction beof Greek natural philosophers and medical practitioners tween science, which in the view of the Vienna Cirto distinguish their methods and their accounts of nature cle possessed empirically verifiable statements, and what
from the mythological or mystical accounts of their pre- they pejoratively called 'metaphysics’, which lacked such
statements, can be seen as representing another aspect of
decessors and contemporaries.[6]
the demarcation problem.[12] Logical positivism is often
discussed in the context of the demarcation between sciAristotle described at length what was inence and non-science or pseudoscience. However, “The
volved in having scientific knowledge of someverificationist proposals had the aim of solving a distinctly
thing. To be scientific, he said, one must deal
different demarcation problem, namely that between sciwith causes, one must use logical demonstraence and metaphysics.”[13]
tion, and one must identify the universals which
'inhere' in the particulars of sense. But above
all, to have science one must have apodictic cer2.1.3 Falsifiability
tainty. It is the last feature which, for Aristotle,
most clearly distinguished the scientific way of
Falsifiability is the demarcation criterion proposed by
Karl Popper as opposed to verificationism: “statements
— Larry Laudan, Physics, Philosophy,
or systems of statements, in order to be ranked as scienand Psychoanalysis, “The Demise of the
tific, must be capable of conflicting with possible, or conDemarcation Problem”
ceivable observations”.[14] Popper saw demarcation as a
central problem in the philosophy of science. Unlike the
G. E. R. Lloyd notes that there was a sense in which the Vienna Circle, Popper stated that his proposal was not a
groups engaged in various forms of inquiry into nature set criterion of “meaningfulness”.
out to “legitimate their own positions,”[7] laying “claim to
a new kind of wisdom ... that purported to yield superior
enlightenment, even superior practical effectiveness.”[8]
Medical writers in the Hippocratic tradition maintained
that their discussions were based on necessary demonstrations, a theme developed by Aristotle in his Posterior An16
Popper’s demarcation criterion has been
criticized both for excluding legitimate science… and for giving some pseudosciences the
status of being scientific… According to Larry
Laudan (1983, 121), it “has the untoward con-
sequence of countenancing as 'scientific' every
crank claim which makes ascertainably false
assertions”. Astrology, rightly taken by Popper as an unusually clear example of a pseudoscience, has in fact been tested and thoroughly
refuted… Similarly, the major threats to the
scientific status of psychoanalysis, another of
his major targets, do not come from claims that
it is untestable but from claims that it has been
tested and failed the tests.[14]
— Sven Ove Hansson, The Stanford
Encyclopedia of Philosophy, “Science and
— Sven Ove Hansson, The Stanford
Encyclopedia of Philosophy, “Science and
Popper criticized Kuhn’s demarcation criterion, saying
that astrologers are engaged in puzzle solving, and that
therefore Kuhn’s criterion recognized astrology as a science. He stated that Kuhn’s criterion leads to a “major
disaster…[the] replacement of a rational criterion of science by a sociological one”.[14]
2.1.5 Feyerabend and Lakatos
In Popper’s later work, he stated that falsifiability is both
a necessary and a sufficient criterion for demarcation. He
described falsifiability as a property of “the logical structure of sentences and classes of sentences,” so that a statement’s scientific or non-scientific status does not change
over time. This has been summarized as a statement being falsifiable “if and only if it logically contradicts some
(empirical) sentence that describes a logically possible
event that it would be logically possible to observe.”[14]
Thomas Kuhn, an American historian and philosopher
of science, is often connected with what has been called
postpositivism or postempiricism. In his 1962 book
The Structure of Scientific Revolutions, Kuhn divided the
process of doing science into two different endeavors,
which he called normal science and extraordinary science (which he sometimes also called “revolutionary science”). “In Kuhn’s view, 'it is normal science, in which
Sir Karl’s sort of testing does not occur, rather than extraordinary science which most nearly distinguishes science from other enterprises’…"[14] That is, the utility of
a scientific paradigm for puzzle-solving, which suggests
solutions to new problems while continuing to satisfy all
of the problems solved by the paradigm that it replaces.
Kuhn’s view of demarcation is most clearly
expressed in his comparison of astronomy with
astrology. Since antiquity, astronomy has been
a puzzle-solving activity and therefore a science. If an astronomer’s prediction failed, then
this was a puzzle that he could hope to solve
for instance with more measurements or with
adjustments of the theory. In contrast, the astrologer had no such puzzles since in that discipline “particular failures did not give rise to
research puzzles, for no man, however skilled,
could make use of them in a constructive attempt to revise the astrological tradition"…
Therefore, according to Kuhn, astrology has
never been a science.[14]
Kuhn’s work largely called into question Popper’s demarcation, and emphasized the human, subjective quality of
scientific change. Paul Feyerabend was concerned that
the very question of demarcation was insidious: science
itself had no need of a demarcation criterion, but instead
some philosophers were seeking to justify a special position of authority from which science could dominate public discourse.[15] Feyerabend argued that science does not
in fact occupy a special place in terms of either its logic or
method, and no claim to special authority made by scientists can be upheld. He argued that, within the history
of scientific practice, no rule or method can be found
that has not been violated or circumvented at some point
in order to advance scientific knowledge. Both Lakatos
and Feyerabend suggest that science is not an autonomous
form of reasoning, but is inseparable from the larger body
of human thought and inquiry.
2.1.6 Thagard
Paul R. Thagard has proposed another set of principles
to try to overcome these difficulties, and believes it is important for society to find a way of doing so. According to
Thagard’s method, a theory is not scientific if it satisfies
two conditions:
1. The theory has been less progressive
than alternative theories over a long period of time, and faces many unsolved
problems; and...
2. The community of practitioners makes
little attempt to develop the theory towards solutions of the problems, shows
no concern for attempts to evaluate the
theory in relation to others, and is selective in considering confirmations and
Thagard specifies that sometimes theories will spend
some time as merely “unpromising” before they truly deserve the title of pseudoscience. He cites astrology as
an example: it was stagnant compared to advances in
physics during the 17th century, and only later became practically and philosophically significant than whether
“pseudoscience” in the advent of alternative explanations it is scientific or not. In his judgment, the demarcation
provided by psychology during the 19th century.
between science and non-science was a pseudo-problem
Thagard also states that his criteria should not be inter- that would best be replaced by focusing on the distinction
preted so narrowly as to allow willful ignorance of alterna- between reliable and unreliable knowledge, without bothtive explanations, or so broadly as to discount our modern ering to ask whether that knowledge is scientific or not.
science compared to science of the future. His definition He would consign phrases like “pseudo-science” or “un[2]
is a practical one, which generally seeks to distinguish scientific” to the rhetoric of politicians or sociologists.
pseudoscience as areas of inquiry which are stagnant and Others have disagreed with Laudan. Sebastian Lutz, for
without active scientific investigation.
example, argues that demarcation does not have to be
a single necessary and sufficient condition as Laudan
implied.[2] Rather, Laudan’s reasoning at the most establishes that there has to be one necessary criterion and
2.1.7 Some historians’ perspectives
one possibly different sufficient criterion.[21] Other critMany historians of science are concerned with the de- ics have argued for multiple demarcation criteria suggestvelopment of science from its primitive origins; conse- ing that there should be one set of criteria for the natural
quently they define science in sufficiently broad terms to sciences; another set of criteria for the social sciences,
include early forms of natural knowledge. In the article and claims involving the supernatural could have a set of
on science in the eleventh edition of the Encyclopædia pseudoscientific criteria. Massimo Pigliucci wrote that
Britannica, the scientist and historian William Cecil science generally conforms to Ludwig Wittgenstein's conDampier Whetham defined science as “ordered knowl- cept of family resemblances.[22]
edge of natural phenomena and of the relations between
them.”[17] In his study of Greek science, Marshall Clagett
defined science as “first, the orderly and systematic com- 2.1.9 See also
prehension, description and/or explanation of natural
• Boundary-work
phenomena and, secondly, the [mathematical and logical]
tools necessary for the undertaking.”[18] A similar definition appeared more recently in David Pingree’s study
of early science: “Science is a systematic explanation of 2.1.10 References
perceived or imaginary phenomena, or else is based on
such an explanation. Mathematics finds a place in sci- [1] Resnik, David B. (2000). “A pragmatic approach to the
demarcation problem”. Studies In History and Philosophy
ence only as one of the symbolical languages in which
of Science Part A 31 (2): 249–267. doi:10.1016/S0039scientific explanations may be expressed.”
These def3681(00)00004-2.
initions tend to focus more on the subject matter of science than on its method and from these perspectives, the [2] Laudan, Larry (1983), “The Demise of the Demarcation
philosophical concern to establish a line of demarcation
Problem”, in Cohen, R.S.; Laudan, L., Physics, Philosobetween science and non-science becomes “problematic,
phy and Psychoanalysis: Essays in Honor of Adolf Grünif not futile.”[20]
baum, Boston Studies in the Philosophy of Science 76,
Dordrecht: D. Reidel, pp. 111–127, ISBN 90-277-15335
Larry Laudan concluded, after examining various historical attempts to establish a demarcation criterion, that
“philosophy has failed to deliver the goods” in its attempts
to distinguish science from non-science—to distinguish
science from pseudoscience. None of the past attempts
would be accepted by a majority of philosophers nor, in
his view, should they be accepted by them or by anyone
else. He stated that many well-founded beliefs are not
scientific and, conversely, many scientific conjectures are
not well-founded. He also stated that demarcation criteria
were historically used as "machines de guerre" in polemical disputes between “scientists” and “pseudo-scientists.”
Advancing a number of examples from everyday practice
of football and carpentry and non-scientific scholarship
such as literary criticism and philosophy, he saw the question of whether a belief is well-founded or not to be more
[3] Lakatos, I.; Feyerabend, P.; Motterlini, M. (1999). For
and Against Method: Including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence. University of Chicago Press. p. 20. ISBN
9780226467740. LCCN 99013581. The demarcation
problem may be formulated in the following terms: what
distinguishes science from pseudoscience? This is an extreme way of putting it, since the more general problem,
called the Generalized Demarcation Problem, is really the
problem of the appraisal of scientific theories, and attempts to answer the question: when is one theory better
than another?
[4] Gauch, Hugh G., Jr. (2003). Scientific Method in Practice.
pp. 3–7. ISBN 978-0-521-81689-2.
[5] Cover, J. A.; Curd, Martin, eds. (1998). Philosophy of
Science: The Central Issues. pp. 1–82. ISBN 978-0-39397175-0.
[6] Lloyd, G. E. R. (1983), Science, Folklore and Ideology:
Studies in the Life Sciences in Ancient Greece, Cambridge:
Cambridge University Press, pp. 79–80, ISBN 0-52127307-2, Faced with ... competition from a variety of
more or less exploitative rival healers, the doctors responsible for many or most of the Hippocratic treatises unite,
at least, in their desire to turn the practice of healing into
a τἐχνη.... [N]ot only do they reject interference in most
cases from priests and prophets, they also criticise many
current practices and assumptions.
[7] Lloyd, G. E. R. (1983), Science, Folklore and Ideology:
Studies in the Life Sciences in Ancient Greece, Cambridge:
Cambridge University Press, p. 215, ISBN 0-521-273072
[8] Lloyd, G.E.R. (1986), The Revolutions of Wisdom: Studies in the Claims and Practice of Ancient Greek Science,
Sather Classical Lectures 52, Berkeley and Los Angeles:
University of California Press, pp. 117–118, ISBN 0-52006742-8
[9] Lloyd, G.E.R. (1986), The Revolutions of Wisdom: Studies in the Claims and Practice of Ancient Greek Science,
Sather Classical Lectures 52, Berkeley and Los Angeles:
University of California Press, pp. 141–147, ISBN 0-52006742-8
[19] Pingree, David (1992), “Hellenophilia versus the History
of Science”, Isis 83: 554–563, doi:10.1086/356288
[20] McCluskey, Stephen C. (2005), “Different Astronomies,
Different Cultures and the Question of Cultural Relativism”, in Fountain, John W.; Sinclair, Rolf M., Current
Studies in Archaeoastronomy: Conversations Across Time
and Space, Durham, NC: Carolina Academic Press, p. 71,
ISBN 0-89089-771-9
[21] Lutz, Sebastian (2011), “On an Allegedly Essential Feature of Criteria for the Demarcation of Science” (PDF),
The Reasoner 5 (8): 125–126 External link in |journal=
[22] Pigliucci, Massimo (2013). “The Demarcation Problem:
A (Belated) Response to Laudan” in Pigliucci, Massimo;
Boudry, Maarten, eds. Philosophy of Pseudoscience: Reconsidering the Demarcation Problem chapter 1. ISBN
978-0-226-05196-3. Pigliucci’s chapter is available online at
2.2 Scientific realism
Scientific realism is, at the most general level, the view
that the world described by science is the real world,
[10] Lloyd, G.E.R. (1986), The Revolutions of Wisdom: Studas it is, independent of what it might be taken to be.
ies in the Claims and Practice of Ancient Greek Science,
Within philosophy of science, it is often framed as an
Sather Classical Lectures 52, Berkeley and Los Angeles:
University of California Press, pp. 213–214, ISBN 0-520- answer to the question “how is the success of science
to be explained?" The debate over the success of sci06742-8
ence in this context centers primarily on the status of
[11] Lloyd, G.E.R. (1979), Magic Reason and Experience: unobservable entities apparently talked about by scienStudies in the Origin and Development of Greek Science, tific theories. Generally, those who are scientific realists
Cambridge: Cambridge University Press, pp. 15–27, assert that one can make valid claims about unobservables
ISBN 0-521-29641-2
(viz., that they have the same ontological status) as ob[12] Grayling, AC., Wittgenstein: A Very Short Introduction, servables, as opposed to instrumentalism.
Oxford University Press, 2001, pp. 67-68.
[13] Hansson, Sven Ove (2008). Zalta, Edward N., ed.
“Science and Pseudo-Science”. The Stanford Encyclopedia of Philosophy (Fall 2008 ed.). 4.1 The Logical Positivists.
[14] Hansson, Sven Ove (2008). Zalta, Edward N., ed.
“Science and Pseudo-Science”. The Stanford Encyclopedia of Philosophy (Fall 2008 ed.). 4.2 Falsificationism.
[15] Taylor, C.A. (1996). Defining Science: A Rhetoric of
Demarcation. Rhetoric of the Human Sciences Series. University of Wisconsin Press. p. 41. ISBN
9780299150341. LCCN 96000180.
[16] Why Astrology Is A Pseudoscience, Paul R. Thagard, In
Philosophy of Science Association 1978 Volume 1, edited
by P.D. Asquith and I. Hacking (East Lansing: Philosophy
of Science Association, 1978).
[17] Dampier Whetham, William Cecil (1911), “Science”,
Encyclopædia Britannica, New York: Encyclopedia Britannica, Inc.
[18] Clagett, Marshall (1963), Greek Science in Antiquity, New
York: Collier Books, p. 4
2.2.1 Main features
Scientific realism involves the two basic positions. First,
it is a set of claims about the features of an ideal scientific
theory; an ideal theory is the sort of theory science aims
to produce. Second, it is the commitment that science
will eventually produce theories very much like an ideal
theory and that science has done pretty well thus far in
some domains. It is important to note that one might be a
scientific realist regarding some sciences while not being
a realist regarding others. For example, one might hold
realist attitudes toward physics, chemistry and biology,
and not toward economics, psychology and sociology.
According to scientific realism, an ideal scientific theory
has the following features:
• The claims the theory makes are either true or false,
depending on whether the entities talked about by
the theory exist and are correctly described by the
theory. This is the semantic commitment of scientific realism.
• The entities described by the scientific theory ex- 2.2.2 History
ist objectively and mind-independently. This is the
Scientific realism is related to much older philosophical
metaphysical commitment of scientific realism.
positions including rationalism and realism. However, it
• There are reasons to believe some significant portion
is a thesis about science developed in the twentieth cenof what the theory says. This is the epistemological
tury. Portraying scientific realism in terms of its ancient,
medieval, and early modern cousins is at best misleading.
Scientific realism is developed largely as a reaction to
logical positivism. Logical positivism was the first philosophy of science in the twentieth century and the forerunner of scientific realism, holding that a sharp distinction can be drawn between observational terms and theoretical terms, the latter capable of semantic analysis in
Scientific realism usually holds that science makes
observational and logical terms.
progress, i.e. scientific theories usually get successively
better, or, rather, answer more and more questions. For Logical positivism encountered difficulties with:
this reason, many people, scientific realist or otherwise,
hold that realism should make sense of the progress of
• The verification theory of meaning (for which see
science in terms of theories being successively more like
Hempel (1950)).
the ideal theory that scientific realists describe.
• Troubles with the analytic-synthetic distinction (for
which see Quine (1950)).
Characteristic claims
• The theory ladenness of observation (for which see
Kuhn (1970) and Quine (1960)).
The following claims are typical of those held by scientific
realists. Due to the wide disagreements over the nature
• Difficulties moving from the observationality of
of science’s success and the role of realism in its success,
terms to observationality of sentences (for which see
a scientific realist would agree with some but not all of
Putnam (1962)).
the following positions.
• The vagueness of the observational-theoretical dis• The best scientific theories are at least partially true.
tinction (for which see Maxwell (1962)).
Combining the first and the second claim entails that an
ideal scientific theory says definite things about genuinely
existing entities. The third claim says that we have reasons to believe that many scientific claims about these entities are true.
• The best theories do not employ central terms that
These difficulties for logical positivism suggest, but do not
are non referring expressions.
entail, scientific realism, and lead to the development of
• To say that a theory is approximately true is suffi- realism as a philosophy of science.
cient explanation of the degree of its predictive sucRealism became the dominant philosophy of science afcess.
ter positivism. Bas van Fraassen developed constructive
• The approximate truth of a theory is the only expla- empiricism as an alternative to realism. Responses to
nation of its predictive success.
van Fraassen have sharpened realist positions and lead to
• Even if a theory employs expressions that do not some revisions of scientific realism.
have a reference, a scientific theory may be approximately true.
2.2.3 Arguments for and against
Scientific theories are in a historical process of
progress towards a true account of the physical One of the main arguments for scientific realism centers on the notion that scientific knowledge is progressive
in nature, and that it is able to predict phenomena sucScientific theories make genuine, existential claims. cessfully. Many realists (e.g., Ernan McMullin, Richard
Theoretical claims of scientific theories should be Boyd) think the operational success of a theory lends creread literally and are definitively either true or false. dence to the idea that its more unobservable aspects exist,
because they were how the theory reasoned its predicThe degree of the predictive success of a theory tions. For example, a scientific realist would argue that
is evidence of the referential success of its central science must derive some ontological support for atoms
from the outstanding phenomenological success of all the
The goal of science is an account of the physical theories using them.
world that is literally true. Science has been success- Arguments for scientific realism often appeal to abductive
ful because this is the goal that it has been making reasoning or “inference to the best explanation” (Lipton,
2004). For instance, one argument commonly used - the
progress towards.
“miracle argument” - starts out by observing that scientific theories are highly successful in predicting and explaining a variety of phenomena, often with great accuracy. Thus, it is argued that the best explanation - the only
explanation that renders the success of science to not be
what Hilary Putnam calls “a miracle” - is the view that
our scientific theories (or at least the best ones) provide
true descriptions of the world, or approximately so.[2]
clever hoaxes) can account for the same data. Realists
claim that, in addition to empirical adequacy, there are
other criteria for theory choice, such as parsimony.
2.2.4 See also
• Anti-realism
• Constructivist epistemology
On the other hand, pessimistic induction, one of the main
arguments against realism, argues that the history of sci• Critical realism
ence contains many theories once regarded as empirically
successful but which are now believed to be false. Ad• Instrumentalism
ditionally, the history of science contains many empir• Naïve realism
ically successful theories whose unobservable terms are
not believed to genuinely refer. For example, the efflu• Pessimistic induction
vial theory of static electricity is an empirically successful
• Philosophical realism
theory whose central unobservable terms have been replaced by later theories. Realists reply that replacement
• Scientific materialism
of particular realist theories with better ones is to be expected due to the progressive nature of scientific knowl• Social constructionism
edge, and when such replacements occur only superfluous
unobservables are dropped. For example, Albert Einstein's theory of special relativity showed that the con- 2.2.5 Footnotes
cept of the luminiferous ether could be dropped because
it had contributed nothing to the success of the theories [1] Jarrett Leplin (1984), Scientific Realism, University of
California Press, p. 1, ISBN 0-520-05155-6
of mechanics and electromagnetism. On the other hand,
when theory replacement occurs, a well-supported con- [2]
cept, such as the concept of atoms, is not dropped but is
incorporated into the new theory in some form.
Also against scientific realism social constructivists might
2.2.6 Further reading
argue that scientific realism is unable to account for the
rapid change that occurs in scientific knowledge during
• Bunge, Mario. (2006). Chasing Reality: Strife over
periods of revolution. Constructivists may also argue that
Realism. Toronto Studies in Philosophy: University
the success of theories is only a part of the construction.
of Toronto Press
However, these arguments ignore the fact that many sci• Bunge, Mario. (2001). Scientific Realism: Selected
entists are not realists. In fact, during what is perhaps
Essays of Mario Bunge. Mahner, M. (Ed.) New
the most notable example of revolution in science—the
York: Prometheus Books
development of quantum mechanics in the 1920s—the
dominant philosophy of science was logical positivism.
• Devitt, Michael, “Scientific realism”. In: OxThe alternative realist Bohm interpretation and manyford handbook of contemporary analytic philosophy
worlds interpretation of quantum mechanics do not make
such a revolutionary break with the concepts of classical
• Hempel, Carl. (1950). “Empiricist Criteria of Cognitive Significance” in Boyd, Richard et al. eds.
Another argument against scientific realism, deriving
(1990). The Philosophy of Science Cambridge: MIT
from the underdetermination problem, is not so historPress..
ically motivated as these others. It claims that observational data can in principle be explained by multiple
• Kukla, A. (2000). Social constructivism and the
theories that are mutually incompatible. Realists might
philosophy of science. London: Routledge.
counter by saying that there have been few actual cases
of underdetermination in the history of science. Usually
• Kuhn, Thomas. (1970). The Structure of Scientific
the requirement of explaining the data is so exacting that
Revolutions, 2nd Edition. Chicago: University of
scientists are lucky to find even one theory that fulfills
Chicago Press.
it. Furthermore, if we take the underdetermination ar• Laudan, Larry. (1981). “A Confutation of Convergument seriously, it implies that we can know about only
gent Realism” Philosophy of Science
what we have directly observed. For example, we could
not theorize that dinosaurs once lived based on the fossil
• Leplin, Jarrett. (1984). Scientific Realism. Califorevidence because other theories (e.g., that the fossils are
nia: University of California Press.
• Leplin, Jarrett. (1997). A Novel Defense of Scientific
Realism. Oxford: Oxford University Press.
• Lipton, Peter. (2004). Inference to the best explanation, 2nd edition. London: Routledge.
type is explanatory. It is explanatory knowledge that provides scientific understanding of
the world. (Salmon, 1990)
2.3.1 Accounts of scientific inquiry
• Maxwell, Grover (1962). “The Ontological Status
of Theoretical Entities” in Feigl and Maxwell ScienClassical model
tific Explanation, Space, and Time vol. 3, Minnesota
Studies in the Philosophy of Science, 3-15.
The classical model of scientific inquiry derives from
• Okasha, Samir. (2002). Philosophy of science: A Aristotle, who distinguished the forms of approxivery short introduction. Oxford: Oxford University mate and exact reasoning, set out the threefold scheme
Press. See especially chapter 4, “Realism and Anti- of abductive, deductive, and inductive inference, and
also treated the compound forms such as reasoning by
• Putnam, Hilary. (1962). “What Theories are Not”
in Ernst Nagel et al. (1962). Logic, Methodology,
and Philosophy of Science Stanford University Press. Pragmatic model
• Psillos, Stathis. (1999). Scientific realism: How sci- Main article: Pragmatic theory of truth
ence tracks truth. London: Routledge.
• Quine, W.V.O. (1951). “Two Dogmas of Empiricism” in his (1953). From a Logical Point of View Logical empiricism
Cambridge: Harvard University Press.
Wesley Salmon (1990) began his historical survey of sci• Quine, W.V.O. (1960). Word and Object Cam- entific explanation with what he called the received view,
bridge: MIT Press.
as it was received from Hempel and Oppenheim in the
• Sankey, H. (2001). “Scientific Realism: An years beginning with their Studies in the Logic of ExplanaElaboration and a Defense” retrieved from http:// tion (1948) and culminating in Hempel’s Aspects of Scientific Explanation (1965). Salmon summed up his analysis
of these developments by means of the following Table.
In this classification, a deductive-nomological (D-N) explanation of an occurrence is a valid deduction whose
conclusion states that the outcome to be explained did in
• Stanford Encyclopedia of Philosophy entry
fact occur. The deductive argument is called an explanation, its premisses are called the explanans (L: explaining)
and the conclusion is called the explanandum (L: to be
2.3 Models of scientific inquiry
explained). Depending on a number of additional qualifications, an explanation may be ranked on a scale from
In the philosophy of science, models of scientific in- potential to true.
quiry have two functions: first, to provide a descriptive Not all explanations in science are of the D-N type, howaccount of how scientific inquiry is carried out in prac- ever. An inductive-statistical (I-S) explanation accounts
tice, and second, to provide an explanatory account of for an occurrence by subsuming it under statistical laws,
why scientific inquiry succeeds as well as it appears to do rather than categorical or universal laws, and the mode
in arriving at genuine knowledge.
of subsumption is itself inductive instead of deductive.
External links
The search for scientific knowledge extends far back into antiquity. At some point
in the past, at least by the time of Aristotle,
philosophers recognized that a fundamental
distinction should be drawn between two kinds
of scientific knowledge — roughly, knowledge
that and knowledge why. It is one thing to
know that each planet periodically reverses the
direction of its motion with respect to the background of fixed stars; it is quite a different
matter to know why. Knowledge of the former type is descriptive; knowledge of the latter
The D-N type can be seen as a limiting case of the more
general I-S type, the measure of certainty involved being
complete, or probability 1, in the former case, whereas it
is less than complete, probability < 1, in the latter case.
In this view, the D-N mode of reasoning, in addition to
being used to explain particular occurrences, can also be
used to explain general regularities, simply by deducing
them from still more general laws.
Finally, the deductive-statistical (D-S) type of explanation, properly regarded as a subclass of the D-N type,
explains statistical regularities by deduction from more
comprehensive statistical laws. (Salmon 1990, pp. 8–9).
Such was the received view of scientific explanation from
the point of view of logical empiricism, that Salmon says
“held sway” during the third quarter of the last century
(Salmon, p. 10).
be weighted relative to one another, especially
when they conflict.”
— Alexander Bird, Methodological incommensurability
Choice of a theory
It also is debatable whether existing scientific theories satisfy all these criteria, and they may represent goals not
See also: Commensurability (philosophy of science)
yet achieved, a set of “New Year’s resolutions”, if you
like. For example, Item 3: explanatory power over all
During the course of history, one theory has succeeded existing observations, is satisfied by no one theory at the
another, and some have suggested further work while oth- moment.[7]
ers have seemed content just to explain the phenomena.
The reasons why one theory has replaced another are not
Whatever might be the ultimate goals of
always obvious or simple. The philosophy of science insome scientists, science, as it is currently praccludes the question: What criteria are satisfied by a 'good'
ticed, depends on multiple overlapping detheory. This question has a long history, and many sciscriptions of the world, each of which has a
entists as well as philosophers have considered it. The
domain of applicability. In some cases this doobjective is to be able to choose one theory as preferable
main is very large, but in others quite small.[8]
to another without introducing cognitive bias.[1] Several
— E.B. Davies, Epistemological pluralism,
often proposed criteria were summarized by Colyvan.[2]
p. 4
A good theory:
1. Is elegant (Formal elegance; no ad hoc modifica- The desiderata of a “good” theory have been debated for
centuries, going back perhaps even earlier than Occam’s
2. Contains few arbitrary or adjustable elements (sim- razor, which often is taken as an attribute of a good
Occam’s razor might fall under the heading of
“elegance”, the first item on the list, but too zealous an ap3. Agrees with and explains all existing observations plication was cautioned by Einstein: “Everything should
be made as simple as possible, but no simpler.”[10] It is ar(unificatory/explanatory power)
guable that parsimony and elegance “typically pull in dif4. Makes detailed predictions about future observa- ferent directions.”[11] The falsifiability item on the list is
tions that can disprove or falsify the model if they related to the criterion proposed by Popper as demarcatare not borne out.
ing a scientific theory from a theory like astrology: both
“explain” observations, but the scientific theory takes the
5. Is fruitful: the emphasis by Colyvan is not only upon risk of making predictions that decide whether it is right
prediction and falsification, but also upon a theory’s or wrong:[12][13]
seminality in suggesting future work.
Stephen Hawking supports items 1-4, but does not mention fruitfulness.[3] On the other hand, Kuhn emphasizes
the importance of seminality.[4]
The goal here is to make the choice between theories less
arbitrary. Nonetheless, these criteria contain subjective
elements, and are heuristics rather than part of scientific
method.[5] Also, criteria such as these do not necessarily
decide between alternative theories. Quoting Bird:[6]
“They [such criteria] cannot determine scientific choice. First, which features of a theory satisfy these criteria may be disputable
(e.g. does simplicity concern the ontological
commitments of a theory or its mathematical
form?). Secondly, these criteria are imprecise,
and so there is room for disagreement about
the degree to which they hold. Thirdly, there
can be disagreement about how they are to
“It must be possible for an empirical scientific system to be refuted by experience.”
“Those among us who are unwilling to expose their ideas to the hazard of refutation do
not take part in the game of science.”
— Karl Popper, The logic of scientific
discovery, p. 18 and p. 280
Thomas Kuhn argued that changes in scientists’ views of
reality not only contain subjective elements, but result
from group dynamics, “revolutions” in scientific practice
and changes in “paradigms”.[14] As an example, Kuhn
suggested that the Sun-centric Copernican “revolution”
replaced the Earth-centric views of Ptolemy not because
of empirical failures, but because of a new “paradigm”
that exerted control over what scientists felt to be the
more fruitful way to pursue their goals (Colyvan’s requirement of “fruitfulness”).
Aspects of scientific inquiry
Deduction and induction
Deductive logic and inductive logic are quite different in
their approaches.
is useful in such widely divergent enterprises as science
and crime scene detective work. One makes a set of observations, and seeks to explain what one sees. The observer forms a hypothesis in an attempt to explain what
he/she has observed. The hypothesis will have implications, which will point to certain other observations that
would naturally result from either a repeat of the experiment or making more observations from a slightly different set of circumstances. If the predicted observations
hold true, one feels excitement that they may be on the
right track. However, the hypothesis has not been proven.
The hypothesis implies that certain observations should
follow, but positive observations do not imply the hypothesis. They only make it more believable. It is quite possible that some other hypothesis could also account for the
known observations, and may do better with future experiments. The implication flows in only one direction,
as in the syllogism used in the discussion on deduction.
Therefore, it is never correct to say that a scientific principle or hypothesis/theory has been proven. (At least not
in the rigorous sense of proof used in deductive systems).
Deductive logic is the reasoning of proof, or logical implication. It is the logic used in mathematics and other
axiom based systems such as formal logic. In a deductive system, there will be axioms (postulates) which are
not proven. Indeed, they cannot be proven without circularity. There will also be primitive terms which are not
defined, as they cannot be defined without circularity. For
example, one can define a line as a set of points, but to
then define a point as the intersection of two lines would
be circular. Because of these interesting characteristics
of deductive systems, Bertrand Russell humorously referred to mathematics as “the field where we don't know
what we are talking about, nor whether or not what we
say is true”. All theorems and corollaries are proven by
exploring the implications of the axioms and other theorems that have previously been developed. New terms A classic example of this is the study of gravitation. Neware defined using the primitive terms and other derived ton formed a law for gravitation stating that the force of
definitions based on those primitive terms.
gravitation is directly proportional to the product of the
In a deductive system, one can correctly use the term two masses, and inversely proportional to the square of
“proof”, as applying to a theorem. To say that a theo- the distance between them. For over 170 years, all obserrem is proven means that it is impossible for the axioms vations seemed to validate his equation. However, teleto be true and the theorem to be false. For example, we scopes eventually became powerful enough to see a slight
discrepancy in the orbit of Mercury. Scientists tried evcould do a simple syllogism such as the following:
erything imaginable to explain the discrepancy, but they
could not do so using the objects that would bear on the
1. Arches National Park lies within the state of Utah.
orbit of Mercury. Eventually Einstein developed his theory of General Relativity and it explained the orbit of
2. I am standing in Arches National Park.
Mercury and all other known observations dealing with
3. Therefore, I am standing in the state of Utah.
gravitation. During the long period of time when scientists were making observations that seemed to validate
Notice that it is not possible (assuming all of the trivial Newton’s theory, they did not in fact prove his theory to
qualifying criteria are supplied) to be in Arches and not be be true. However, it must have seemed at the time that
in Utah. However, one can be in Utah while not in Arches they did. It only took one counter-example (Mercury’s
National Park. The implication only works in one direc- orbit) to prove that there was something wrong with his
tion. Statements (1) and (2) taken together imply state- theory. This is typical of inductive logic. All of the obserment (3). Statement (3) does not imply anything about vations that seem to validate the theory, do not prove its
statements (1) or (2). Notice that we have not proven truth. But one counter-example can prove it false. That
statement (3), but we have shown that statements (1) and means that deductive logic is used in the evaluation of a
(2) together imply statement (3). In mathematics, what is theory. In other words, if A implies B, then not B improven is not the truth of a particular theorem, but that the plies not A. Einstein’s theory of General Relativity has
axioms of the system imply the theorem. In other words, been supported by many observations using the best sciit is impossible for the axioms to be true and the theo- entific instruments and experiments. However, his theory
rem to be false. The strength of deductive systems is that now has the same status as Newton’s theory of gravitation
they are sure of their results. The weakness is that they prior to seeing the problems in the orbit of Mercury. It
are abstract constructs which are, unfortunately, one step is highly credible and validated with all we know, but it
removed from the physical world. They are very useful is not proven. It is only the best we have at this point in
however, as mathematics has provided great insights into time.
natural science by providing useful models of natural phenomena. One result is the development of products and Another example of correct scientific reasoning is shown
in the current search for the Higgs Boson. Scientists on
processes that benefit mankind.
the Compact Muon Solenoid experiment at the Large
Learning about the physical world requires the use of in- Hadron Collider have conducted experiments yielding
ductive logic. This is the logic of theory building. It
tantalizing data suggesting the existence of the Higgs. 2.3.4 See also
However, realizing that the results could possibly be ex• Deductive-nomological
plained as a background fluctuation or, possible, the
Higgs, they are cautious and waiting for further data from
• Explanandum and explanans
future experiments. Said Guido Tonelli:
“We cannot exclude the presence of the Standard Model
Higgs between 115 and 127 GeV because of a modest
excess of events in this mass region that appears, quite
consistently, in five independent channels,” Tonelli said.
“As of today what we see is consistent either with a background fluctuation or with the presence of the boson.”
• Hypothetico-deductive method
• Inquiry
• Scientific method
A brief overview of the scientific method would then 2.3.5
contain these steps as a minimum:
2. Form a hypothesis that might explain the observations. (Inductive Step)
[1] Thomas Kuhn formally stated this need for the “norms for
rational theory choice”. One of his discussions is reprinted
in Thomas S Kuhn (2002-11-01). “Chapter 9: Rationality and Theory Choice”. In James Conant, John Haugeland, eds. The Road since Structure: Philosophical Essays,
1970–1993 (2nd ed.). University of Chicago Press. pp.
208 ff. ISBN 0226457990.
3. Identify the implications and outcomes that must
follow, if the hypothesis is to be true.
[2] Mark Colyvan (2001). The Indispensability of Mathematics. Oxford University Press. pp. 78–79. ISBN
1. Make a set of observations regarding the phenomenon being studied.
4. Perform other experiments or observations to see if
any of the predicted outcomes fail.
5. If any predicted outcomes fail, the hypothesis is
proven false since if A implies B, then not B implies not A. (Deductive Logic) It is then necessary
to change the hypothesis and go back to step 3. If the
predicted outcomes are confirmed, the hypothesis is
not proved, but rather can be said to be consistent
with known data.
When a hypothesis has survived a sufficient number of
tests, it may be promoted to a 'Theory'. A theory is a
hypothesis that has survived many tests and seems to be
consistent with other established scientific theories. Since
a theory is a promoted hypothesis, it is of the same 'logical' species and shares the same logical limitations. Just
as a hypothesis cannot be proven but can be disproved,
that same is true for a theory. It is a difference of degree,
not kind.
Arguments from analogy are another type of inductive reasoning. In arguing from analogy, one infers that
since two things are alike in several respects, they are
likely to be alike in another respect. This is, of course,
an assumption. It is natural to attempt to find similarities between two phenomena and wonder what one can
learn from those similarities. However, to notice that two
things share attributes in several respects does not imply
any similarities in other respects. It is possible that the
observer has already noticed all of the attributes that are
shared and any other attributes will be distinct. Argument from analogy is an unreliable method of reasoning
that can lead to erroneous conclusions, and thus cannot
be used to establish scientific facts.
[3] Stephen Hawking, Leonard Mlodinow (2010). “What is
reality?". The Grand Design. Random House Digital, Inc.
p. 51. ISBN 0553907077. See also: model-dependent
[4] Thomas S Kuhn (1966). The structure of scientific revolutions (PDF) (3rd ed.). University of Chicago Press. p.
157. ISBN 0226458083. That decision must be based
less on past achievement than on future promise.
[5] For example, Hawking/Mlodinow say (The Grand Design,
p. 52) “The above criteria are obviously subjective. Elegance, for example, is not something easily measured,
but it is highly prized among scientists.” The idea of 'too
baroque' is connected to 'simplicity': “a theory jammed
with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not
simpler”.(The Grand Design, p. 52) See also: Simon Fitzpatrick (April 5, 2013). “Simplicity in the Philosophy
of Science”. Internet Encyclopedia of Philosophy. and
Baker, Alan (Feb 25, 2010). Edward N. Zalta, ed, ed.
“Simplicity”. The Stanford Encyclopedia of Philosophy
(Summer 2011 Edition).
[6] Bird, Alexander (Aug 11, 2011). Edward N. Zalta, ed, ed.
"§4.1 Methodological Incommensurability”. The Stanford
Encyclopedia of Philosophy (Spring 2013 Edition).
[7] See Stephen Hawking, Leonard Mlodinow (2010). The
Grand Design. Random House Digital, Inc. p. 8. ISBN
0553907077. It is a whole family of different theories,
each of which is a good description of observations only
in some range of physical situations...But just as there is
no map that is a good representation of the earth’s entire
surface, there is no single theory that is a good representation of observations in all situations.
[8] E Brian Davies (2006).
PhilSci Archive.
“Epistemological pluralism”.
[9] Occam’s razor, sometimes referred to as “ontological parsimony”, is roughly stated as: Given a choice between two
theories, the simplest is the best. This suggestion commonly is attributed to William of Ockham in the 14thcentury, although it probably predates him. See Baker,
Alan (February 25, 2010). “Simplicity; §2: Ontological parsimony”. The Stanford Encyclopedia of Philosophy
(Summer 2011 Edition). Retrieved 2011-11-14.
[10] This quote may be a paraphrase. See MobileReference
(2011). Famous Quotes from 100 Great People. MobileReference. ISBN 1611980763. MobilReference is a
Boston-based e-book publisher.
[11] Baker, Alan (Feb 25, 2010). Edward N. Zalta, ed, ed.
“Simplicity”. The Stanford Encyclopedia of Philosophy
(Summer 2011 Edition).
[12] Karl Popper. “Science: Conjectures and refutations”
(PDF). Texas A&M University The motivation & cognition interface lab. Retrieved 2013-01-22. This lecture by
Popper was first published as part of the book Conjectures
and Refutations and is linked here.
[13] Karl Raimund Popper (2002). The logic of scientific discovery (Reprint of translation of 1935 Logik der Forchung
ed.). Routledge/Taylor & Francis Group. pp. 18, 280.
ISBN 0415278430.
[14] Thomas S Kuhn (1966). The structure of scientific revolutions (PDF) (3rd ed.). University of Chicago Press. ISBN
Further reading
• An Introduction to Logic and Scientific Method
(1934) by Ernest Nagel and Morris Raphael Cohen
• Dictionary of Philosophy (1942) by Dagobert D.
External links
For interesting explanations regarding the orbit of Mercury and General Relativity, the following links are useful:
• Precession of the perihelion of Mercury
• The Confrontation between General Relativity and
Chapter 3
Philosophy of particular sciences
3.1 Philosophy of physics
3.1.2 Philosophy of space and time
In philosophy, the philosophy of physics studies the
fundamental philosophical questions underlying modern
physics, the study of matter and energy and how they
interact. The philosophy of physics begins by reflecting
on the basic metaphysical and epistemological questions
posed by physics: causality, determinism, and the nature
of physical law. It then turns to questions raised by important topics in contemporary physics:
Main article: Philosophy of space and time
• Physical cosmology: space, time, and the origin and
ultimate fate of the universe;
• Thermodynamics and statistical mechanics: energy,
work, randomness, information;
• Quantum mechanics: the rival interpretations
thereof, and its counterintuitive conclusions.
Centuries ago, the study of causality, and of the fundamental nature of space, time, matter, and the universe were part of metaphysics. Today the philosophy
of physics is essentially a part of the philosophy of science. Physicists utilize the scientific method to delineate
the universals and constants governing physical phenomena, and the philosophy of physics reflects on the results
of this empirical research.
Purpose of physics
According to Niels Bohr, the purpose of physics is:[1]
not to disclose the real essence of phenomena but only to track down... relations between
the manifold aspects of experience.
The existence and nature of space and time (or spacetime) are central topics in the philosophy of physics.[2]
Main article: Time in physics
Time is considered to be a fundamental quantity (that
is, a quantity which cannot be defined in terms of other
quantities), because at present nothing is more basic than
time. Thus time is defined via measurement—by its standard time interval. Currently, the standard time interval
(called “conventional second", or simply “second”) is defined as 9,192,631,770 oscillations of a hyperfine transition in the 133 caesium atom. (ISO 31-1). What time
is and how it works follows from the above definition.
Time then can be combined mathematically with the fundamental quantities of space and mass to define concepts
such as velocity, momentum, energy, and fields.
Both Newton and Galileo,[3] as well as most people up
until the 20th century, thought that time was the same for
everyone everywhere. Our modern conception of time is
based on Einstein's theory of relativity and Minkowski's
spacetime, in which rates of time run differently in different inertial frames of reference, and space and time are
merged into spacetime. Time may be quantized, with the
theoretical smallest time being on the order of the Planck
time. Einstein’s general relativity as well as the redshift
of the light from receding distant galaxies indicate that
the entire Universe and possibly space-time itself began
about 13.8 billion years ago in the big bang. Whether and
how the universe will ever end are open questions (see
Ultimate fate of the universe).
Time travel
Many, particularly realists, find this minimal formulation an inadequate formulation of the purpose of physics, Main article: Time travel
which they view as providing, in addition, a deeper world
Some theories, most notably special and general relativity,
A second, similar type of time travel is permitted by
general relativity. In this type a distant observer sees time
passing more slowly for a clock at the bottom of a deep
gravity well, and a clock lowered into a deep gravity well
and pulled back up will indicate that less time has passed
compared to a stationary clock that stayed with the distant
These effects are to some degree similar to hibernation,
or cooling of live objects (which slow down the rates of
chemical processes in the subject) almost indefinitely suspending their life thus resulting in “time travel” toward the
future, but never backward. They do not violate causality.
This is not typical of the “time travel” featured in science
fiction (where causality is violated at will), and there is
little doubt surrounding its existence. “Time travel” will
hereafter refer to travel with some degree of freedom into
the past or future of proper time.
Many in the scientific community believe that time travel
is highly unlikely, because it violates causality i.e. the
logic of cause and effect. For example, what happens if
you attempt to go back in time and kill yourself at an earlier stage in your life (or your grandfather, which leads
to the grandfather paradox)? Stephen Hawking once suggested that the absence of tourists from the future constitutes a strong argument against the existence of time
travel— a variant of the Fermi paradox, with time travelers instead of alien visitors. Hitherto there is no experimental evidence of time travel, making it a mere hypothesis as opposed to an empirical fact.
Time, in many philosophies, is seen as change.
suggest that suitable geometries of spacetime, or certain
types of motion in space, may allow time travel into the
past and future. Concepts that aid such understanding
include the closed timelike curve.
Albert Einstein's special theory of relativity (and, by extension, the general theory) predicts time dilation that
could be interpreted as time travel. The theory states
that, relative to a stationary observer, time appears to
pass more slowly for faster-moving bodies: for example,
a moving clock will appear to run slow; as a clock approaches the speed of light its hands will appear to nearly
stop moving. The effects of this sort of time dilation are
discussed further in the popular "twin paradox". These
results are experimentally observable and affect the operation of GPS satellites and other high-tech systems used
in daily life.
Main article: Space
Space is one of the few fundamental quantities in physics,
meaning that it cannot be defined via other quantities
because there is nothing more fundamental known at
present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined
via measurement. Currently, the standard space interval,
called a standard metre or simply metre, is defined as the
distance traveled by light in a vacuum during a time interval of 1/299792458 of a second (exact).
In classical physics, space is a three-dimensional
Euclidean space where any position can be described
using three coordinates. Special and general relativity
use spacetime rather than space; spacetime is modeled
as a four-dimensional space (with the time axis being
imaginary in special relativity and real in general relativity, and currently there are many theories which use more
than four spatial dimensions.
Philosophy of quantum mechanics
Main article: Interpretation of quantum mechanics
Quantum mechanics is a large focus of contemporary philosophy of physics, specifically concerning the correct interpretation of quantum mechanics. Very broadly, much
of the philosophical work that is done in quantum theory is trying to make sense of superposition states:[4] the
property that particles seem to not just be in one determinate position at one time, but are somewhere 'here',
and also 'there' at the same time. Such a radical view
turns a lot of our common sense metaphysical ideas on
their head. Much of contemporary philosophy of quantum mechanics aims to make sense of what the very empirically successful formalism of quantum mechanics tells
us about the physical world.
Heisenberg, de Broglie, Dirac, Bohr, Jeans, Weyl,
Compton, Thomson, Schrödinger, Jordan, Millikan,
Lemaître, Reichenbach, et al. were all supporters of
Uncertainty principle
Main article: Uncertainty principle
The uncertainty principle is a mathematical relation asserting an upper limit to the accuracy of the simultaneous measurement of any pair of conjugate variables, e.g.
position and momentum. In the formalism of operator
notation, this limit is the evaluation of the commutator of
the variables’ corresponding operators.
The uncertainty principle arose as an answer to the question: How does one measure the location of an electron
around a nucleus if an electron is a wave? When quantum
The 18th century saw many advances in the domain of
mechanics was developed, it was seen to be a relation bescience. After Newton, most scientists agreed on the pretween the classical and quantum descriptions of a system
supposition that the universe is governed by strict natuusing wave mechanics.
ral laws that can be discovered and formalized by means
of scientific observation and experiment. This position In March 1926, working in Niels Bohr's institute,
is known as determinism. However, determinism seems Werner Heisenberg formulated the principle of uncerto preclude the possibility of free will. That is, if the tainty thereby laying the foundation of what became
universe, and thus any person in it, is governed by strict known as the Copenhagen interpretation of quantum meand universal laws, then that means that a person’s be- chanics. Heisenberg had been studying the papers of Paul
havior could be predicted based on sufficient knowledge Dirac and Pascual Jordan. He discovered a problem with
of the circumstances that obtained prior to that person’s measurement of basic variables in the equations. His
behavior. This appears to contradict the person’s percep- analysis showed that uncertainties, or imprecisions, altion of free will, except as interpreted in compatibilism. ways turned up if one tried to measure the position and
Conversely, if we accept that human beings do have the momentum of a particle at the same time. Heisen(libertarian or incompatibilist) free will, then we must ac- berg concluded that these uncertainties or imprecisions in
cept that the world is not entirely governed by natural law. the measurements were not the fault of the experimenter,
Some have argued that if the world is not entirely gov- but fundamental in nature and are inherent mathematierned by natural law, then the task of science is rendered cal properties of operators in quantum mechanics arising
impossible. However, the development of quantum me- from definitions of these operators.
chanics gave thinkers alternatives to these strictly bound The term Copenhagen interpretation of quantum mepossibilities, proposing a model for a universe that fol- chanics was often used interchangeably with and as a synlows general rules but never had a predetermined future. onym for Heisenberg’s uncertainty principle by detracDeterminism
See also: Indeterminism, Indeterminism in science and
Bohr–Einstein debates
Against the proponents of determinism like Einstein and
Max Planck, indeterminism—championed by the English
astronomer Sir Arthur Eddington[5] —says that a physical
object has an ontologically undetermined component that
is not due to the epistemological limitations of physicists’
understanding. The uncertainty principle, then, would
not necessarily be due to hidden variables but to an indeterminism in nature itself.
tors (such as Einstein and the physicist Alfred Landé)
who believed in determinism and saw the common features of the Bohr-Heisenberg theories as a threat. Within
the Copenhagen interpretation of quantum mechanics the
uncertainty principle was taken to mean that on an elementary level, the physical universe does not exist in a
deterministic form, but rather as a collection of probabilities, or possible outcomes. For example, the pattern
(probability distribution) produced by millions of photons passing through a diffraction slit can be calculated using quantum mechanics, but the exact path of each photon
cannot be predicted by any known method. The Copenhagen interpretation holds that it cannot be predicted by
any method, not even with theoretically infinitely precise
I hold space to be something merely relative, as time is,
that I hold it to be an order of coexistences, as time is an
The idea of complementarity is critical in quantum me- order of successions.”[15]
chanics. It says that light can behave both like a particle
and like a wave. When the double-slit experiment was
performed, light acted in some cases as a wave, and some Quotes from Einstein’s work on the importance of the
cases as a particle. Physicists had no convincing theory to philosophy of physics
explain this until Bohr and complementarity came along.
History of the philosophy of physics
Aristotelian physics
Aristotelian physics viewed the universe as a sphere with a
center. Matter, composed of the classical elements, earth,
water, air, and fire, sought to go down towards the center
of the universe, the center of the earth, or up, away from
it. Things in the aether such as the moon, the sun, planets,
or stars circled the center of the universe.[7] Movement is
defined as change in place,[7] i.e. space.[8]
Newtonian physics
The implicit axions of Aristotelian physics with respect
to movement of matter in space were superseded in
Newtonian physics by Newton’s First Law of Motion.[9]
“Every body” includes the Moon, and an apple; and includes all types of matter, air as well as water, stones,
or even a flame. Nothing has a natural or inherent motion.[10] Absolute space being three-dimensional
Euclidean space, infinite and without a center.[10] Being
“at rest” means being at the same place in absolute space
over time.[11] The topology and affine structure of space
must permit movement in a straight line at a uniform
volocity; thus both space and time must have definite, stable dimensions.[12]
Einstein was interested in the philosophical implications of his
Gottfried Wilhelm Leibniz, 1646 – 1716, was a contemporary of Newton. He contributed a fair amount to the
statics and dynamics emerging around him, often disagreeing with Descartes and Newton. He devised a new
theory of motion (dynamics) based on kinetic energy and
potential energy, which posited space as relative, whereas
Newton was thoroughly convinced that space was absolute. An important example of Leibniz’s mature physical
thinking is his Specimen Dynamicum of 1695.[13]
Until the discovery of subatomic particles and the
quantum mechanics governing them, many of Leibniz’s
speculative ideas about aspects of nature not reducible to
statics and dynamics made little sense. For instance, he
anticipated Albert Einstein by arguing, against Newton,
that space, time and motion are relative, not absolute:[14]
“As for my own opinion, I have said more than once, that
Albert Einstein was extremely interested in the philosophical conclusions of his work. He writes:
“I fully agree with you about the significance and educational value of methodology
as well as history and philosophy of science.
So many people today—and even professional
scientists—seem to me like somebody who has
seen thousands of trees but has never seen a
forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation
from which most scientists are suffering. This
independence created by philosophical insight
is—in my opinion—the mark of distinction between a mere artisan or specialist and a real
seeker after truth.” Einstein. letter to Robert
A. Thornton, 7 December 1944. EA 61-574.
“How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there no more valuable work in his specialty? I hear many of my
colleagues saying, and I sense it from many
more, that they feel this way. I cannot share
this sentiment. ... Concepts that have proven
useful in ordering things easily achieve such an
authority over us that we forget their earthly
origins and accept them as unalterable givens.
Thus they come to be stamped as 'necessities
of thought,' 'a priori givens,' etc.”
“The path of scientific advance is often
made impassable for a long time through such
errors. For that reason, it is by no means an
idle game if we become practiced in analyzing
the long-commonplace concepts and exhibiting [revealing, exposing? -Ed.] those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By
this means, their all-too-great authority will be
broken.” Einstein, 1916, “Memorial notice for
Ernst Mach,” Physikalische Zeitschrift 17: 10102.
See also
[1] N.Bohr, Atomic Theory and the Description of Human
Knowledge (Cambridge University Press, Cambridge,
1934) p.19. Found in: R.Plaga (1997). “Proposal for
an experimental test of the many-worlds interpretation of
quantum mechanics”. Foundations of Physics, v. 27, p.
[2] first page of the introduction, Tim Maudlin (2012-07-22).
Philosophy of Physics: Space and Time: Space and Time
(Princeton Foundations of Contemporary Philosophy) .
Princeton University Press. Kindle Edition. "...the existence and nature of space and time (or space-time) is a
central topic.”
[3] Roger Penrose, 2004. The Road to Reality: A Complete
Guide to the Laws of the Universe. London: Jonathan
Cape. ISBN 0-224-04447-8 (hardcover), 0-09-9440687 (paperback).
[5] de Koninck, Charles (2008). “The philosophy of Sir
Arthur Eddington and The problem of indeterminism”.
The writings of Charles de Koninck. Notre Dame, Ind.
:: University of Notre Dame Press,. ISBN 978-0-26802595-3. OCLC 615199716.
[6] Niels Bohr, Atomic Physics and Human Knowledge, p. 38
[7] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (p. 3). Princeton University
Press. Kindle Edition."Because it is a sphere, Aristotle’s
universe contains a geometrically privileged center, and
Aristotle makes reference to that center in characterizing the natural motions of different sorts of matter. “Upward,”“downward,” and “uniform circular motion” all are
defined in terms of the center of the universe.”
[8] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (p. 4). Princeton University
Press. Kindle Edition. “Aristotle adopts the concept of
space, and the correlative concept of motion, that we all
intuitively employ.”
[9] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (pp. 4-5). Princeton University Press. Kindle Edition. “Newtonian physics is implicit
in his First Law of Motion: Law I : Every body perseveres in its state either of rest or of uniform motion in a
straight line, except insofar as it is compelled to change its
state by impressed forces. 1 This single law smashes the
Aristotelian universe to smithereens.”
[10] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (pp. 5). Princeton University
Press. Kindle Edition.
[11] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (pp. 9-10). Princeton University Press. Kindle Edition. “Newton believed in the existence of a spatial arena with the geometrical structure of
E3 . He believed that this infinite three-dimensional space
exists at every moment of time. And he also believed
something much more subtle and controversial, namely,
that identically the same points of space persist through
[12] Tim Maudlin (2012-07-22). Philosophy of Physics: Space
and Time: Space and Time (Princeton Foundations of
Contemporary Philosophy) (p. 12). Princeton University Press. Kindle Edition. " must have a topology, an affine structure, and a metric; time must be onedimensional with a topology and a metric; and, most
importantly, the individual parts of space must persist
through time.
[13] Ariew and Garber 117, Loemker §46, W II.5. On Leibniz
and physics, see the chapter by Garber in Jolley (1995) and
Wilson (1989).
[14] Rafael Ferraro (2007). Einstein’s Space-Time: An Introduction to Special and General Relativity. Springer. p. 1.
ISBN 978-0-387-69946-2.
[15] See H. G. Alexander, ed., The Leibniz-Clarke Correspondence, Manchester: Manchester University Press, pp. 25–
Further reading
• David Albert, 1994. Quantum Mechanics and Experience. Harvard Univ. Press.
• John D. Barrow and Frank J. Tipler, 1986. The Cosmological Anthropic Principle. Oxford Univ. Press.
• Beisbart, C. and S. Hartmann, eds., 2011. “Probabilities in Physics”. Oxford Univ. Press.
• John S. Bell, 2004 (1987), Speakable and Unspeakable in Quantum Mechanics. Cambridge Univ.
• Carl Friedrich von Weizsäcker, 1980. The Unity of
Nature. Farrar Straus & Giroux.
• Werner Heisenberg, 1971. Physics and Beyond: Encounters and Conversations. Harper & Row (World
Perspectives series), 1971.
• William Berkson, 1974. Fields of Force. Routledge
and Kegan Paul, London. ISBN 0-7100-7626-6
• Encyclopedia Britannica, Philosophy of Physics,
David Z. Albert
• David Bohm, 1980. Wholeness and the Implicate 3.1.8 External links
Order. Routledge.
• Stanford Encyclopedia of Philosophy:
• Nick Bostrom, 2002. Anthropic Bias: Observation
Selection Effects in Science and Philosophy. Rout• "Absolute and Relational Theories of Space
and Motion"—Nick Huggett and Carl Hoefer
• Thomas Brody, 1993, Ed. by Luis de la Peña and
Peter E. Hodgson The Philosophy Behind Physics
Springer ISBN 3-540-55914-0
• Harvey Brown, 2005. Physical Relativity. Spacetime structure from a dynamical perspective. Oxford
Univ. Press.
• "Being and Becoming in Modern Physics"—
Steven Savitt
• "Boltzmann’s Work in Statistical Physics"—
Jos Uffink
• "Conventionality of Simultaneity"—Allen Janis
• Butterfield, J., and John Earman, eds., 2007. Philosophy of Physics, Parts A and B. Elsevier.
• "Early Philosophical Interpretations of General Relativity"—Thomas A. Ryckman
• Craig Callender and Nick Huggett, 2001. Physics
Meets Philosophy at the Planck Scale. Cambridge
Univ. Press.
• "Experiments in Physics"—Allan Franklin
• David Deutsch, 1997. The Fabric of Reality. London: The Penguin Press.
• "Intertheory Relations in Physics"—Robert
• Bernard d'Espagnat, 1989. Reality and the Physicist. Cambridge Univ. Press. Trans. of Une incertaine réalité; le monde quantique, la connaissance et
la durée.
• "Naturalism"—David Papineau
• --------, 1995. Veiled Reality. Addison-Wesley.
• "Holism and Nonseparability in Physics"—
Richard Healey
• "Philosophy of Statistical Mechanics"—
Lawrence Sklar
• "Physicalism"—Daniel Sojkal
• "Quantum Mechanics"—Jenann Ismael
• --------, 2006. On Physics and Philosophy. Princeton Univ. Press.
• "Reichenbach’s Common Cause Principle"—
Frank Artzenius
• Roland Omnes, 1994. The Interpretation of Quantum Mechanics. Princeton Univ. Press.
• "Structural Realism"—James Ladyman
• --------, 1999.
Univ. Press.
Quantum Philosophy.
• Huw Price, 1996. Time’s Arrow and Archimedes’s
Point. Oxford Univ. Press.
• Lawrence Sklar, 1992. Philosophy of Physics. Westview Press. ISBN 0-8133-0625-6, ISBN 978-08133-0625-4
• Victor Stenger, 2000. Timeless Reality. Prometheus
• "Structuralism in Physics"—Heinz-Juergen
• "Symmetry and Symmetry Breaking"—
Katherine Brading and Elena Castellani
• "Thermodynamic Asymmetry in Time"—
Craig Callender
• "Time"—by Ned Markosian
• "Uncertainty principle"—Jan Hilgevoord and
Jos Uffink
• "The Unity of Science"—Jordi Cat
3.2 Philosophy of biology
The philosophy of biology is a subfield of philosophy of
science, which deals with epistemological, metaphysical,
and ethical issues in the biological and biomedical sciences. Although philosophers of science and philosophers generally have long been interested in biology (e.g.,
Aristotle, Descartes, and even Kant), philosophy of biology only emerged as an independent field of philosophy
in the 1960s and 1970s. Philosophers of science then began paying increasing attention to biology, from the rise
of Neodarwinism in the 1930s and 1940s to the discovery of the structure of DNA in 1953 to more recent advances in genetic engineering. Other key ideas include
the reduction of all life processes to biochemical reactions, and the incorporation of psychology into a broader
metaphysics. Furthermore, progress in biology urges
modern societies to rethink traditional values concerning
all aspects of human life. The possibility of genetic modification of human stem cells, for example, has led to an
ongoing controversy on how certain biological techniques
could infringe upon ethical consensus (see bioethics).
Some of the questions addressed by these philosophers
of biology include:
• “What is life?"[1]
• “What makes humans uniquely human?";
• “What is the basis of moral thinking?";
• “What are the factors we use for aesthetic judgments?";
• “Is evolution compatible with Christianity or other
religious systems?"
The philosophy of biology can be seen as following an
empirical tradition, favoring naturalism. Many contemporary philosophers of biology have largely avoided traditional questions about the distinction between life and
non-life. Instead, they have examined the practices,
theories, and concepts of biologists with a view toward
better understanding biology as a scientific discipline (or
group of scientific fields). Scientific ideas are philosophically analyzed and their consequences are explored. It
is sometimes difficult to delineate philosophy of biology
as separate from theoretical biology. A few of the questions philosophers of biology have attempted to answer,
for example, include:
Increasingly, ideas drawn from philosophical ontology
and logic are being used by biologists in the domain
of bioinformatics. Ontologies such as the Gene Ontology are being used to annotate the results of biological experiments in a variety of model organisms in order to create logically tractable bodies of data available for reasoning and search. The Gene Ontology itself is a species-neutral graph-theoretical representation
of biological types joined together by formally defined
Philosophy of biology today has become a very visible,
well-organized discipline - with its own journals, conferences, and professional organizations. The largest of the
latter is the International Society for the History, Philosophy, and Social Studies of Biology (ISHPSSB); the name
• “What is a biological species?"
of the Society reflecting the interdisciplinary nature of
• “How is rationality possible, given our biological the field.
• “How do organisms coordinate their common behavior?"
3.2.2 Reductionism, holism, and vitalism
One subject within philosophy of biology deals with the
relationship between reductionism and holism, contend• “How might our biological understandings of race, ing views with epistemological and methodological significance, but also with ethical and metaphysical connosexuality, and gender reflect social values?"
• “What is natural selection, and how does it operate
in nature?"
• Scientific reductionism is the view that higher-level
• “Are there genome editing agents?"
• “How do medical doctors explain disease?"
• “From where do language and logic stem?";
• “How is ecology related to medicine?"
A subset of philosophers of biology with a more explicitly naturalistic orientation hope that biology will provide scientific answers to such fundamental problems of
epistemology, ethics, aesthetics, anthropology and even
biological processes reduce to physical and chemical processes. For example, the biological process
of respiration is explained as a biochemical process
involving oxygen and carbon dioxide.
• Holism is the view that emphasizes higher-level processes, also called emergent properties: phenomena at a larger level that occur due to the pattern of interactions between the elements of a system over time. For example, to explain why one
species of finch survives a drought while others die
out, the holistic method looks at the entire ecosystem. Reducing an ecosystem to its parts in this
case would be less effective at explaining overall behavior (in this case, the decrease in biodiversity).
As individual organisms must be understood in the
context of their ecosystems, holists argue, so must
lower-level biological processes be understood in
the broader context of the living organism in which
they take part. Proponents of this view cite our
growing understanding of the multidirectional and
multilayered nature of gene modulation (including
epigenetic changes) as an area where a reductionist
view is inadequate for full explanatory power.[2] See
also Holism in science.
• Vitalism is the view, rejected by mainstream biologists since the 19th century, that there is a lifeforce (called the “vis viva”) that has thus far been unmeasurable scientifically that gives living organisms
their “life.” Vitalists often claimed that the vis viva
acts with purposes according to its pre-established
“form” (see teleology). Examples of vitalist philosophy are found in many religions. Mainstream biologists reject vitalism on the grounds that it opposes
the scientific method. The scientific method was designed as a methodology to build an extremely reliable understanding of the world, that is, a supportable, evidenced understanding. Following this epistemological view, mainstream scientists reject phenomena that have not been scientifically measured
or verified, and thus reject vitalism.
Some philosophers of biology have attempted to explain
the rise and fall of reductionism, vitalism, and holism
throughout the history of biology. For example, these
philosophers claim that the ideas of Charles Darwin
ended the last remainders of teleological views from biology. Debates in these areas of philosophy of biology turn
on how one views reductionism.
to leave out a lot of what characterised living organisms namely, a historical component in the form of an inherited genotype.
Biologists with philosophic interests responded, emphasising the dual nature of the living organism. On the one
hand there was the genetic programme (represented in
nucleic acids) - the genotype. On the other there was its
extended body or soma - the phenotype. In accommodating the more probabilistic and non-universal nature of
biological generalisations, it was a help that standard philosophy of science was in the process of accommodating
similar aspects of 20th century physics.
This led to a distinction between proximate causes and explanations - “how” questions dealing with the phenotype;
and ultimate causes - “why” questions, including evolutionary causes, focused on the genotype. This clarification was part of the great reconciliation, by Ernst Mayr,
among others, in the 1940s, between Darwinian evolution by natural selection and the genetic model of inheritance. A commitment to conceptual clarification has
characterised many of these philosophers since. Trivially, this has reminded us of the scientific basis of all
biology, while noting its diversity - from microbiology to
ecology. A complete philosophy of biology would need
to accommodate all these activities. Less trivially, it has
unpacked the notion of "teleology". Since 1859, scientists have had no need for a notion of cosmic teleology a programme or a law that can explain and predict evolution. Darwin provided that. But teleological explanations (relating to purpose or function) have remained
stubbornly useful in biology - from the structural configuration of macromolecules to the study of co-operation in
social systems. By clarifying and restricting the use of the
term to describe and explain systems controlled strictly
scientifically by genetic programmes, or other physical
systems, teleological questions can be framed and investigated while remaining committed to the physical nature
of all underlying organic processes.
Similar attention has been given to the concepts of natural
selection (what is the target of natural selection? An autonomous philosophy of biol- the individual? the environment? the genome? the
species?); adaptation; diversity and classification; species
and speciation; and macroevolution.
All processes in organisms obey physical laws, the difference from inanimate processes lying in their organisation and their being subject to control by coded information. This has led some biologists and philosophers
(for example, Ernst Mayr and David Hull) to return to the
strictly philosophical reflections of Charles Darwin to resolve some of the problems which confronted them when
they tried to employ a philosophy of science derived from
classical physics. This latter, positivist approach emphasised a strict determinism (as opposed to high probability) and to the discovery of universally applicable laws,
testable in the course of experiment. It was difficult for
biology, beyond a basic microbiological level, to live up to
these structures. Standard philosophy of science seemed
Just as biology has developed as an autonomous discipline in full conversation with the other sciences, there
is a great deal of work now being carried on by biologists
and philosophers to develop a dedicated philosophy of
biological science which, while in full conversation with
all other philosophic disciplines, attempts to give answers
to the real questions raised by scientific investigations in
Another autonomous philosophy of biology is represented by Guenther Witzany and his theory of biocommunication: Living nature is structured and organized by
language and communication within and among cells, tissues, organs and organisms. This means that besides hu-
man language and communication every living entity is
competent to use signs with which it can differentiate between self and non-self. The communicative competence
serves for coordination of group behavior (tissues, organs, organisms). Biocommunication research is applied
to all organismic kingdoms based on empirical data.[3]
Additionally the biocommunication method investigates
nucleotide sequences as natural code which is structured
according combinatorial, context-sensitive and contentspecific rules. Natural genome editing from a biocommunicative perspective consequently is investigated as competent agent-driven generation and integration of meaningful nucleotide sequences into pre-existing genomic
content arrangements of host organisms. Such natural
genome editing agents can (re)combine and (re)regulate
host genome content according to context-dependent (i.e.
adaptational) purposes. Such active agent-driven processes contradict passive error replication (mutation) narratives to explain emergence of genetic diversity.
scientific discovery is by some considered to be the
fourth paradigm, after empiricism, theory and computer
simulation.[5] Others reject the idea that data driven research is about to replace theory.[6][7] As Krakauer et
al. put it: “machine learning is a powerful means of
preprocessing data in preparation for mechanistic theory building, but should not be considered the final goal
of a scientific inquiry.”[8] In regard to cancer biology,
Raspe et al. state: “A better understanding of tumor biology is fundamental for extracting the relevant information from any high throughput data.” [9] The journal Science chose cancer immunotherapy as the breakthrough
of 2013. According to their explanation a lesson to be
learned from the successes of cancer immunotherapy is
that they emerged from decoding of basic biology. [10]
Theory in biology is less strict formalized as it is
in physics. Besides 1) the classic physics way of
mathematical-analytical, there is 2) statistical based,
3) computer simulation and 4) conceptual/verbal
theorizing/modeling.[11] Dougherty and Bittner state
that in order for biology to progress as a science, it has
3.2.4 Other perspectives
to move to more rigorous mathematical modeling, or
While the overwhelming majority of English-speaking otherwise risk to be “empty talk”.
scholars operating under the banner of "philosophy of In tumor biology research, the characterization of cellubiology" work within the Anglo-American tradition of lar signaling processes has largely focused on identifying
analytical philosophy, there is a stream of philosophic the function of individual genes and proteins. Janes [13]
work in continental philosophy which seeks to deal with showed however the context-dependent nature of signalissues deriving from biological science. The commu- ing driving cell decisions demonstrating the need for a
nication difficulties involved between these two tradi- more system based approach.[14] The lack of attention for
tions are well known, not helped by differences in lan- context dependency in preclinical research is also illusguage. Gerhard Vollmer is often thought of as a bridge trated by the observation that preclinical testing rarely inbut, despite his education and residence in Germany, he cludes predictive biomarkers that, when advanced to clinlargely works in the Anglo-American tradition, partic- ical trials, will help to distinguish those patients who are
ularly pragmatism, and is famous for his development likely to benefit from a drug.[15]
of Lorenz’s and Quine’s idea of evolutionary epistemology. On the other hand, one scholar who has attempted
to give a more continental account of the philosophy of 3.2.6 See also
biology is Hans Jonas. His "The Phenomenon of Life"
• Bioethics
(New York, 1966) sets out boldly to offer an "existential
interpretation of biological facts", starting with the or• Biosemiotics
ganism’s response to stimulus and ending with man con• Evolutionary anthropology
fronting the Universe, and drawing upon a detailed reading of phenomenology. This is unlikely to have much in• Evolutionary psychology
fluence on mainstream philosophy of biology, but indicates, as does Vollmer’s work, the current powerful influ• Golden Eurydice Award
ence of biological thought on philosophy. A more engag• Mechanism (biology)
ing account is given by the late Virginia Tech philosopher
Marjorie Grene.
• Neuroaesthetics
Scientific discovery process
Research in biology continues to be less guided by theory than it is in other sciences.[4] This is especially the
case in the context of life sciences, where the availability
of high throughput screening techniques for the different omics fields and the perceived complexity, makes the
science predominantly data driven. This data-intensive
• Philosophy of chemistry
• Philosophy of mind
• Philosophy of physics
• Philosophy of science
• Physics envy
• Sociobiology
Notable philosophers of biology
• John Beatty
Biologists with an interest in the philosophical aspects of biology
• Francisco J. Ayala
• Richard Boyd
• Patrick Bateson
• Lindley Darden
• Richard Dawkins
• Daniel Dennett
• John Dupré
• Jared Diamond
• Michael Ghiselin
• François Jacob
• Carla Fehr
• Stephen Jay Gould
• Marjorie Grene
• Richard Lewontin
• Peter Godfrey-Smith
• James R. Griesemer
• Humberto Maturana
• Ernst Mayr
• Jacques Monod
• Paul E. Griffiths
• Denis Noble
• David Hull
• Joan Roughgarden
• Philip Stuart Kitcher
• Rolf Sattler
• John Maynard Smith
• Tim Lewens
• Edward O. Wilson
• Helen Longino
• Jonas Salk
• Jane Maienschein
• Roberta Millstein
• Sandra Mitchell
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• Griffiths, P., 2007, “The Phenomena of Homology”,
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Pigliucci, M. & Preston, K. (eds.), Phenotypic Integration: Studying the Ecology and Evolution of
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& Ruse, M. (eds.)
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• Gould, S. J., 1977, Ontogeny and Phylogeny, Cambridge, MA, Belknap Press.
• Hull, D., 1974, Philosophy of Biological Science,
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• Gould, S. J., 1980, The Panda’s Thumb, New York,
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• Hull, D., 1977, “A Logical Empiricist Looks at Biology”, The British Journal for the Philosophy of Science, 28(2), p. 181-189.
• Hull, D., 1978, “A Matter of Individuality”, Philosophy of Science, 45, p. 335-60.
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• Hull, D., 1980, “Individuality and Selection”, Annual Review of Ecology and Systematics, 11, p. 11332.
• Laland, K., Odling-Smee, J. & Gilbert, S. F.,
2008, “EvoDevo and Niche Construction: Building Bridges”, Journal of Experimental Zoology (Mol
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• Lewens, T., 2009, “Seven kinds of adaptationism”,
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• Hull, D., 1989b, “A Function for Actual Examples
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• Kimura, M., 1983, The Neutral Theory of Molecular Evolution, Cambridge, Cambridge University
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• Krohs, U. & Kroes, P. (eds.) 2009, Functions in
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MA, Harvard University Press.
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Philosophy of Science, 72, p. 287-310.
• Lloyd, E., 2007, “Units and Levels of Selection”, in
Hull, D. & Ruse, M. (eds.), p. 44-65.
• Machamer, P., Darden, L., Craver, C., 2000,
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• Maynard-Smith, J., 1969, “The status of neoDarwinism”, in Waddington, C. H., ed. Towards a
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• Maynard-Smith, J., 1976, “Group Selection”,
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on Evolution and Optimality, Cambridge, MA, MIT
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• Mayr, E., 1963, Animal Species and Evolution,
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• Mayr, E., 1982, The Growth of Biological Thought,
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Stanford Encyclopedia of Philosophy
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3.3 Philosophy of mathematics
The philosophy of mathematics is the branch of
philosophy that studies the philosophical assumptions,
foundations, and implications of mathematics. The aim
of the philosophy of mathematics is to provide an account
of the nature and methodology of mathematics and to understand the place of mathematics in people’s lives. The
logical and structural nature of mathematics itself makes
this study both broad and unique among its philosophical
The terms philosophy of mathematics and mathematical
• West-Eberhard, M. J., 2003, Phenotypic Plasticity philosophy are frequently used as synonyms. The latter, however, may be used to refer to several other arand Evolution, Oxford, Oxford University Press.
eas of study. One refers to a project of formalizing
• Williams, G. C., 1966, Adaptation and Natural Se- a philosophical subject matter, say, aesthetics, ethics,
lection, Princeton, Princeton University Press.
logic, metaphysics, or theology, in a purportedly more
exact and rigorous form, as for example the labors of
scholastic theologians, or the systematic aims of Leibniz
and Spinoza. Another refers to the working philosophy
of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some
understand the term “mathematical philosophy” to be an
allusion to the approach to the foundations of mathematics taken by Bertrand Russell in his books The Principles
of Mathematics and Introduction to Mathematical Philosophy.
to critical analysis. There are traditions of mathematical
philosophy in both Western philosophy and Eastern philosophy. Western philosophies of mathematics go as far
back as Plato, who studied the ontological status of mathematical objects, and Aristotle, who studied logic and issues related to infinity (actual versus potential).
Greek philosophy on mathematics was strongly influenced by their study of geometry. For example, at one
time, the Greeks held the opinion that 1 (one) was not a
number, but rather a unit of arbitrary length. A number was defined as a multitude. Therefore, 3, for example, represented a certain multitude of units, and was
3.3.1 Recurrent themes
thus not “truly” a number. At another point, a similar
argument was made that 2 was not a number but a funRecurrent themes include:
damental notion of a pair. These views come from the
heavily geometric straight-edge-and-compass viewpoint
• What is the role of Mankind in developing matheof the Greeks: just as lines drawn in a geometric problem
are measured in proportion to the first arbitrarily drawn
• What are the sources of mathematical subject mat- line, so too are the numbers on a number line measured
in proportion to the arbitrary first “number” or “one”.
These earlier Greek ideas of numbers were later upended
• What is the ontological status of mathematical entiby the discovery of the irrationality of the square root
of two. Hippasus, a disciple of Pythagoras, showed that
• What does it mean to refer to a mathematical object? the diagonal of a unit square was incommensurable with
its (unit-length) edge: in other words he proved there
• What is the character of a mathematical proposi- was no existing (rational) number that accurately depicts
the proportion of the diagonal of the unit square to its
• What is the relation between logic and mathematics? edge. This caused a significant re-evaluation of Greek
philosophy of mathematics. According to legend, fellow
Pythagoreans were so traumatized by this discovery that
• What is the role of hermeneutics in mathematics?
they murdered Hippasus to stop him from spreading his
• What kinds of inquiry play a role in mathematics?
heretical idea. Simon Stevin was one of the first in Europe
to challenge Greek ideas in the 16th century. Beginning
• What are the objectives of mathematical inquiry?
with Leibniz, the focus shifted strongly to the relationship
• What gives mathematics its hold on experience?
between mathematics and logic. This perspective dominated the philosophy of mathematics through the time of
• What are the human traits behind mathematics?
Frege and of Russell, but was brought into question by
developments in the late 19th and early 20th centuries.
• What is mathematical beauty?
• What is the source and nature of mathematical
20th century
• What is the relationship between the abstract world A perennial issue in the philosophy of mathematics conof mathematics and the material universe?
cerns the relationship between logic and mathematics at
their joint foundations. While 20th century philosophers
continued to ask the questions mentioned at the outset of
3.3.2 History
this article, the philosophy of mathematics in the 20th
The origin of mathematics is subject to argument. century was characterized by a predominant interest in
Whether the birth of mathematics was a random happen- formal logic, set theory, and foundational issues.
ing or induced by necessity duly contingent upon other It is a profound puzzle that on the one hand mathematisubjects, say for example physics, is still a matter of pro- cal truths seem to have a compelling inevitability, but on
lific debates.
the other hand the source of their “truthfulness” remains
Many thinkers have contributed their ideas concerning elusive. Investigations into this issue are known as the
the nature of mathematics. Today, some philosophers of foundations of mathematics program.
mathematics aim to give accounts of this form of inquiry At the start of the 20th century, philosophers of
and its products as they stand, while others emphasize a mathematics were already beginning to divide into
role for themselves that goes beyond simple interpretation various schools of thought about all these questions,
broadly distinguished by their pictures of mathematical
epistemology and ontology. Three schools, formalism,
intuitionism, and logicism, emerged at this time, partly in
response to the increasingly widespread worry that mathematics as it stood, and analysis in particular, did not live
up to the standards of certainty and rigor that had been
taken for granted. Each school addressed the issues that
came to the fore at that time, either attempting to resolve
them or claiming that mathematics is not entitled to its
status as our most trusted knowledge.
Surprising and counter-intuitive developments in formal
logic and set theory early in the 20th century led to new
questions concerning what was traditionally called the
foundations of mathematics. As the century unfolded, the
initial focus of concern expanded to an open exploration
of the fundamental axioms of mathematics, the axiomatic
approach having been taken for granted since the time of
Euclid around 300 BCE as the natural basis for mathematics. Notions of axiom, proposition and proof, as well
as the notion of a proposition being true of a mathematical object (see Assignment (mathematical logic)), were
formalized, allowing them to be treated mathematically.
The Zermelo–Fraenkel axioms for set theory were formulated which provided a conceptual framework in which
much mathematical discourse would be interpreted. In
mathematics, as in physics, new and unexpected ideas had
arisen and significant changes were coming. With Gödel
numbering, propositions could be interpreted as referring
to themselves or other propositions, enabling inquiry into
the consistency of mathematical theories. This reflective
critique in which the theory under review “becomes itself the object of a mathematical study” led Hilbert to
call such study metamathematics or proof theory.[2]
At the middle of the century, a new mathematical theory was created by Samuel Eilenberg and Saunders
Mac Lane, known as category theory, and it became a
new contender for the natural language of mathematical thinking.[3] As the 20th century progressed, however, philosophical opinions diverged as to just how wellfounded were the questions about foundations that were
raised at the century’s beginning. Hilary Putnam summed
up one common view of the situation in the last third of
the century by saying:
When philosophy discovers something
wrong with science, sometimes science has
to be changed—Russell’s paradox comes to
mind, as does Berkeley's attack on the actual
infinitesimal—but more often it is philosophy
that has to be changed. I do not think that the
difficulties that philosophy finds with classical
mathematics today are genuine difficulties; and
I think that the philosophical interpretations of
mathematics that we are being offered on every hand are wrong, and that “philosophical interpretation” is just what mathematics doesn't
Philosophy of mathematics today proceeds along several
different lines of inquiry, by philosophers of mathematics, logicians, and mathematicians, and there are many
schools of thought on the subject. The schools are addressed separately in the next section, and their assumptions explained.
3.3.3 Major themes
Mathematical realism
Mathematical realism, like realism in general, holds that
mathematical entities exist independently of the human
mind. Thus humans do not invent mathematics, but
rather discover it, and any other intelligent beings in the
universe would presumably do the same. In this point of
view, there is really one sort of mathematics that can be
discovered; triangles, for example, are real entities, not
the creations of the human mind.
Many working mathematicians have been mathematical
realists; they see themselves as discoverers of naturally
occurring objects. Examples include Paul Erdős and Kurt
Gödel. Gödel believed in an objective mathematical reality that could be perceived in a manner analogous to
sense perception. Certain principles (e.g., for any two
objects, there is a collection of objects consisting of precisely those two objects) could be directly seen to be true,
but the continuum hypothesis conjecture might prove undecidable just on the basis of such principles. Gödel suggested that quasi-empirical methodology could be used
to provide sufficient evidence to be able to reasonably assume such a conjecture.
Within realism, there are distinctions depending on what
sort of existence one takes mathematical entities to have,
and how we know about them. Major forms of mathematical realism include Platonism.
Mathematical anti-realism
Mathematical anti-realism generally holds that mathematical statements have truth-values, but that they do not
do so by corresponding to a special realm of immaterial
or non-empirical entities. Major forms of mathematical
anti-realism include Formalism and Fictionalism.
3.3.4 Contemporary schools of thought
Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because
such a view is seen to parallel Plato's Theory of Forms and
a “World of Ideas” (Greek: eidos (εἶδος)) described in
Plato’s allegory of the cave: the everyday world can only
imperfectly approximate an unchanging, ultimate reality. Both Plato’s cave and Platonism have meaningful, not
just superficial connections, because Plato’s ideas were
preceded and probably influenced by the hugely popular
Pythagoreans of ancient Greece, who believed that the
world was, quite literally, generated by numbers.
Translators of the works of Plato rebelled against practical versions of his culture’s practical mathematics. However, Plato himself and Greeks had copied 1,500 older
Egyptian fraction abstract unities, one being a hekat unity
scaled to (64/64) in the Akhmim Wooden Tablet, thereby
not getting lost in fractions.
Gödel’s Platonism postulates a special kind of mathematical intuition that lets us perceive mathematical objects
directly. (This view bears resemblances to many things
Husserl said about mathematics, and supports Kant's idea
that mathematics is synthetic a priori.) Davis and Hersh
have suggested in their book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position
carefully, they may retreat to formalism (see below).
A major question considered in mathematical Platonism
is this: precisely where and how do the mathematical entities exist, and how do we know about them? Is there a
world, completely separate from our physical one, that is
occupied by the mathematical entities? How can we gain
access to this separate world and discover truths about
the entities? One answer might be the Ultimate Ensemble, which is a theory that postulates all structures that ex- Some mathematicians hold opinions that amount to more
ist mathematically also exist physically in their own uni- nuanced versions of Platonism.
Full-blooded Platonism is a modern variation of PlaPlato spoke of mathematics by:
tonism, which is in reaction to the fact that different sets
of mathematical entities can be proven to exist depending
How do you mean?
on the axioms and inference rules employed (for instance,
I mean, as I was saying, that arithmetic has
the law of the excluded middle, and the axiom of choice).
a very great and elevating effect, compelling
It holds that all mathematical entities exist, however they
the soul to reason about abstract number, and
may be provable, even if they cannot all be derived from
rebelling against the introduction of visible or
a single consistent set of axioms.
tangible objects into the argument. You know
how steadily the masters of the art repel and
ridicule any one who attempts to divide absolute unity when he is calculating, and if you diEmpiricism is a form of realism that denies that mathevide, they multiply, taking care that one shall
matics can be known a priori at all. It says that we discontinue one and not become lost in fractions.
cover mathematical facts by empirical research, just like
That is very true.
facts in any of the other sciences. It is not one of the clasNow, suppose a person were to say to them:
sical three positions advocated in the early 20th century,
O my friends, what are these wonderful numbut primarily arose in the middle of the century. Howbers about which you are reasoning, in which,
ever, an important early proponent of a view like this was
as you say, there is a unity such as you demand,
John Stuart Mill. Mill’s view was widely criticized, beand each unit is equal, invariable, indivisible, cause, according to critics, such as A.J. Ayer,[5] it makes
-what would they answer?
statements like “2 + 2 = 4” come out as uncertain, con— Plato, Chapter 7. “The Republic”
tingent truths, which we can only learn by observing in(Jowett translation).
stances of two pairs coming together and forming a quartet.
In context, chapter 8, of H.D.P. Lee’s translation, reports Contemporary mathematical empiricism, formulated by
the education of a philosopher contains five mathematical Quine and Putnam, is primarily supported by the
indispensability argument: mathematics is indispensable
to all empirical sciences, and if we want to believe in the
reality of the phenomena described by the sciences, we
1. mathematics;
ought also believe in the reality of those entities required
2. arithmetic, written in unit fraction “parts” using the- for this description. That is, since physics needs to talk
oretical unities and abstract numbers;
about electrons to say why light bulbs behave as they do,
then electrons must exist. Since physics needs to talk
3. plane geometry and solid geometry also considered about numbers in offering any of its explanations, then
the line to be segmented into rational and irrational numbers must exist. In keeping with Quine and Putnam’s
unit “parts";
overall philosophies, this is a naturalistic argument. It argues for the existence of mathematical entities as the best
4. astronomy
explanation for experience, thus stripping mathematics of
5. harmonics
being distinct from the other sciences.
Putnam strongly rejected the term "Platonist" as implylogical concepts through explicit definitions.
ing an over-specific ontology that was not necessary to
2. The theorems of mathematics can be derived from
mathematical practice in any real sense. He advocated
logical axioms through purely logical deduction.
a form of “pure realism” that rejected mystical notions
of truth and accepted much quasi-empiricism in mathematics. Putnam was involved in coining the term “pure Gottlob Frege was the founder of logicism. In his seminal Die Grundgesetze der Arithmetik (Basic Laws of Arithrealism” (see below).
metic) he built up arithmetic from a system of logic with
The most important criticism of empirical views of math- a general principle of comprehension, which he called
ematics is approximately the same as that raised against “Basic Law V” (for concepts F and G, the extension of
Mill. If mathematics is just as empirical as the other sci- F equals the extension of G if and only if for all objects
ences, then this suggests that its results are just as falli- a, Fa if and only if Ga), a principle that he took to be
ble as theirs, and just as contingent. In Mill’s case the acceptable as part of logic.
empirical justification comes directly, while in Quine’s
case it comes indirectly, through the coherence of our sci- Frege’s construction was flawed. Russell discovered that
entific theory as a whole, i.e. consilience after E.O. Wil- Basic Law V is inconsistent (this is Russell’s paradox).
son. Quine suggests that mathematics seems completely Frege abandoned his logicist program soon after this, but
certain because the role it plays in our web of belief is in- it was continued by Russell and Whitehead. They atcredibly central, and that it would be extremely difficult tributed the paradox to “vicious circularity” and built up
what they called ramified type theory to deal with it. In
for us to revise it, though not impossible.
this system, they were eventually able to build up much
For a philosophy of mathematics that attempts to over- of modern mathematics but in an altered, and excessively
come some of the shortcomings of Quine and Gödel’s ap- complex form (for example, there were different natuproaches by taking aspects of each see Penelope Maddy's ral numbers in each type, and there were infinitely many
Realism in Mathematics. Another example of a realist types). They also had to make several compromises in
theory is the embodied mind theory (below). For a mod- order to develop so much of mathematics, such as an
ern revision of mathematical empiricism see New Em- "axiom of reducibility". Even Russell said that this axpiricism (below).
iom did not really belong to logic.
For experimental evidence suggesting that human infants Modern logicists (like Bob Hale, Crispin Wright, and percan do elementary arithmetic, see Brian Butterworth.
haps others) have returned to a program closer to Frege’s.
Mathematical monism
Max Tegmark's mathematical universe hypothesis goes
further than full-blooded Platonism in asserting that not
only do all mathematical objects exist, but nothing else
does. Tegmark’s sole postulate is: All structures that exist mathematically also exist physically. That is, in the
sense that “in those [worlds] complex enough to contain
self-aware substructures [they] will subjectively perceive
themselves as existing in a physically 'real' world”.[6][7]
Logicism is the thesis that mathematics is reducible to
logic, and hence nothing but a part of logic.[8]:41 Logicists hold that mathematics can be known a priori, but
suggest that our knowledge of mathematics is just part of
our knowledge of logic in general, and is thus analytic, not
requiring any special faculty of mathematical intuition.
In this view, logic is the proper foundation of mathematics, and all mathematical statements are necessary logical
They have abandoned Basic Law V in favor of abstraction principles such as Hume’s principle (the number of
objects falling under the concept F equals the number of
objects falling under the concept G if and only if the extension of F and the extension of G can be put into oneto-one correspondence). Frege required Basic Law V to
be able to give an explicit definition of the numbers, but
all the properties of numbers can be derived from Hume’s
principle. This would not have been enough for Frege because (to paraphrase him) it does not exclude the possibility that the number 3 is in fact Julius Caesar. In addition, many of the weakened principles that they have
had to adopt to replace Basic Law V no longer seem so
obviously analytic, and thus purely logical.
Main article: Formalism (mathematics)
Formalism holds that mathematical statements may be
thought of as statements about the consequences of certain string manipulation rules. For example, in the
“game” of Euclidean geometry (which is seen as consisting of some strings called “axioms”, and some “rules of
Rudolf Carnap (1931) presents the logicist thesis in two inference” to generate new strings from given ones), one
can prove that the Pythagorean theorem holds (that is, one
can generate the string corresponding to the Pythagorean
1. The concepts of mathematics can be derived from theorem). According to formalism, mathematical truths
are not about numbers and sets and triangles and the orems, which states that sufficiently expressive consislike—in fact, they are not “about” anything at all.
tent axiom systems can never prove their own consistency.
Another version of formalism is often known as Since any such axiom system would contain the finitary
deductivism. In deductivism, the Pythagorean theorem arithmetic as a subsystem, Gödel’s theorem implied that it
is not an absolute truth, but a relative one: if one as- would be impossible to prove the system’s consistency relsigns meaning to the strings in such a way that the rules ative to that (since it would then prove its own consistency,
of the game become true (i.e., true statements are as- which Gödel had shown was impossible). Thus, in order
signed to the axioms and the rules of inference are truth- to show that any axiomatic system of mathematics is in
fact consistent, one needs to first assume the consistency
preserving), then one must accept the theorem, or, rather,
the interpretation one has given it must be a true state- of a system of mathematics that is in a sense stronger than
the system to be proven consistent.
ment. The same is held to be true for all other mathematical statements. Thus, formalism need not mean that Hilbert was initially a deductivist, but, as may be clear
mathematics is nothing more than a meaningless sym- from above, he considered certain metamathematical
bolic game. It is usually hoped that there exists some methods to yield intrinsically meaningful results and was
interpretation in which the rules of the game hold. (Com- a realist with respect to the finitary arithmetic. Later, he
pare this position to structuralism.) But it does allow the held the opinion that there was no other meaningful mathworking mathematician to continue in his or her work and ematics whatsoever, regardless of interpretation.
leave such problems to the philosopher or scientist. Many Other formalists, such as Rudolf Carnap, Alfred Tarski,
formalists would say that in practice, the axiom systems and Haskell Curry, considered mathematics to be the into be studied will be suggested by the demands of science vestigation of formal axiom systems. Mathematical logior other areas of mathematics.
cians study formal systems but are just as often realists as
they are formalists.
Formalists are relatively tolerant and inviting to new approaches to logic, non-standard number systems, new set
theories etc. The more games we study, the better. However, in all three of these examples, motivation is drawn
from existing mathematical or philosophical concerns.
The “games” are usually not arbitrary.
The main critique of formalism is that the actual mathematical ideas that occupy mathematicians are far removed from the string manipulation games mentioned
above. Formalism is thus silent on the question of which
axiom systems ought to be studied, as none is more meaningful than another from a formalistic point of view.
David Hilbert
A major early proponent of formalism was David Hilbert,
whose program was intended to be a complete and
consistent axiomatization of all of mathematics. Hilbert
aimed to show the consistency of mathematical systems
from the assumption that the “finitary arithmetic” (a subsystem of the usual arithmetic of the positive integers,
chosen to be philosophically uncontroversial) was consistent. Hilbert’s goals of creating a system of mathematics
that is both complete and consistent were seriously undermined by the second of Gödel’s incompleteness the-
Recently, some formalist mathematicians have proposed
that all of our formal mathematical knowledge should be
systematically encoded in computer-readable formats, so
as to facilitate automated proof checking of mathematical proofs and the use of interactive theorem proving
in the development of mathematical theories and computer software. Because of their close connection with
computer science, this idea is also advocated by mathematical intuitionists and constructivists in the “computability” tradition (see below). See QED project for
a general overview.
The French mathematician Henri Poincaré was among
the first to articulate a conventionalist view. Poincaré's
use of non-Euclidean geometries in his work on differential equations convinced him that Euclidean geometry
should not be regarded as a priori truth. He held that
axioms in geometry should be chosen for the results they
produce, not for their apparent coherence with human in-
tuitions about the physical world.
claim that only questions regarding the behavior of finite
algorithms are meaningful and should be investigated in
mathematics. This has led to the study of the computable
numbers, first introduced by Alan Turing. Not surprisingly, then, this approach to mathematics is sometimes
Psychologism in the philosophy of mathematics is the associated with theoretical computer science.
position that mathematical concepts and/or truths are
grounded in, derived from or explained by psychological
Constructivism Main article: Mathematical construcfacts (or laws).
John Stuart Mill seems to have been an advocate of a type
of logical psychologism, as were many 19th-century German logicians such as Sigwart and Erdmann as well as a Like intuitionism, constructivism involves the regulative
number of psychologists, past and present: for example, principle that only mathematical entities which can be
Gustave Le Bon. Psychologism was famously criticized explicitly constructed in a certain sense should be adby Frege in his The Foundations of Arithmetic, and many mitted to mathematical discourse. In this view, matheof his works and essays, including his review of Husserl's matics is an exercise of the human intuition, not a game
Philosophy of Arithmetic. Edmund Husserl, in the first played with meaningless symbols. Instead, it is about envolume of his Logical Investigations, called “The Pro- tities that we can create directly through mental activity.
legomena of Pure Logic”, criticized psychologism thor- In addition, some adherents of these schools reject nonoughly and sought to distance himself from it. The “Pro- constructive proofs, such as a proof by contradiction.
legomena” is considered a more concise, fair, and thorough refutation of psychologism than the criticisms made Finitism Finitism is an extreme form of
by Frege, and also it is considered today by many as be- constructivism, according to which a mathematical
ing a memorable refutation for its decisive blow to psy- object does not exist unless it can be constructed from
chologism. Psychologism was also criticized by Charles natural numbers in a finite number of steps. In her book
Sanders Peirce and Maurice Merleau-Ponty.
Philosophy of Set Theory, Mary Tiles characterized those
Main article: Mathematical intuitionism
In mathematics, intuitionism is a program of methodological reform whose motto is that “there are no
non-experienced mathematical truths” (L.E.J. Brouwer).
From this springboard, intuitionists seek to reconstruct
what they consider to be the corrigible portion of mathematics in accordance with Kantian concepts of being, becoming, intuition, and knowledge. Brouwer, the founder
of the movement, held that mathematical objects arise
from the a priori forms of the volitions that inform the
perception of empirical objects.[9]
A major force behind intuitionism was L.E.J. Brouwer,
who rejected the usefulness of formalized logic of any
sort for mathematics. His student Arend Heyting postulated an intuitionistic logic, different from the classical
Aristotelian logic; this logic does not contain the law of
the excluded middle and therefore frowns upon proofs by
contradiction. The axiom of choice is also rejected in
most intuitionistic set theories, though in some versions
it is accepted. Important work was later done by Errett
Bishop, who managed to prove versions of the most important theorems in real analysis within this framework.
who allow countably infinite objects as classical finitists,
and those who deny even countably infinite objects as
strict finitists.
The most famous proponent of finitism was Leopold Kronecker,[10] who said:
God created the natural numbers, all else is
the work of man.
Ultrafinitism is an even more extreme version of
finitism, which rejects not only infinities but finite quantities that cannot feasibly be constructed with available
Main article: Mathematical structuralism
Structuralism is a position holding that mathematical theories describe structures, and that mathematical objects
are exhaustively defined by their places in such structures,
consequently having no intrinsic properties. For instance,
it would maintain that all that needs to be known about
the number 1 is that it is the first whole number after 0.
Likewise all the other whole numbers are defined by their
places in a structure, the number line. Other examples of
In intuitionism, the term “explicit construction” is not mathematical objects might include lines and planes in
cleanly defined, and that has led to criticisms. Attempts geometry, or elements and operations in abstract algebra.
have been made to use the concepts of Turing machine Structuralism is an epistemologically realistic view in that
or computable function to fill this gap, leading to the it holds that mathematical statements have an objective
truth value. However, its central claim only relates to
what kind of entity a mathematical object is, not to what
kind of existence mathematical objects or structures have
(not, in other words, to their ontology). The kind of existence mathematical objects have would clearly be dependent on that of the structures in which they are embedded; different sub-varieties of structuralism make different ontological claims in this regard.[11]
The Ante Rem, or fully realist, variation of structuralism
has a similar ontology to Platonism in that structures are
held to have a real but abstract and immaterial existence.
As such, it faces the usual problems of explaining the interaction between such abstract structures and flesh-andblood mathematicians.
In Re, or moderately realistic, structuralism is the equivalent of Aristotelian realism. Structures are held to exist inasmuch as some concrete system exemplifies them.
This incurs the usual issues that some perfectly legitimate
structures might accidentally happen not to exist, and that
a finite physical world might not be “big” enough to accommodate some otherwise legitimate structures.
matician Keith Devlin has investigated similar concepts
with his book The Math Instinct, as has neuroscientist
Stanislas Dehaene with his book The Number Sense. For
more on the philosophical ideas that inspired this perspective, see cognitive science of mathematics.
New empiricism A more recent empiricism returns to
the principle of the English empiricists of the 18th and
19th centuries, in particular John Stuart Mill, who asserted that all knowledge comes to us from observation
through the senses. This applies not only to matters of
fact, but also to “relations of ideas”, as Hume called them:
the structures of logic which interpret, organize and abstract observations.
To this principle it adds a materialist connection: all the
processes of logic which interpret, organize and abstract
observations, are physical phenomena which take place
in real time and physical space: namely, in the brains of
human beings. Abstract objects, such as mathematical
objects, are ideas, which in turn exist as electrical and
chemical states of the billions of neurons in the human
The Post Res or eliminative variant of structuralism brain.
is anti-realist about structures in a way that parallels
This second concept is reminiscent of the social construcnominalism. According to this view mathematical systivist approach, which holds that mathematics is produced
tems exist, and have structural features in common. If
by humans rather than being “discovered” from abstract,
something is true of a structure, it will be true of all sysa priori truths. However, it differs sharply from the contems exemplifying the structure. However, it is merely
structivist implication that humans arbitrarily construct
convenient to talk of structures being “held in common”
mathematical principles that have no inherent truth but
between systems: they in fact have no independent exiswhich instead are created on a conveniency basis. On
the contrary, new empiricism shows how mathematics,
although constructed by humans, follows rules and principles that will be agreed on by all who participate in the
Embodied mind theories
process, with the result that everyone practicing mathematics comes up with the same answer—except in those
Embodied mind theories hold that mathematical thought areas where there is philosophical disagreement on the
is a natural outgrowth of the human cognitive apparatus meaning of fundamental concepts. This is because the
which finds itself in our physical universe. For example, new empiricism perceives this agreement as being a physthe abstract concept of number springs from the experi- ical phenomenon, one which is observed by other humans
ence of counting discrete objects. It is held that mathe- in the same way that other physical phenomena, like the
matics is not universal and does not exist in any real sense, motions of inanimate bodies, or the chemical interaction
other than in human brains. Humans construct, but do not of various elements, are observed.
discover, mathematics.
Combining the materialist principle with Millisian episWith this view, the physical universe can thus be seen temology evades the principal difficulty with classical
as the ultimate foundation of mathematics: it guided the empiricism—that all knowledge comes from the senses.
evolution of the brain and later determined which ques- That difficulty lies in the observation that mathematical
tions this brain would find worthy of investigation. How- truths based on logical deduction appear to be more cerever, the human mind has no special claim on reality or tainly true than knowledge of the physical world itself.
approaches to it built out of math. If such constructs as (The physical world in this case is taken to mean the porEuler’s identity are true then they are true as a map of the tion of it lying outside the human brain.)
human mind and cognition.
Kant argued that the structures of logic which organize,
Embodied mind theorists thus explain the effectiveness of interpret and abstract observations were built into the humathematics—mathematics was constructed by the brain man mind and were true and valid a priori. Mill, on the
in order to be effective in this universe.
contrary, said that we believe them to be true because we
The most accessible, famous, and infamous treatment of have enough individual instances of their truth to generalthis perspective is Where Mathematics Comes From, by ize: in his words, “From instances we have observed, we
George Lakoff and Rafael E. Núñez. In addition, mathe- feel warranted in concluding that what we found true in
those instances holds in all similar ones, past, present and
future, however numerous they may be”.[12] Although the
psychological or epistemological specifics given by Mill
through which we build our logical apparatus may not
be completely warranted, his explanation still nonetheless manages to demonstrate that there is no way around
Kant’s a priori logic. To recant Mill’s original idea in an
empiricist twist: “Indeed, the very principles of logical
deduction are true because we observe that using them
leads to true conclusions”, which is itself an a priori presupposition.
If all this is true, then where do the world senses come
in? The early empiricists all stumbled over this point.
Hume asserted that all knowledge comes from the senses,
and then gave away the ballgame by excepting abstract
propositions, which he called “relations of ideas”. These,
he said, were absolutely true (although the mathematicians who thought them up, being human, might get them
wrong). Mill, on the other hand, tried to deny that abstract ideas exist outside the physical world: all numbers,
he said, “must be numbers of something: there are no
such things as numbers in the abstract”. When we count
to eight or add five and three we are really counting spoons
or bumblebees. “All things possess quantity”, he said,
so that propositions concerning numbers are propositions
concerning “all things whatever”. But then in almost a
contradiction of himself he went on to acknowledge that
numerical and algebraic expressions are not necessarily
attached to real world objects: they “do not excite in our
minds ideas of any things in particular”. Mill’s low reputation as a philosopher of logic, and the low estate of
empiricism in the century and a half following him, derives from this failed attempt to link abstract thoughts to
the physical world, when it may be more plausibly arguable that abstraction consists precisely of separating the
thought from its physical foundations.
The conundrum created by our certainty that abstract
deductive propositions, if valid (i.e. if we can “prove”
them), are true, exclusive of observation and testing in the
physical world, gives rise to a further reflection ... What
if thoughts themselves, and the minds that create them,
are physical objects, existing only in the physical world?
This would reconcile the contradiction between our belief in the certainty of abstract deductions and the empiricist principle that knowledge comes from observation
of individual instances. We know that Euler’s equation is
true because every time a human mind derives the equation, it gets the same result, unless it has made a mistake, which can be acknowledged and corrected. We observe this phenomenon, and we extrapolate to the general
proposition that it is always true.
Aristotelian realism Main article: Aristotle’s theory
of universals
Similar to empiricism in emphasizing the relation of
mathematics to the real world, Aristotelian realism holds
that mathematics studies properties such as symmetry,
continuity and order that can be literally realized in the
physical world (or in any other world there might be). It
contrasts with Platonism in holding that the objects of
mathematics, such as numbers, do not exist in an “abstract” world but can be physically realized. For example,
the number 4 is realized in the relation between a heap
of parrots and the universal “being a parrot” that divides
the heap into so many parrots.[13] Aristotelian realism is
defended by James Franklin and the Sydney School in
the philosophy of mathematics and is close to the view
of Penelope Maddy that when an egg carton is opened,
a set of three eggs is perceived (that is, a mathematical
entity realized in the physical world).[14] A problem for
Aristotelian realism is what account to give of higher infinities, which may not be realizable in the physical world.
Fictionalism in mathematics was brought to fame in 1980
when Hartry Field published Science Without Numbers,
which rejected and in fact reversed Quine’s indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and
therefore should be accepted as a body of truths talking
about independently existing entities, Field suggested that
mathematics was dispensable, and therefore should be
considered as a body of falsehoods not talking about anything real. He did this by giving a complete axiomatization of Newtonian mechanics with no reference to numbers or functions at all. He started with the “betweenness”
of Hilbert’s axioms to characterize space without coordinatizing it, and then added extra relations between points
to do the work formerly done by vector fields. Hilbert’s
geometry is mathematical, because it talks about abstract
points, but in Field’s theory, these points are the concrete
points of physical space, so no special mathematical objects at all are needed.
Having shown how to do science without using numbers,
Field proceeded to rehabilitate mathematics as a kind of
useful fiction. He showed that mathematical physics is a
conservative extension of his non-mathematical physics
(that is, every physical fact provable in mathematical
physics is already provable from Field’s system), so that
mathematics is a reliable process whose physical applicaThis applies not only to physical principles, like the law of tions are all true, even though its own statements are false.
gravity, but to abstract phenomena that we observe only Thus, when doing mathematics, we can see ourselves as
telling a sort of story, talking as if numbers existed. For
in human brains: in ours and in those of others.
Field, a statement like “2 + 2 = 4” is just as fictitious as
"Sherlock Holmes lived at 221B Baker Street”—but both
are true according to the relevant fictions.
By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical
physics, and about fiction in general. Field’s approach
has been very influential, but is widely rejected. This is
in part because of the requirement of strong fragments
of second-order logic to carry out his reduction, and because the statement of conservativity seems to require
quantification over abstract models or deductions.
Social constructivism or social realism
Social constructivism or social realism theories see mathematics primarily as a social construct, as a product of
culture, subject to correction and change. Like the other
sciences, mathematics is viewed as an empirical endeavor
whose results are constantly evaluated and may be discarded. However, while on an empiricist view the evaluation is some sort of comparison with “reality”, social
constructivists emphasize that the direction of mathematical research is dictated by the fashions of the social group
performing it or by the needs of the society financing it.
However, although such external forces may change the
direction of some mathematical research, there are strong
internal constraints—the mathematical traditions, methods, problems, meanings and values into which mathematicians are enculturated—that work to conserve the
historically defined discipline.
This runs counter to the traditional beliefs of working
mathematicians, that mathematics is somehow pure or
objective. But social constructivists argue that mathematics is in fact grounded by much uncertainty: as
mathematical practice evolves, the status of previous
mathematics is cast into doubt, and is corrected to the degree it is required or desired by the current mathematical
community. This can be seen in the development of analysis from reexamination of the calculus of Leibniz and
Newton. They argue further that finished mathematics is
often accorded too much status, and folk mathematics not
enough, due to an overemphasis on axiomatic proof and
peer review as practices. However, this might be seen as
merely saying that rigorously proven results are overemphasized, and then “look how chaotic and uncertain the
rest of it all is!"
The social nature of mathematics is highlighted in its
subcultures. Major discoveries can be made in one
branch of mathematics and be relevant to another, yet
the relationship goes undiscovered for lack of social contact between mathematicians. Social constructivists argue each speciality forms its own epistemic community
and often has great difficulty communicating, or motivating the investigation of unifying conjectures that might
relate different areas of mathematics. Social constructivists see the process of “doing mathematics” as actually creating the meaning, while social realists see a deficiency either of human capacity to abstractify, or of
human’s cognitive bias, or of mathematicians’ collective
intelligence as preventing the comprehension of a real
universe of mathematical objects. Social constructivists
sometimes reject the search for foundations of mathematics as bound to fail, as pointless or even meaningless.
Contributions to this school have been made by Imre
Lakatos and Thomas Tymoczko, although it is not clear
that either would endorse the title. More recently Paul
Ernest has explicitly formulated a social constructivist
philosophy of mathematics.[15] Some consider the work
of Paul Erdős as a whole to have advanced this view (although he personally rejected it) because of his uniquely
broad collaborations, which prompted others to see and
study “mathematics as a social activity”, e.g., via the
Erdős number. Reuben Hersh has also promoted the
social view of mathematics, calling it a “humanistic”
approach,[16] similar to but not quite the same as that associated with Alvin White;[17] one of Hersh’s co-authors,
Philip J. Davis, has expressed sympathy for the social
view as well.
A criticism of this approach is that it is trivial, based on
the trivial observation that mathematics is a human activity. To observe that rigorous proof comes only after unrigorous conjecture, experimentation and speculation is
true, but it is trivial and no-one would deny this. So it’s a
bit of a stretch to characterize a philosophy of mathematics in this way, on something trivially true. The calculus
of Leibniz and Newton was reexamined by mathematicians such as Weierstrass in order to rigorously prove the
theorems thereof. There is nothing special or interesting about this, as it fits in with the more general trend of
unrigorous ideas which are later made rigorous. There
needs to be a clear distinction between the objects of
study of mathematics and the study of the objects of study
of mathematics. The former doesn't seem to change a
great deal; the latter is forever in flux. The latter is what
the social theory is about, and the former is what Platonism et al. are about.
However, this criticism is rejected by supporters of the
social constructivist perspective because it misses the
point that the very objects of mathematics are social constructs. These objects, it asserts, are primarily semiotic
objects existing in the sphere of human culture, sustained
by social practices (after Wittgenstein) that utilize physically embodied signs and give rise to intrapersonal (mental) constructs. Social constructivists view the reification
of the sphere of human culture into a Platonic realm, or
some other heaven-like domain of existence beyond the
physical world, a long-standing category error.
Beyond the traditional schools
Rather than focus on narrow debates about the true nature of mathematical truth, or even on practices unique to
mathematicians such as the proof, a growing movement
from the 1960s to the 1990s began to question the idea
of seeking foundations or finding any one right answer to
why mathematics works. The starting point for this was
Eugene Wigner's famous 1960 paper The Unreasonable
Effectiveness of Mathematics in the Natural Sciences, in
which he argued that the happy coincidence of mathematics and physics being so well matched seemed to be
unreasonable and hard to explain.
The embodied-mind or cognitive school and the social
school were responses to this challenge, but the debates
raised were difficult to confine to those.
Innovations in the philosophy of language during the 20th
century renewed interest in whether mathematics is, as
is often said, the language of science. Although some
mathematicians and philosophers would accept the statement "mathematics is a language", linguists believe that
the implications of such a statement must be considered.
For example, the tools of linguistics are not generally applied to the symbol systems of mathematics, that is, mathematics is studied in a markedly different way than other
languages. If mathematics is a language, it is a different type of language than natural languages. Indeed, because of the need for clarity and specificity, the language
of mathematics is far more constrained than natural languages studied by linguists. However, the methods developed by Frege and Tarski for the study of mathematical
language have been extended greatly by Tarski’s student
Richard Montague and other linguists working in formal
semantics to show that the distinction between mathematical language and natural language may not be as great as
it seems.
Quasi-empiricism One parallel concern that does not
actually challenge the schools directly but instead questions their focus is the notion of quasi-empiricism in
mathematics. This grew from the increasingly popular
assertion in the late 20th century that no one foundation
of mathematics could be ever proven to exist. It is also
sometimes called “postmodernism in mathematics” although that term is considered overloaded by some and
insulting by others. Quasi-empiricism argues that in doing their research, mathematicians test hypotheses as well
as prove theorems. A mathematical argument can transmit falsity from the conclusion to the premises just as well 3.3.5 Arguments
as it can transmit truth from the premises to the conclusion. Quasi-empiricism was developed by Imre Lakatos, Indispensability argument for realism
inspired by the philosophy of science of Karl Popper.
This argument, associated with Willard Quine and Hilary
Lakatos’ philosophy of mathematics is sometimes re- Putnam, is considered by Stephen Yablo to be one of the
garded as a kind of social constructivism, but this was most challenging arguments in favor of the acceptance
not his intention.
of the existence of abstract mathematical entities, such
The form of the argument is as
Such methods have always been part of folk mathematics as numbers and sets.
by which great feats of calculation and measurement are follows.
sometimes achieved. Indeed, such methods may be the
only notion of proof a culture has.
1. One must have ontological commitments to all entities that are indispensable to the best scientific theHilary Putnam has argued that any theory of matheories, and to those entities only (commonly referred
matical realism would include quasi-empirical methods.
to as “all and only”).
He proposed that an alien species doing mathematics
might well rely on quasi-empirical methods primarily, be2. Mathematical entities are indispensable to the best
ing willing often to forgo rigorous and axiomatic proofs,
scientific theories. Therefore,
and still be doing mathematics—at perhaps a somewhat
greater risk of failure of their calculations. He gave a de3. One must have ontological commitments to mathetailed argument for this in New Directions.[18]
matical entities.[22]
Popper’s “two senses” theory Realist and constructivist theories are normally taken to be contraries. However, Karl Popper[19] argued that a number statement
such as “2 apples + 2 apples = 4 apples” can be taken
in two senses. In one sense it is irrefutable and logically
true. In the second sense it is factually true and falsifiable. Another way of putting this is to say that a single
number statement can express two propositions: one of
which can be explained on constructivist lines; the other
on realist lines.[20]
Language Main article: Philosophy of language
The justification for the first premise is the most controversial. Both Putnam and Quine invoke naturalism to justify the exclusion of all non-scientific entities, and hence
to defend the “only” part of “all and only”. The assertion
that “all” entities postulated in scientific theories, including numbers, should be accepted as real is justified by
confirmation holism. Since theories are not confirmed in
a piecemeal fashion, but as a whole, there is no justification for excluding any of the entities referred to in wellconfirmed theories. This puts the nominalist who wishes
to exclude the existence of sets and non-Euclidean geometry, but to include the existence of quarks and other
undetectable entities of physics, for example, in a difficult
Epistemic argument against realism
lar sense of exhilaration at understanding as the original
author of the proof, much as, he argues, the viewer of
The anti-realist "epistemic argument” against Platonism a masterpiece has a sense of exhilaration similar to the
has been made by Paul Benacerraf and Hartry Field. Pla- original painter or sculptor. Indeed, one can study mathtonism posits that mathematical objects are abstract enti- ematical and scientific writings as literature.
ties. By general agreement, abstract entities cannot inter- Philip J. Davis and Reuben Hersh have commented that
act causally with concrete, physical entities. (“the truth- the sense of mathematical beauty is universal amongst
values of our mathematical assertions depend on facts in- practicing mathematicians. By way of example, they provolving Platonic entities that reside in a realm outside of vide two proofs of the irrationality of √2. The first is the
space-time”[23] ) Whilst our knowledge of concrete, phys- traditional proof by contradiction, ascribed to Euclid; the
ical objects is based on our ability to perceive them, and second is a more direct proof involving the fundamental
therefore to causally interact with them, there is no paral- theorem of arithmetic that, they argue, gets to the heart
lel account of how mathematicians come to have knowl- of the issue. Davis and Hersh argue that mathematicians
edge of abstract objects.[24][25][26] (“An account of math- find the second proof more aesthetically appealing beematical truth ... must be consistent with the possibility cause it gets closer to the nature of the problem.
of mathematical knowledge.”[27] ) Another way of making the point is that if the Platonic world were to disap- Paul Erdős was well known for his notion of a hypothetipear, it would make no difference to the ability of math- cal “Book” containing the most elegant or beautiful mathematicians to generate proofs, etc., which is already fully ematical proofs. There is not universal agreement that a
accountable in terms of physical processes in their brains. result has one “most elegant” proof; Gregory Chaitin has
argued against this idea.
Field developed his views into fictionalism. Benacerraf also developed the philosophy of mathematical struc- Philosophers have sometimes criticized mathematicians’
turalism, according to which there are no mathematical sense of beauty or elegance as being, at best, vaguely
objects. Nonetheless, some versions of structuralism are stated. By the same token, however, philosophers of
mathematics have sought to characterize what makes one
compatible with some versions of realism.
proof more desirable than another when both are logically
The argument hinges on the idea that a satisfactory sound.
naturalistic account of thought processes in terms of brain
processes can be given for mathematical reasoning along Another aspect of aesthetics concerning mathematics is
with everything else. One line of defense is to main- mathematicians’ views towards the possible uses of mathtain that this is false, so that mathematical reasoning uses ematics for purposes deemed unethical or inapproprisome special intuition that involves contact with the Pla- ate. The best-known exposition of this view occurs in
tonic realm. A modern form of this argument is given by G.H. Hardy's book A Mathematician’s Apology, in which
Hardy argues that pure mathematics is superior in beauty
Sir Roger Penrose.[28]
to applied mathematics precisely because it cannot be
Another line of defense is to maintain that abstract ob- used for war and similar ends. Some later mathematijects are relevant to mathematical reasoning in a way that cians have characterized Hardy’s views as mildly dated,
is non-causal, and not analogous to perception. This ar- with the applicability of number theory to modern-day
gument is developed by Jerrold Katz in his book Realistic cryptography.
A more radical defense is denial of physical reality, i.e.
the mathematical universe hypothesis. In that case, a 3.3.7 See also
mathematician’s knowledge of mathematics is one mathRelated works
ematical object making contact with another.
Historical topics
• History and philosophy of science
Many practicing mathematicians have been drawn to their
• History of mathematics
subject because of a sense of beauty they perceive in it.
• History of philosophy
One sometimes hears the sentiment that mathematicians
would like to leave philosophy to the philosophers and
get back to mathematics—where, presumably, the beauty
3.3.8 Notes
In his work on the divine proportion, H.E. Huntley relates
the feeling of reading and understanding someone else’s
proof of a theorem of mathematics to that of a viewer of
a masterpiece of art—the reader of a proof has a simi-
[1] Maziars, Edward A. (1969). “Problems in the Philosophy of Mathematics (Book Review)". Philosophy of Science 36 (3): 325. doi:10.1086/288262.. For example,
when Edward Maziars proposes in a 1969 book review “to
distinguish philosophical mathematics (which is primarily
a specialised task for a mathematician) from mathematical philosophy (which ordinarily may be the philosopher’s
metier)", he uses the term mathematical philosophy as being synonymous with philosophy of mathematics.
[2] Kleene, Stephen (1971). Introduction to Metamathematics. Amsterdam, Netherlands: North-Holland Publishing
Company. p. 5.
[3] Mac Lane, Saunders (1998), Categories for the Working
Mathematician, 2nd edition, Springer-Verlag, New York,
• Putnam, Hilary (1967), “Mathematics Without
Foundations”, Journal of Philosophy 64/1, 5-22.
Reprinted, pp. 168–184 in W.D. Hart (ed., 1996).
[5] Ayer, Alfred Jules (1952). Language, Truth, & Logic.
New York: Dover Publications, Inc. p. 74 ff. ISBN 9780-486-20010-1.
[15] Ernest, Paul. “Is Mathematics Discovered or Invented?".
University of Exeter. Retrieved 2008-12-26.
[16] Hersh, Reuben (February 10, 1997). What Kind of a
Thing is a Number?. Interview with John Brockman.
Edge Foundation. Retrieved 2008-12-26.
[17] “Humanism and Mathematics Education”. Math Forum.
Humanistic Mathematics Network Journal. Retrieved
[18] Tymoczko, Thomas (1998), New Directions in the Philosophy of Mathematics. ISBN 978-0691034980.
[19] Popper, Karl Raimund (1946) Aristotelian Society Supplementary Volume XX.
[20] Gregory, Frank Hutson (1996) Arithmetic and Reality: A
Development of Popper’s Ideas. City University of Hong
Kong. Republished in Philosophy of Mathematics Education Journal No. 26 (December 2011)
[21] Yablo, S. (November 8, 1998). “A Paradox of Existence”.
[6] Tegmark, Max (February 2008). “The Mathematical Universe”. Foundations of Physics 38 (2): 101–
150. arXiv:0704.0646. Bibcode:2008FoPh...38..101T.
[22] Putnam, H. Mathematics, Matter and Method. Philosophical Papers, vol. 1. Cambridge: Cambridge University
Press, 1975. 2nd. ed., 1985.
[7] Tegmark (1998), p. 1.
[23] Field, Hartry, 1989, Realism, Mathematics, and Modality,
Oxford: Blackwell, p. 68
[8] Carnap, Rudolf (1931), “Die logizistische Grundlegung
der Mathematik”, Erkenntnis 2, 91-121. Republished,
“The Logicist Foundations of Mathematics”, E. Putnam
and G.J. Massey (trans.), in Benacerraf and Putnam
(1964). Reprinted, pp. 41–52 in Benacerraf and Putnam
[9] Audi, Robert (1999), The Cambridge Dictionary of Philosophy, Cambridge University Press, Cambridge, UK,
1995. 2nd edition. Page 542.
[10] From an 1886 lecture at the 'Berliner NaturforscherVersammlung', according to H. M. Weber's memorial
article, as quoted and translated in Gonzalez Cabillon,
Julio (2000-02-03). “FOM: What were Kronecker’s
f.o.m.?". Retrieved 2008-07-19. Gonzalez gives as the
sources for the memorial article, the following: 'Weber,
H: “Leopold Kronecker”, _Jahresberichte der Deutschen
Mathematiker Vereinigung_, vol ii (1893) pp 5-31. Cf
page 19. See also _Mathematische Annalen_ vol xliii
(1893) pp 1-25'.
[11] Brown, James (2008). Philosophy of Mathematics. New
York: Routledge. ISBN 978-0-415-96047-2.
[12] A System of Logic Ratiocinative and Inductive, The Collected Works of John Stuart Mill published by the University of Toronto Press in 1973. Book II, Chapter vi,
Section 2 (Toronto edition 1975, Vol.7, p. 254)
[13] Franklin, James (2014), "An Aristotelian Realist Philosophy of Mathematics", Palgrave Macmillan, Basingstoke;
Franklin, James (2011), "Aristotelianism in the philosophy of mathematics,” Studia Neoaristotelica 8, 3-15.
[14] Maddy, Penelope (1990), Realism in Mathematics, Oxford
University Press, Oxford, UK.
[24] “Since abstract objects are outside the nexus of causes and
effects, and thus perceptually inaccessible, they cannot be
known through their effects on us” Katz, J. Realistic Rationalism, p15
[25] ,Philosophy
Mathematical_Knowledge_A_Dilemma Mathematical Knowledge: A
[26] Standard Encyclopaedia of Philosophy
[27] Benacceraf, 1973, p409
[28] Review of The Emperor’s New Mind
3.3.9 Further reading
• Aristotle, "Prior Analytics", Hugh Tredennick
(trans.), pp. 181–531 in Aristotle, Volume 1, Loeb
Classical Library, William Heinemann, London,
UK, 1938.
• Benacerraf, Paul, and Putnam, Hilary (eds., 1983),
Philosophy of Mathematics, Selected Readings, 1st
edition, Prentice-Hall, Englewood Cliffs, NJ, 1964.
2nd edition, Cambridge University Press, Cambridge, UK, 1983.
• Berkeley, George (1734), The Analyst; or, a
Discourse Addressed to an Infidel Mathematician.
Wherein It is examined whether the Object, Principles, and Inferences of the modern Analysis are more
distinctly conceived, or more evidently deduced, than
Religious Mysteries and Points of Faith, London &
Dublin. Online text, David R. Wilkins (ed.), Eprint.
• Bourbaki, N. (1994), Elements of the History of
Mathematics, John Meldrum (trans.), SpringerVerlag, Berlin, Germany.
• Irvine, A., ed (2009), The Philosophy of Mathematics, in Handbook of the Philosophy of Science series,
North-Holland Elsevier, Amsterdam.
• Chandrasekhar, Subrahmanyan (1987), Truth and
Beauty. Aesthetics and Motivations in Science, University of Chicago Press, Chicago, IL.
• Klein, Jacob (1968), Greek Mathematical Thought
and the Origin of Algebra, Eva Brann (trans.), MIT
Press, Cambridge, MA, 1968. Reprinted, Dover
Publications, Mineola, NY, 1992.
• Colyvan, Mark (2004), “Indispensability Arguments in the Philosophy of Mathematics”, Stanford
Encyclopedia of Philosophy, Edward N. Zalta (ed.),
• Davis, Philip J. and Hersh, Reuben (1981), The
Mathematical Experience, Mariner Books, New
York, NY.
• Devlin, Keith (2005), The Math Instinct: Why You're
a Mathematical Genius (Along with Lobsters, Birds,
Cats, and Dogs), Thunder’s Mouth Press, New York,
• Dummett, Michael (1991 a), Frege, Philosophy of
Mathematics, Harvard University Press, Cambridge,
• Dummett, Michael (1991 b), Frege and Other
Philosophers, Oxford University Press, Oxford, UK.
• Kline, Morris (1959), Mathematics and the Physical
World, Thomas Y. Crowell Company, New York,
NY, 1959. Reprinted, Dover Publications, Mineola,
NY, 1981.
• Kline, Morris (1972), Mathematical Thought from
Ancient to Modern Times, Oxford University Press,
New York, NY.
• König, Julius (Gyula) (1905), "Über die Grundlagen der Mengenlehre und das Kontinuumproblem”,
Mathematische Annalen 61, 156-160. Reprinted,
“On the Foundations of Set Theory and the Continuum Problem”, Stefan Bauer-Mengelberg (trans.),
pp. 145–149 in Jean van Heijenoort (ed., 1967).
• Körner, Stephan, The Philosophy of Mathematics,
An Introduction. Harper Books, 1960.
• Dummett, Michael (1993), Origins of Analytical
Philosophy, Harvard University Press, Cambridge,
• Lakoff, George, and Núñez, Rafael E. (2000),
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, Basic
Books, New York, NY.
• Ernest, Paul (1998), Social Constructivism as a Philosophy of Mathematics, State University of New
York Press, Albany, NY.
• Lakatos, Imre 1976 Proofs and Refutations:The
Logic of Mathematical Discovery (Eds) J. Worrall &
E. Zahar Cambridge University Press
• George, Alexandre (ed., 1994), Mathematics and
Mind, Oxford University Press, Oxford, UK.
• Lakatos, Imre 1978 Mathematics, Science and Epistemology: Philosophical Papers Volume 2 (Eds)
J.Worrall & G.Currie Cambridge University Press
• Hadamard, Jacques (1949), The Psychology of
Invention in the Mathematical Field, 1st edition,
Princeton University Press, Princeton, NJ. 2nd edition, 1949. Reprinted, Dover Publications, New
York, NY, 1954.
• Hardy, G.H. (1940), A Mathematician’s Apology,
1st published, 1940. Reprinted, C.P. Snow (foreword), 1967. Reprinted, Cambridge University
Press, Cambridge, UK, 1992.
• Hart, W.D. (ed., 1996), The Philosophy of Mathematics, Oxford University Press, Oxford, UK.
• Hendricks, Vincent F. and Hannes Leitgeb (eds.).
Philosophy of Mathematics: 5 Questions, New York:
Automatic Press / VIP, 2006.
• Huntley, H.E. (1970), The Divine Proportion: A
Study in Mathematical Beauty, Dover Publications,
New York, NY.
• Lakatos, Imre 1968 Problems in the Philosophy of
Mathematics North Holland
• Leibniz, G.W., Logical Papers (1666–1690),
G.H.R. Parkinson (ed., trans.), Oxford University
Press, London, UK, 1966.
• Maddy, Penelope (1997), Naturalism in Mathematics, Oxford University Press, Oxford, UK.
• Maziarz, Edward A., and Greenwood, Thomas
(1995), Greek Mathematical Philosophy, Barnes and
Noble Books.
• Mount, Matthew, Classical Greek Mathematical Philosophy, .
• Parsons, Charles (2014). Philosophy of Mathematics in the Twentieth Century: Selected Essays. Cambridge, MA: Harvard University Press. ISBN 9780-674-72806-6.
• Peirce, Benjamin (1870), “Linear Associative Algebra”, § 1. See American Journal of Mathematics 4
• Peirce, C.S., Collected Papers of Charles Sanders
Peirce, vols. 1-6, Charles Hartshorne and Paul Weiss
(eds.), vols. 7-8, Arthur W. Burks (ed.), Harvard
University Press, Cambridge, MA, 1931 – 1935,
1958. Cited as CP (volume).(paragraph).
• Peirce, C.S., various pieces on mathematics and
logic, many readable online through links at the
Charles Sanders Peirce bibliography, especially under Books authored or edited by Peirce, published
in his lifetime and the two sections following it.
• Plato, “The Republic, Volume 1”, Paul Shorey
(trans.), pp. 1–535 in Plato, Volume 5, Loeb Classical Library, William Heinemann, London, UK,
• Plato, “The Republic, Volume 2”, Paul Shorey
(trans.), pp. 1–521 in Plato, Volume 6, Loeb Classical Library, William Heinemann, London, UK,
• Resnik, Michael D. Frege and the Philosophy of
Mathematics, Cornell University, 1980.
• Resnik, Michael (1997), Mathematics as a Science of
Patterns, Clarendon Press, Oxford, UK, ISBN 9780-19-825014-2
• Tait, William W. (1986), “Truth and Proof: The
Platonism of Mathematics”, Synthese 69 (1986),
341-370. Reprinted, pp. 142–167 in W.D. Hart
(ed., 1996).
• Tarski, A. (1983), Logic, Semantics, Metamathematics: Papers from 1923 to 1938, J.H. Woodger
(trans.), Oxford University Press, Oxford, UK,
1956. 2nd edition, John Corcoran (ed.), Hackett
Publishing, Indianapolis, IN, 1983.
• Ulam, S.M. (1990), Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and
His Los Alamos Collaborators, A.R. Bednarek and
Françoise Ulam (eds.), University of California
Press, Berkeley, CA.
• van Heijenoort, Jean (ed. 1967), From Frege To
Gödel: A Source Book in Mathematical Logic, 18791931, Harvard University Press, Cambridge, MA.
• Wigner, Eugene (1960), "The Unreasonable Effectiveness of Mathematics in the Natural Sciences",
Communications on Pure and Applied Mathematics
13(1): 1-14. Eprint
• Wilder, Raymond L. Mathematics as a Cultural System, Pergamon, 1980.
• Witzany, Guenther (2011), Can mathematics explain the evolution of human language?, Communicative and Integrative Biology, 4(5): 516-520.
• Robinson, Gilbert de B. (1959), The Foundations 3.3.10 External links
of Geometry, University of Toronto Press, Toronto,
Canada, 1940, 1946, 1952, 4th edition 1959.
• Philosophy of mathematics at PhilPapers
• Raymond, Eric S. (1993), “The Utility of Mathematics”, Eprint.
• Philosophy of mathematics at the Indiana Philosophy Ontology Project
• Smullyan, Raymond M. (1993), Recursion Theory
for Metamathematics, Oxford University Press, Oxford, UK.
• Philosophy of Mathematics entry by Leon Horsten
in the Stanford Encyclopedia of Philosophy
• Russell, Bertrand (1919), Introduction to Mathematical Philosophy, George Allen and Unwin, London,
UK. Reprinted, John G. Slater (intro.), Routledge,
London, UK, 1993.
• Shapiro, Stewart (2000), Thinking About Mathematics: The Philosophy of Mathematics, Oxford University Press, Oxford, UK
• Strohmeier, John, and Westbrook, Peter (1999), Divine Harmony, The Life and Teachings of Pythagoras, Berkeley Hills Books, Berkeley, CA.
• Styazhkin, N.I. (1969), History of Mathematical
Logic from Leibniz to Peano, MIT Press, Cambridge, MA.
• Philosophy of mathematics entry in the Internet Encyclopedia of Philosophy
• The London Philosophy Study Guide offers many
suggestions on what to read, depending on the student’s familiarity with the subject:
• Philosophy of Mathematics
• Mathematical Logic
• Set Theory & Further Logic
• R.B. Jones’ philosophy of mathematics page
• Philosophy of mathematics at DMOZ
• The Philosophy of Real Mathematics Blog
• Kaina Stoicheia by C.S. Peirce.
• Philosophia Mathematica journal
• The Philosophy of Mathematics Education Journal
3.4 Philosophy of chemistry
The philosophy of chemistry considers the methodology
and underlying assumptions of the science of chemistry.
It is explored by philosophers, chemists, and philosopherchemist teams. For much of its history, philosophy of
science has been dominated by the philosophy of physics,
but the philosophical questions that arise from chemistry
have received increasing attention since the latter part of
the 20th century.[1][2]
Philosophers of chemistry discuss issues of symmetry
and chirality in nature. Organic (i.e., carbon-based)
molecules are those most often chiral. Amino acids,
nucleic acids and sugars, all of which are found exclusively as a single enantiomer in organisms, are the basic chemical units of life. Chemists, biochemists, and
biologists alike debate the origins of this homochirality.
Philosophers debate facts regarding the origin of this phenomenon, namely whether it emerged contingently, amid
a lifeless racemic environment or if other processes were
at play. Some speculate that answers can only be found
in comparison to extraterrestrial life, if it is ever found.
Other philosophers question whether there exists a bias
toward assumptions of nature as symmetrical, thereby
causing resistance to any evidence to the contrary.
One of the most topical issues is determining to what extent physics, specifically, quantum mechanics, explains
chemical phenomena. Can chemistry, in fact, be reduced
to physics as has been assumed by many, or are there inexplicable gaps? Some authors, for example, Roald Hoffmann,[6] have recently suggested that a number of dif3.4.1 Foundations of chemistry
ficulties exist in the reductionist program with concepts
like aromaticity, pH, reactivity, nucleophilicity, for exMajor philosophical questions arise as soon as one at- ample. The noted philosopher of science, Karl Popper,
tempts to define chemistry and what it studies. Atoms among others, predicted as much.
and molecules are often assumed to be the fundamental
units of chemical theory,[3] but traditional descriptions of
molecular structure and chemical bonding fail to account
for the properties of many substances, including metals 3.4.2 Philosophers of chemistry
and metal complexes[4] and aromaticity.[5]
Additionally, chemists frequently use non-existent chem- Several philosophers and scientists have focused on
ical entities like resonance structures[4][5] to explain the the philosophy of chemistry in recent years, notably,
structure and reactions of different substances; these ex- the Dutch philosopher Jaap van Brakel, who wrote
planatory tools use the language and graphical represen- The Philosophy of Chemistry in 2000, and the Maltese
tations of molecules to describe the behavior of chemi- philosopher-chemist Eric Scerri, editor of the journal
cals and chemical reactions that in reality do not behave “Foundations of Chemistry” and author of Normative and
Descriptive Philosophy of Science and the Role of Chemas straightforward molecules.
istry in Philosophy of Chemistry, 2004, among other arSome chemists and philosophers of chemistry prefer to ticles. Scerri is especially interested in the philosophical
think of substances, rather than microstructures, as the foundations of the periodic table, and how physics and
fundamental units of study in chemistry. There is not al- chemistry intersect in relation to it, which he contends is
ways a one-to-one correspondence between the two meth- not merely a matter for science, but for philosophy.[7]
ods of classifying substances.[3] For example, many rocks
exist as mineral complexes composed of multiple ions Although in other fields of science students of the method
that do not occur in fixed proportions or spatial relation- are generally not practitioners in the field, in chemistry
(particularly in synthetic organic chemistry) intellectual
ships to one another.[4]
method and philosophical foundations are often explored
A related philosophical problem is whether chemistry by investigators with active research programmes. Elias
is the study of substances or reactions.[3] Atoms, even James Corey developed the concept of "retrosynthesis"
in a solid, are in perpetual motion and under the right published a seminal work “The logic of chemical syntheconditions many chemicals react spontaneously to form sis” which deconstructs these thought processes and specnew products. A variety of environmental variables con- ulates on computer-assisted synthesis. Other chemists
tribute to a substance’s properties, including temperature such as K. C. Nicolaou (co-author of Classics in Total Synand pressure, proximity to other molecules and the pres- thesis) have followed in his lead.
ence of a magnetic field.[3][4][5] As Schummer puts it,
“Substance philosophers define a chemical reaction by the
change of certain substances, whereas process philosophers define a substance by its characteristic chemical 3.4.3 Further reading
Review articles
• Philosophy of Chemistry article on the Stanford Encyclopedia of Philosophy
• Foundations of Chemistry, an international peerreviewed journal for History and Philosophy of
Chemistry as well as Chemical Education published
by Springer.
[3] Schummer, Joachim. (2006). Philosophy of science. In
Encyclopedia of philosophy, second edition. New York,
NY: Macmillan.
[4] Ebbing, D., & Gammon, S. (2005). General chemistry.
Boston, MA: Houghton Mifflin.
[5] Pavia, D., Lampman, G., & Kriz, G. (2004). Organic
chemistry, volume 1. Mason, OH: Cenage Learning.
[6] The Same and Not the Same (Columbia, 1995, pp. 19-20)
[7] Scerri, Eric R. (2008). Collected Papers on Philosophy of
Chemistry. London: Imperial College Press. ISBN 9781-84816-137-5.
• Hyle: International Journal for Philosophy of
Chemistry, an English-language peer-reviewed
journal associated with the University of Karlsruhe, 3.4.6 External links
• Philosophy of Chemistry entry by Michael Weisberg, Paul Needham, and Robin Hendry in the
Stanford Encyclopedia of Philosophy
• Philosophy of Chemistry, J. van Brakel, Leuven University Press, 2000. ISBN 90-5867-063-5
• International Society for the Philosophy of Chemistry
• Philosophy of Chemistry: Synthesis of a New Discipline, Davis Baird, Eric Scerri, Lee McIntyre (eds.),
Dordrecht: Springer, 2006. ISBN 1-4020-3256-0
• International Society for the Philosophy of Chemistry Summer symposium 2011
• The Periodic Table: Its Story and Its Significance,
E.R. Scerri, Oxford University Press, New York,
2006. ISBN 0-19-530573-6
• Collected Papers on Philosophy of Chemistry, E.R.
Scerri, Imperial College Press, London, 2008.
ISBN 978-1848161375
• Of Minds and Molecules: New Philosophical Perspectives on Chemistry, Nalini Bhushan and Stuart
Rosenfeld (eds.), Oxford University Press, 2000,
Reviewed by Michael Weisberg
• Website for Eric Scerri, author and founder-editor
of Foundations of Chemistry
3.5 Philosophy of economics
See also: History of economic thought
Philosophy and economics, also philosophy of economics, may refer to the branch of philosophy that studies issues relating to economics or, alternatively, to the
branch of economics that studies its own foundations and
status as a moral science.[1]
• Philosophy of Chemistry : Growth of a New Discipline, Eric Scerri, Lee McIntyre (eds.), Heidelberg:
Springer, 2015. ISBN 978-94-017-9363-6
See also
Definition and ontology of economics
The question usually addressed in any subfield of philosophy (the philosophy of X) is “what is X?" A philosophical approach to the question “what is economics?" is less
• The central science
likely to produce an answer than it is to produce a survey
of the definitional and territorial difficulties and controversies. Similar considerations apply as a prologue to fur3.4.5 References
ther discussion of methodology in a subject. Definitions
[1] Weisberg, M. (2001). Why not a philosophy of chem- of economics have varied over time from the modern oriistry? American Scientist. Retrieved April 10, 2009.
gins of the subject, reflecting programmatic concerns and
distinctions of expositors.[2]
• History of chemistry
[2] Scerri, E.R., & McIntyre, L. (1997). The case for the
philosophy of chemistry. Synthese, 111: 213–232. Retrieved April 10, 2009 from http://philsci-archive.pitt.
Ontological questions continue with further “what is...”
questions addressed at fundamental economic phenomena, such as “what is (economic) value?" or “what is a
market?". While it is possible to respond to such questions with real verbal definitions, the philosophical value
of posing such questions actually aims at shifting entire perspectives as to the nature of the foundations of
economics. In the rare cases that attempts at ontological shifts gain wide acceptance, their ripple effects can
spread throughout the entire field of economics.[3]
Methodology and epistemology of economics
Main article: Economic methodology
ethical studies may enrich both areas, even including predictive and descriptive economics as to rationality of behavior, given social interdependence.[8]
Ethics and justice overlap disciplines in different ways.
Approaches are regarded as more philosophical when
they study the fundamentals - for example, John Rawls' A
Theory of Justice (1971)[9] and Robert Nozick's Anarchy,
State and Utopia (1974). 'Justice' in economics is a
subcategory of welfare economics[10] with models frequently representing the ethical-social requirements of a
given theory. “Practical” matters include such subjects as
law[11] and cost–benefit analysis[12]
An epistemology deals with how we know things. In
the philosophy of economics this means asking questions
such as: what kind of a "truth claim” is made by economic
theories - for example, are we claiming that the theories
relate to reality or perceptions? How can or should we
prove economic theories - for example, must every economic theory be empirically verifiable? How exact are
economic theories and can they lay claim to the status of
an exact science - for example, are economic predictions
as reliable as predictions in the natural sciences, and why
or why not? Another way of expressing this issue is to
ask whether economic theories can state “laws”. Philosophers of science and economists have explored these issues intensively since the work of Alexander Rosenberg
and Daniel Hausman dating to 3 decades ago.[4]
Utilitarianism, one of the ethical methodologies, has
its origins inextricably interwoven with the emergence
of modern economic thought. Today utilitarianism has
spread throughout applied ethics as one of a number
of approaches. Non-utilitarian approaches in applied
ethics are also now used when questioning the ethics
of economic systems - e.g. rights-based (deontological)
Rational Choice, Decision Theory and Game Theory
Non-mainstream economic thinking
Main articles: decision theory and game theory
Philosophical approaches in decision theory focus on
foundational concepts in decision theory - for example, on the natures of choice or preference, rationality,
risk and uncertainty, economic agents.[5] Game theory is
shared between a number of disciplines, but especially
mathematics, economics and philosophy. Game theory
is still extensively discussed within the field of the philosophy of economics. Game theory is closely related to
and builds on decision theory and is likewise very strongly
Ethics and justice
Main articles: Distributive justice and Justice (economics)
The ethics of economic systems deals with the issues such
as how it is right (just, fair) to keep or distribute economic
goods. Economic systems as a product of collective activity allow examination of their ethical consequences for all
of their participants. Ethics and economics relates ethical
studies to welfare economics.[7] It has been argued that
a closer relation between welfare economics and modern
Many political ideologies have been an immediate outgrowth of reflection on the ethics of economic systems.
Marx, for example, is generally regarded primarily as a
philosopher, his most notable work being on the philosophy of economics.
Main article: Heterodox economics
The philosophy of economics defines itself as including
the questioning of foundations or assumptions of economics. The foundations and assumption of economics
have been questioned from the perspective of noteworthy but typically under-represented groups. These areas
are therefore to be included within the philosophy of economics.
• Cross-cultural perspectives on economics: an example is the Buddhist-inspired Bhutanese "Gross
National Happiness" concept (suggested as a better development measure than GNI/GDP). Amartya
Sen is a renowned advocate for the integration of cross-cultural phenomena into economic
thinking.[14] Related area: economic anthropology.
• Feminist perspectives on economics: e.g. Drucilla Barker & Edith Kuiper eds., Towards a feminist
philosophy of economics. Routledge. 2003. ISBN
0-415-28388-4.; see also feminist economics.
Figures cited in the scholarly literature
Related disciplines
The ethics of economic systems is an area of overlap between business ethics and the philosophy of economics.
People who write on the ethics of economic systems are
more likely to call themselves political philosophers than
business ethicists or economic philosophers. There is significant overlap between theoretical issues in economics
and the philosophy of economics. As economics is generally accepted to have its origins in philosophy, the history
of economics overlaps with the philosophy of economics.
Some universities offer joint degrees that combine
philosophy, politics and economics. These degrees cover
many of the problems that are discussed in Philosophy
and Economics, but are more broadly construed. A small
number of universities, notably the LSE, the Erasmus
University Rotterdam, Copenhagen Business School and
the University of Bayreuth offer master’s degree programs specialized in philosophy and Economics.
[1] D. Wade Hands (2008). “philosophy and economics,”
The New Palgrave Dictionary of Economics, 2nd Edition.
• Daniel M. Hausman and Michael S. McPherson (1993).
“Taking Ethics Seriously: Economics and Contemporary Moral Philosophy,” Journal of Economic Literature,
31(2), pp. 671-731.
• _____ and _____, 2005, 2nd Ed. Economic Analysis
and Moral Philosophy, Part III: Liberty, rights, equality,
and justice. pp. 157-214. Description and preview links.
[2] • Roger E. Backhouse and Steven Medema (2008). “economics, definition of,” The New Palgrave Dictionary of
Economics, 2nd Edition. Abstract.
• _____. 2009. “Retrospectives: On the Definition of
Economics,” Journal of Economic Perspectives, 23(1), pp.
221–33. Abstract.
• Adam Smith ([1776] 1976). An Inquiry into the Nature
and Causes of the Wealth of Nations. Oxford University
Press. p. 428.
• John Stuart Mill (1844). “On the Definition of Political
Economy; and on the Method of Investigation Proper to It”,
Essay V, in Essays on Some Unsettled Questions of Political Economy.
• Lionel Robbins (1932). An Essay on the Nature and Significance of Economic Science, Macmillan, p. 16.
[3] • Roger E. Backhouse and Steven Medema (2008). “economics, definition of,” The New Palgrave Dictionary of
Economics, 2nd Edition. Abstract.
• Uskali Mäki (2008). “scientific realism and ontology,”
The New Palgrave Dictionary of Economics, 2nd Edition.
[4] • D. Wade Hands (2008). “philosophy and economics,”
The New Palgrave Dictionary of Economics, 2nd Edition.
• Roger E. Backhouse (2008). “methodology of economics,” The New Palgrave Dictionary of Economics, 2nd
Edition. Abstract.
• Alexander Rosenberg (1976). Microeconomic Laws:
A Philosophical Analysis, University of Pittsburgh Press.
Description and preview.
• _____ (1983). “If Economics Isn't Science, What Is It?"
Philosophical Forum, 14, pp. 296-314.
• _____ (1986). “What Rosenberg’s Philosophy of
Economics Is Not,” Philosophy of Science, 53(1), pp.
• Douglas W. Hands (1984). “What Economics Is Not:
An Economist’s Response to Rosenberg,” Philosophy of
Science, 51(3), p p. 495−503.
• Bruce J. Caldwell ([1982] 1994). Beyond Positivism:
Economic Methodology in the Twentieth Century, 2nd ed.
Routledge. Preview.
• Daniel M. Hausman (1980). “How to Do Philosophy of
Economics,” PSA: Proceedings of the Biennial Meeting of
the Philosophy of Science Association, 1, pp. 353−362.
• _____ (1983). “The Limits of Economic Science,” in
The Limits of Lawfulness: Studies on the Scope and Nature of Scientific Knowledge, N. Rescher, ed. Reprinted in
D.M. Hausman (1992 Essays on Philosophy and Economic
Methodology, pp. 99-108.
• Daniel M. Hausman (1989). “Economic Methodology
in a Nutshell,” Journal of Economic Perspectives, 3(2), pp.
• _____ (1992). The Inexact and Separate Science of Economics. Description, to ch. 1 link, preview, and reviews,
1st pages: .
• Kevin D. Hoover (1995). “Review Article: Why Does
Methodology Matter for Economics?" Economic Journal,
105(430), pp. 715-734.
• Vernon L. Smith (2003). “Constructivist and Ecological
Rationality in Economics,” American Economic Review,
93(3), pp. 465-508.
• _____ (2008). “experimental economics,” The New Palgrave Dictionary of Economics, 2nd Edition, Abstract.
• Francesco Guala (2005). The Methodology of Experimental Economics, Cambridge. Description/contents
links and ch. 1 excerpt.
[5] Paul Anand (1993,1995). “Foundations of Rational
Choice Under Risk”. Oxford. Oxford University Press.
[6] Cristina Bicchieri (1993). Rationality and Coordination.
Cambridge. Description and chapter-preview links, pp.
v-vi. Game-theory links.
[7] • Amartya K. Sen (1970 [1984]). Collective Choice and
Social Welfare. Elsevier. Description.
• Daniel M. Hausman and Michael S. McPherson (1993).
“Taking Ethics Seriously: Economics and Contemporary Moral Philosophy,” Journal of Economic Literature,
31(2), pp. 671-731.
• _____ and _____ ([1994] 2005), 2nd Ed. Economic
Analysis and Moral Philosophy. Description and preview
• Hal R. Varian (1975). “Distributive Justice, Welfare
Economics, and the Theory of Fairness,” Philosophy &
Public Affairs 4(3), pp. 223−247.
• Hodgson, Bernard (2001). Economics as Moral Science. Description and chapter-preview links, pp. xixiv.
[8] Amartya Sen (1987). On Ethics and Economics, Blackwell, back cover. Description and chapter-preview links.
• Peil, Jan, and Irene van Staveren, eds. (2009).
Handbook of Economics and Ethics, Edward Elgar.
Description and preview.
[9] Amartya Sen (1990). “Justice: Means versus Freedoms,”
Philosophy & Public Affairs, 19(2), pp. 111−121.
[10] In the Journal of Economic Literature classification codes
at JEL: D63, wedged on the same line between 'Equity'
and 'Inequality'.
[11] • Richard Posner (1981). The Economics of Justice.
Description and chapter links, pp. xi-xiii.
• David A. Hoffman and Michael P. O'Shea (2002). “Can
Law and Economics Be Both Practical and Principled?"
Alabama Law Review, 53(2), pp. 335-420.
• Putnam, Hilary (1993). “The Collapse of the
Fact/Value Dichotomy,” in Martha Nussbaum and
Amartya Sen, ed. The Quality of Life, pp. 143–
157. Oxford. Reprinted in Putnam (2002), Part I,
pp. 5 −64.
• _____ (2002). The Collapse of the Fact/Value Dichotomy and Other Essays, Description and chapterpreview links.
[12] Sven Ove Hansson (2010). “cost–benefit analysis: philosophical issues,” The New Palgrave Dictionary of Economics, Online Edition. Abstract.
• Robinson, Joan (1962). Economic Philosophy.
Description and scroll to chapter and previews.
[13] Marc Fleurbaey (2008). “ethics and economics,” The New
Palgrave Dictionary of Economics, 2nd Edition. Abstract.
• Rubinstein, Ariel (2006). “Dilemmas of an Economic Theorist,” Econometrica, 74(4), pp. 865-883
(close Page tab).
[14] Amartya Sen (2008). “Culture and Development.”
• Boulding, Kenneth E. (1969). “Economics as a
Moral Science,” American Economic Review, 59(1),
pp. 1−12.
• Caldwell, Bruce (1987). “positivism,” The New Palgrave: A Dictionary of Economics, v.3, pp. 921–23.
• Downie, R.S. (1987). “moral philosophy,” The New
Palgrave: A Dictionary of Economics, v. 3, pp. 551–
• Hands, D. Wade, ed. (1993). The Philosophy and
Methodology of Economics, Edward Elgar. 3 v. Description and Table of Contents links.
• Szenberg, Michael, ed.
Economists: Their Life Philosophies, Cambridge.
Description and preview.
• Walsh, Vivian (1961). Scarcity and Evil. PrenticeHall.
• _____ (1987). “philosophy and economics,” The
New Palgrave: A Dictionary of Economics, v. 3, pp.
• _____ (1996). Rationality, Allocation, and Reproduction. Cambridge. Description and scroll to
chapter-preview links.
3.5.7 Journals
• Davis, John B., Alain Marciano, Jochen Runde, eds.
(2004). The Elgar Companion to Economics and
Philosophy. Description & Table of Contents links
and Introduction and ch. 1 previews via sidebar
scrolling. Articles from 1925 & 1940-1991.
• Economics and Philosophy
• Hausman, Daniel M. (1992). Essays on Philosophy
and Economic Methodology. Description, ch. 1 link.
Chapter-preview links.
• Philosophy and Public Affairs
• Erasmus Journal for Philosophy and Economics
• Journal of Economic Methodology — Aims & Scope
• Politics, Philosophy & Economics — Aims and
• _____, ed. ([1984] 2008). The Philosophy of Economics: An Anthology, 3rd ed. Cambridge. Description & Table of contents links and Introduction. 3.5.8 External links
From John Stuart Mill on.
• Philosophy-Economics Network website.
• Heilbroner, Robert L. ([1953] 1999). The Worldly
Philosophers: The Lives, Times, and Ideas of the
• Recommended first reading: Philosophy of EcoGreat Economic Thinkers, 7th ed. Scroll to chapternomics (Daniel Little’s entry in the Routledge Enpreview links.
cyclopedia of the Philosophy of Science)
• Philosophy of Economics (Stanford Encyclopedia of example questioning whether psychological phenomena
Philosophy) by Daniel M. Hausman, notable in the can be explained using the methods of neuroscience,
evolutionary theory, and computational modeling, respectively. Although these are all closely related fields,
• Philosophical Issues in Economics some concerns still arise about the appropriateness of im(Cambridge University)
porting their methods into psychology. Some such con• Description of the Philosophy of Economics (Dan cerns are whether psychology, as the study of individuals
as information processing systems (see Donald BroadHausman)
bent), is autonomous from what happens in the brain
(even if psychologists largely agree that the brain in some
• Irrational Fools Philosophy and Economics Blog
sense causes behavior (see supervenience)); whether the
• Homophileconomicus (Philosophy and Economics mind is “hard-wired” enough for evolutionary investigaBlog, with useful links, conference announcements, tions to be fruitful; and whether computational models
course syllabi, news concerning recent research, can do anything more than offer possible implementaetc.)
tions of cognitive theories that tell us nothing about the
• EIPE (Erasmus Institute for Philosophy and Eco- mind (Fodor & Pylyshyn 1988).
nomics, based in Rotterdam, The Netherlands)
• Methodology of Economics: Secular versus Islamic
(Dr. Waleed Addas)
3.6 Philosophy of psychology
Philosophy of psychology is a relatively young field because “scientific” psychology—that is, psychology that favors experimental methods over introspection—came to
dominate psychological studies only in the late 19th century. One of philosophy of psychology’s concerns is to
evaluate the merits of the many different schools of psychology that have been and are practiced. For example,
cognitive psychology's use of internal mental states might
be compared with behaviorism, and the reasons for the
widespread rejection of behaviorism in the mid-20th century examined.
Philosophy of psychology refers to issues at the theoretical foundations of modern psychology. Some of these issues are epistemological concerns about the methodology
of psychological investigation. For example:
Topics that fall within philosophy of mind, of course, go
back much farther. For example, questions about the very
• What is the most appropriate methodology for psy- nature of mind, the qualities of experience, and particular
chology: mentalism, behaviorism, or a compro- issues like the debate between dualism and monism have
been discussed in philosophy for many centuries.
• Are self-reports a reliable data-gathering method?
• What conclusions can be drawn from null hypothesis
• Can first-person experiences (emotions, desires, beliefs, etc.) be measured objectively?
Other issues in philosophy of psychology are philosophical questions about the nature of mind, brain, and
cognition, and are perhaps more commonly thought of
as part of cognitive science, or philosophy of mind, such
• What is a cognitive module?
• Are humans rational creatures?
• What psychological phenomena come up to the standard required for calling it knowledge?
• What is innateness?
Philosophy of psychology also closely monitors contemporary work conducted in cognitive neuroscience,
evolutionary psychology, and artificial intelligence, for
Related to philosophy of psychology are philosophical
and epistemological inquiries about clinical psychiatry
and psychopathology. Philosophy of psychiatry is mainly
concerned with the role of values in psychiatry: derived from philosophical value theory and phenomenology, values-based practice is aimed at improving and humanizing clinical decision-making in the highly complex
environment of mental health care.[1] Philosophy of psychopathology is mainly involved in the epistemological
reflection about the implicit philosophical foundations of
psychiatric classification and evidence-based psychiatry.
Its aim is to unveil the constructive activity underlying the
description of mental phenomena.[2]
3.6.1 See also
• Philosophy of social science
3.6.2 References
[1] Fulford KWM, Stanghellini G. (2008). “The Third Revolution: Philosophy into Practice in Twenty-first Century
Psychiatry”. Dialogues in Philosophy, Mental and Neuro
Sciences 1 (1): 5–14.
[2] Aragona M (2009). Il mito dei fatti. Una introduzione alla
Filosofia della Psicopatologia. Crossing Dialogues.
Further reading
The London Philosophy Study Guide offers many suggestions on what to read, depending on the student’s familiarity with the subject: Philosophy of psychology.
• J. Stacy Adams. 1976. Advances in Experimental Social Psychology. Academic Press, 1976 ISBN
0120152096, 9780120152094.
• Leonard Berkowitz. 1972. Social psychology. Scott
Foresman & Co, 1972.
• Ned Block. 1980. Readings in Philosophy of Psychology, Volume 1. Harvard University Press, 1980.
ISBN 067474876X, 9780674748767.
• Stuart C. Brown, Royal Institute of Philosophy.
1974. Macmillan, 1974. Original from the University of Michigan
• Joseph Margolis. 2008. Philosophy of Psychology. Prentice-Hall foundations of philosophy series. Prentice-Hall, 1984. ISBN 0136643264,
• Ken Richardson. 2008. Understanding psychology.
Open University Press, 1988. ISBN 0335098428,
• George Botterill, Peter Carruthers. 1999. The Philosophy of Psychology. Cambridge University Press.
ISBN 0521559154, 9780521559157.
• Craig Steven Titus. 2009. Philosophical Psychology:
Psychology, Emotions, and Freedom. CUA Press.
ISBN 0977310361, 9780977310364.
• Jose Bermudez. 2005. Philosophy of Psychology:
A Contemporary Introduction. Routledge. ISBN
• Terence Horgan, John Tienson. 1996. Connectionism and the Philosophy of Psychology. MIT Press.
ISBN 0262082489, 9780262082488
External links
• Part 7 of MindPapers: Philosophy of Cognitive Science (contains over 1,500 articles, many with online
Chapter 4
Social accountability
4.1 Epistemological anarchism
distinguish science from religion, magic, or mythology.
He felt the exclusive dominance of science as a means
of directing society was authoritarian and ungrounded.[1]
Promulgation of the theory earned Feyerabend the title
of “the worst enemy of science” from his detractors.[2]
4.1.1 Rationale
The theory draws on the observation that there is no identifiable fixed scientific method that is consistent with the
practices of the paradigm of scientific progress – the
scientific revolution.[2] It is a radical critique of rationalist
and empiricist historiography which tend to represent
the heroes of the scientific revolution as scrupulous researchers reliant on empirical research, whereas Feyerabend countered that Galileo for example, relied on
rhetoric, propaganda and epistemological tricks to support his doctrine of heliocentrism, and that aesthetic criteria, personal whims and social factors were far more
prevalent than the dominant historiographies allowed.[2]
Paul Karl Feyerabend (1924–1994), originator of epistemological anarchism.
Epistemological anarchism is an epistemological theory advanced by Austrian philosopher of science Paul
Feyerabend which holds that there are no useful
and exception-free methodological rules governing the
progress of science or the growth of knowledge. It holds
that the idea that science can or should operate according
to universal and fixed rules is unrealistic, pernicious, and
detrimental to science itself.[1]
The use of the term anarchism in the name reflected the
methodological pluralism prescription of the theory, as
the purported scientific method does not have a monopoly
on truth or useful results. Feyerabend once famously
said that because there is no fixed scientific method,
it is best to have an “anything goes” attitude toward
methodologies.[1] Feyerabend felt that science started as
a liberating movement, but over time it had become increasingly dogmatic and rigid, and therefore had become
increasingly an ideology, and, despite its successes, science had started to attain some oppressive features, and it
was not possible to come up with an unambiguous way to
Scientific laws such as those posited by Aristotelian or
Newtonian physics that assumed the stance of objective
models of the universe have been found to come short in
describing the entirety of the universe. The movement of
universal models from Aristotelian to Newtonian physics
to Einstein's relativity theory, where each preceding theory has been refuted as entirely universal model of reality, illustrates for the epistemological anarchist that scientific theories do not correspond to truth, as they are in
part cultural manifestations, and ergo not objective.[1][3]
Feyerabend drew a comparison between one scientific
paradigm triumphing over or superseding another, in the
same manner a given myth is adapted and appropriated
by a new, triumphant successor myth in comparative
mythology. Feyerabend contended, with Imre Lakatos,
that the demarcation problem of distinguishing on objective grounds science from pseudoscience was irresolvable
and thus fatal to the notion of science run according to
fixed, universal rules.[1]
Feyerabend also notes that science’s success is not solely
due to its own methods, but also to its having taken in
knowledge from unscientific sources. In turn the notion
that there is no knowledge outside science is a 'convenient
fairy-tale' held only by dogmatists who distort history for
the convenience of scientific institutions.[4] For instance,
Copernicus was heavily influenced by Pythagoras, whose
view of the world had previously been rejected as mystical and irrational. Hermetic writings played an important role in the works of Copernicus as well as Newton.[5]
There exists fairly accurate astronomical knowledge that
reaches back even to the Stone Age, measured in stone
observatories in England and the South Pacific.[5] PreModern inventions such as crop rotation, hybrid plants,
chemical inventions and architectural achievements not
yet understood like that of the pyramids are all examples
which threaten the notion that science is the only means
of attaining knowledge.[5]
Feyerabend also criticized science for not having evidence for its own philosophical precepts, particularly the
notions of Uniformity of Law and of Uniformity of Process across time and space. “We have to realize that a unified theory of the physical world simply does not exist,”
said Feyerabend; “we have theories that work in restricted
regions, we have purely formal attempts to condense them
into a single formula, we have lots of unfounded claims
(such as the claim that all of chemistry can be reduced
to physics), phenomena that do not fit into the accepted
framework are suppressed; in physics, which many scientists regard as the one really basic science, we have now
at least three different points of view...without a promise
of conceptual (and not only formal) unification”.[6]
that he was a fellow epistemological anarchist. Lakatos
was the one who suggested and encouraged that Feyerabend write a book based on his philosophy and the lectures he gave in his classes, which turned out to be his
seminal work Against Method.[10]
4.1.3 See also
• Alan Watts
• Comparative mythology
• Criticism of science
• Dada
• Discordianism
• Instrumentalism
• Peter Russell
• Relativism
• Robert Anton Wilson
• Subjectivism
• Surrealism
• Thomas Kuhn
Furthermore, Feyerabend held that deciding between
competing scientific accounts was complicated by the
incommensurability of scientific theories. Incommensu- 4.1.4 References
rability means that scientific theories cannot be reconciled or synthesized because the interpretation and prac- [1] Feyerabend, Paul (1993). Against Method. London:
Verso. ISBN 978-0-86091-646-8.
tice of science is always informed by theoretical assumptions, which leads to proponents of competing theories [2] Paul Feyerabend entry by John Preston in the Stanford Enusing different terms, engaged in different languagecyclopedia of Philosophy, 2007-02-15
games and thus talking past each other. This for Feyerabend was another reason why the idea of science as [3] Feyerabend, Paul (1983). Against Method. Verso. p. 66.
ISBN 978-0-86091-646-8.
proceeding according to universal, fixed laws was both
historically inaccurate and prescriptively useless.
[4] Feyerabend, Paul (1983). Against Method. Verso. p. 306.
ISBN 978-0-86091-646-8.
Other proponents
Terence McKenna was a fan of philosophers such as Feyerabend and Thomas Kuhn.[7]
Ian Hacking was a friend of Feyerabend’s, and they corresponded with and cited each other. He wrote the introduction and praised the last edition of Against Method,
quoting French philosopher Jean Largeault, who called it
“more than a book: it is an event”.[8]
[5] Feyerabend, Paul (1983). Against Method. Verso. pp.
306–307. ISBN 978-0-86091-646-8.
[6] Feyerabend, Paul (1987). Farewell To Reason. Verso. p.
100. ISBN 0-86091-184-5.
[7] McKenna, Terence (1992). The Search of the Original
Tree of Knowledge. Sounds True, Incorporated. ISBN 156455-206-3.
[8] Feyerabend, Paul (2010). Against Method (fourth edition).
Verso. p. introduction. ISBN 1-56455-206-3.
Imre Lakatos was also a friend of Feyerabend’s. The two
wrote letters to each other on the philosophy of science
which would have been published in a book called For
and Against Method, but the death of Lakatos ended their [10] Feyerabend, Paul (1996). Killing Time: The Autobiograplans to produce this dialogue volume.[9] While Lakatos
phy of Paul Feyerabend. University Of Chicago Press. p.
never publicly labeled himself so, Feyerabend contended
139. ISBN 0-226-24532-2.
External links
• Outline of an anarchistic theory of knowledge - a
brief summary of the argument from
Chapter 5
Text and image sources, contributors, and
5.1 Text
• Philosophy of science Source: Contributors: Mav, The Anome,
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Gregbard, DBaba, Skomorokh, Jmatter4, Syntheticzero, Doug4, Enkyo2, ProductofSociety, Kai-Hendrik, TheOldJacobite, Adriansrfr,
Merodack, Addbot, Yobot, Legobot II, Denispir, Amble, Rubinbot, Xqbot, Eeegilbert, J04n, GrouchoBot, Argumzio, Skyerise, Jonkerz,
Solomonfromfinland, Mcc1789, Helpful Pixie Bot, Eflatmajor7th, YFdyh-bot, Erinius and Anonymous: 16
5.2 Images
• File:Albert_Einstein_photo_1921.jpg Source:
jpg License: Public domain Contributors: "Professor Einstein’s Visit to the United States", The Scientific Monthly 12:5 (1921), 482-485,
on p. 483. [1] Original artist: Underwood and Underwood, New York
• File:Amartya_Sen_NIH.jpg Source: License: Public domain Contributors:
Original artist: NIH (according to picture caption)
• File:Ambox_important.svg Source: License: Public domain Contributors: Own work, based off of Image:Ambox scales.svg Original artist: Dsmurat (talk · contribs)
• File:Chicken_farmer_in_Ghana_(5926941911).jpg Source:
in_Ghana_%285926941911%29.jpg License: Public domain Contributors: Chicken farmer in Ghana Original artist: USAID Africa Bureau
• File:Commons-logo.svg Source: License: CC-BY-SA-3.0 Contributors: ? Original artist: ?
• File:Ddraig.svg Source: License: Public domain Contributors: Based on
Image:Flag of Wales 2.svg Original artist: Liftarn
• File:Edit-clear.svg Source: License: Public domain Contributors: The
Tango! Desktop Project. Original artist:
The people from the Tango! project. And according to the meta-data in the file, specifically: “Andreas Nilsson, and Jakub Steiner (although
• File:Einstein_cross.jpg Source: License: Public domain Contributors: Original artist: NASA, ESA, and STScI
• File:Emblem-money.svg Source: License: GPL Contributors: Original artist: perfectska04
• File:Epicycle_and_deferent.svg Source: License:
Public domain Contributors: Based upon data from Thomas S. Kuhn, La rivoluzione copernicana (The Copernican Revolution), Einaudi,
Torino, 2000, p. 78. Also based upon File:Epicycle et deferent.png by Julo Original artist: Own work MLWatts
• File:Folder_Hexagonal_Icon.svg Source: License: Cc-bysa-3.0 Contributors: ? Original artist: ?
• File:Francis_Bacon_statue,_Gray’{}s_Inn.jpg Source:
statue%2C_Gray%27s_Inn.jpg License: CC BY-SA 2.0 Contributors: Original artist: Mike
• File:Friedrich_Hegel_mit_Studenten_Lithographie_F_Kugler.jpg Source:
Friedrich_Hegel_mit_Studenten_Lithographie_F_Kugler.jpg License: Public domain Contributors: Das Wissen des 20.Jahrhunderts, Bildungslexikon, Rheda, 1931 Original artist: Franz Kugler
• File:Hilbert.jpg Source: License: Public domain Contributors: Unknown (uploaded at en:Image:Hilbert.JPG) Original artist: Unknown<a href='//'
Wikidata-logo.svg/20px-Wikidata-logo.svg.png' width='20' height='11' srcset='
Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x' data-file-width='1050' data-file-height='590' /></a>
• File:JeremiahHorrocks.jpg Source: License: Public domain Contributors: Original artist: William Richard Lavender
• File:Karl_Popper.jpg Source: License: No restrictions Contributors: Original artist: LSE library
• File:MontreGousset001.jpg Source: License: CC-BYSA-3.0 Contributors: Self-published work by ZA Original artist: Isabelle Grosjean ZA
• File:Office-book.svg Source: License: Public domain Contributors: This and myself. Original artist: Chris Down/Tango project
• File:Open_book_icon.png Source: License: CC BY-SA
3.0 Contributors: Cropped from File:Collection Extension - Create a book box.png Original artist: He!ko, Aryamanarora
• File:P_philosophy.png Source: License: CC-BY-SA-3.0 Contributors: ? Original artist: ?
• File:Papapishu-Lab-icon-6.svg Source: License:
CC0 Contributors: Original artist: papapishu
• File:Papyrus_text;_fragment_of_Hippocratic_oath._Wellcome_L0034090.jpg Source:
commons/4/4c/Papyrus_text%3B_fragment_of_Hippocratic_oath._Wellcome_L0034090.jpg License: CC BY 4.0 Contributors:
Original artist: ?
• File:Paul_Feyerabend_Berkeley.jpg Source:
License: Attribution Contributors: The uploader on Wikimedia Commons received this from the author/copyright holder. Original artist:
Grazia Borrini-Feyerabend
• File:People_icon.svg Source: License: CC0 Contributors: OpenClipart Original artist: OpenClipart
• File:Phrenology1.jpg Source: License: Public domain Contributors: Friedrich Eduard Bilz (1842–1922): Das neue Naturheilverfahren (75. Jubiläumsausgabe) Original artist: scanned by de:Benutzer:
• File:Portal-puzzle.svg Source: License: Public domain Contributors: ?
Original artist: ?
• File:Psi2.svg Source: License: Public domain Contributors: No machinereadable source provided. Own work assumed (based on copyright claims). Original artist: No machine-readable author provided.
Gdh~commonswiki assumed (based on copyright claims).
• File:Question_book-new.svg Source: License: Cc-by-sa-3.0
Created from scratch in Adobe Illustrator. Based on Image:Question book.png created by User:Equazcion Original artist:
• File:Question_dropshade.png Source: License: Public
domain Contributors: Image created by JRM Original artist: JRM
• File:Socrates.png Source: License: Public domain Contributors:
Transferred from en.wikipedia to Commons. Original artist: The original uploader was Magnus Manske at English Wikipedia Later versions
were uploaded by Optimager at en.wikipedia.
• File:Stylised_Lithium_Atom.svg Source: License:
CC-BY-SA-3.0 Contributors: based off of Image:Stylised Lithium Atom.png by Halfdan. Original artist: SVG by Indolences. Recoloring
and ironing out some glitches done by Rainer Klute.
• File:Symbol_list_class.svg Source: License: Public domain Contributors: ? Original artist: ?
• File:Triangle_illustration.svg Source: License: Public
domain Contributors: self-made with en:Inkscape Original artist: Oleg Alexandrov
• File:Wiki_letter_w_cropped.svg Source: License:
CC-BY-SA-3.0 Contributors: This file was derived from Wiki letter w.svg: <a href='//
Wiki_letter_w.svg' class='image'><img alt='Wiki letter w.svg' src='
letter_w.svg/50px-Wiki_letter_w.svg.png' width='50' height='50' srcset='
Wiki_letter_w.svg/75px-Wiki_letter_w.svg.png 1.5x,
100px-Wiki_letter_w.svg.png 2x' data-file-width='44' data-file-height='44' /></a>
Original artist: Derivative work by Thumperward
• File:Wikibooks-logo.svg Source: License: CC BY-SA 3.0
Contributors: Own work Original artist: User:Bastique, User:Ramac et al.
• File:Wooden_hourglass.jpg Source: License: CC-BYSA-3.0 Contributors: ? Original artist: ?
• File:Wundt-research-group.jpg Source: License:
Public domain Contributors: the English language Wikipedia (log) Original artist: uploaded to Wikipedia by Kenosis
5.3 Content license
• Creative Commons Attribution-Share Alike 3.0