Yousuf Hasan Writing Sample PhD Application Jan. 2014

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Yousuf Hasan
Writing Sample
PhD Application
Jan. 2014
The Newman Problem: Why Carnap’s Ramsey-Approach to Scientific Theories Requires a
Reconceptualization
Abstract
The Newman objection seems to render any form of pure epistemic structuralism
nearly trivial or incoherent. I will show that Carnap’s reinvention of the Ramsey-sentence
approach to scientific theories commits him to a form of structuralism that is subject to
Newman’s pessimistic result. Because the Ramsey device used by Carnap seems to provide an
elegant and promising way to explain away the problem of “surplus meaning” and make sense
of ‘analyticity’ in the theoretical language of science, I propose that we conceptually reengineer
Carnap’s Ramsey-approach in a way that the Newman objection is no longer a problem.
1. Introduction
In this paper, I will argue that Carnap’s Ramsey-approach to scientific theories requires
a reconstruction in order to sidestep the Newman problem. Carnap proposes a rational
reconstruction of a scientific theory as a conjunction of a Ramsey-sentence and a Carnapsentence. The Ramsey-sentence is intended to express the factual content of the theory; while,
the Carnap-sentence is proposed as an analytic-postulate. The union of these two sentences
logically imply the entire theory without naming any theoretical entities. However, Newman’s
theorem in effect shows that any form of pure epistemic structuralism is either almost trivial or
incoherent. If the Ramsey-sentence of a theory is empirically adequate, then it is trivially true
so long as only a cardinality constraint is satisfied. Given that synthetic knowledge about the
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world is not supposed to be trivial (or knowable a priori), the Ramsey-sentence is an unfaithful
representation of the synthetic content of a theory. A conceptual reengineering of the Ramseysentence approach is needed in order to remedy the problem.
I have divided this paper into two parts. Each part is further divided into two sections. In
part one, I will setup Carnap’s Ramsey reconstruction of theories. First, I will explain the
philosophical motivations for Carnap’s Ramsey-sentence approach. Later, I elaborate why, for
Carnap, the Ramsey-language is a useful proposal for a rational reconstruction of our scientific
language. In the second part of the paper, I will argue that a reformulation of the Ramseylanguage is needed to circumvent the Newman problem. I begin by explaining why Carnap’s use
of Ramsey’s device is subject to Newman’s structural pessimism. Afterwards, I show that
Newman’s objection is a serious problem for Carnap’s Ramsification of theories. I conclude that
an adequate expression for the synthetic content of a theory must result in a conceptual
modification of the Ramsey-sentence approach to scientific theories.
2. Philosophical Motivation For The Ramsey Approach
Carnap of the Aufbau (1928) is traditionally interpreted as carrying out a reductive
empiricists’ project.1 According to this interpretation, Carnap’s Aufbau system is principally
motivated by the semantic reduction of t-terms and t-predicates to o-terms and o-predicates. A
complete translation of theoretical discourse to the observational language through the use of
explicit definitions would preserve the meaningfulness of the theoretical language by being
reduced to the confirmable language of observation. Moreover, there would be no need to
1
Quine, W. V. “Two Dogmas of Empiricism.” (1951); revised edition (1961), pp. 13
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inflate ontology beyond o-entities and logico-mathematical entities. T-discourse would simply
be a short-hand way of speaking about o-entities. The newer interpretations, however, by
Friedman2 and others suggest that Carnap of the Aufbau is primarily concerned by the
reduction of theoretical discourse to the pure structure of the world. Carnap, they say,
interpreted the world as a mathematical entity constituted of quadruples of real numbers.3 All
physical magnitudes such as electromagnetic fields or even space-time points are conceived as
n-tuples of reals for Carnap. However, they insist, this does not imply that Carnap was an antirealistic with respect to t-entities. He never denies the existence of t-entities. Instead, by not
naming t-entities, Carnap is in effect proposing a rational reconstruction of the world that is
purported to be metaphysically neutral.
Friedman’s structuralist interpretation of Carnap is not only consistent with the Carnap
of Testability and Meaning (1936)4, but it especially accounts for the later works of Carnap—the
Carnap of ESO (1956) and Beobactungssprache und Theoretische Sprache (1958)5 in particular—
where eventually Carnap reinvents the Ramsey-sentence approach to scientific theories. While
Friedman’s interpretation of Carnap’s motivation behind his Aufbau is more nuanced, there is,
however, prima facie evidence for a reductive empiricist construal of Carnap. As it has been
emphasized by Quine and Goodman,6 Carnap of the Aufbau attempted to use explicit reduction
2
Friedman, M. “Reconsidering Aufbau.” Reconsidering Logical Positivism (1999).
Pincock, C. “Carnap, Russell, and the External World.” The Cambridge Companion to Carnap (2007), pp. 118.
4
Carnap, Rudolf. “Introduction.” Testability and Meaning (1936), pp. 423. Carnap considered the old verification as
an explication of a theory of meaning. Even the replacement of the verification theory by confirmation (1936) was
“far from being an entirely satisfactory solution” (Carnap 423).
5
Carnap, Rudolf. “Beobactungssprache und Theoretische Sprache.” reprinted with an introduction by Ed. Stathis
Psillos. “Rudolf Carnap’s ‘Theoretical Concepts in Science’.” (2000), pp. 162.
6
Leitgeb, Hannes. “New Life for Carnap’s Aufbau.” (2011), pp. 2.
3
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sentences to connect the theoretical discourse to the observational language in a way that
made t-discourse completely connected to experience. But notice that Carnap’s emphasis is on
“experience” instead of “the given”. This suggests that a straight-forward phenomenalistic
reading of Carnap may be overly simplistic. For Carnap did not give special status to “the given”.
It is better to interpret Carnap as a conventionalist who was open to the adoption of both a
phenomenalistic language and a physicalistic (or thing) language for the conceptualization of
the world. There is no reliance on “the given” as a basis for scientific objectivity. As Leigeb
elaborates, “[e]xperiences may be the contents of particular mental states or they may be
particular mental states themselves” (Leigeb 269). The autopsychological was never given the
epistemic privilege of being considered more secure than the knowledge of physical things.
Nowhere in the Aufbau did “Carnap [employ] the traditional vocabulary of ‘certainty’,
‘justification’, ‘doubt’, and so on” (Friedman 119). For these reasons, the motivation behind
Carnap’s Aufbau system is better understood as a structuralist explication for a metaphysically
neutral construction of the world.
In the explicative project of reducing t-discourse to the observational language (1928),
Carnap realized that as a matter of empirical fact the nature of reductive sentences could not
be analytic.7 As a result, t-discourse could not be defined in terms of o-vocabulary in the explicit
sense. This lead Carnap in the mid-thirties to adopt a more workable proposal for the purposes
of connecting t-discourse to the more familiar (and less problematic) o-discourse. Strict
verification was replaced by confirmation (1936). Under Quine’s phenomenalistic reading of
7
For a survey of problems that lead to Carnap’s realization, Cf. Psillos, Stathis. “Carnap’s Neutralism.” Scientific
Realism: How Science Tracks Truth (1999), pp. 39-46.
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Carnap, this meant a complete failure of the Aufbau project and any reasonable hopes for a
reductive empiricist project. While it is true that no amount of reductive sentences would
suffice for explicitly defining t-discourse in virtue of the o-language, the resulting “surplus
meaning” problem disappears with Carnap’s Ramsey-approach to scientific theories (1958). By
constructing a Ramsey-sentence in the Ramsey-language extension of the ordinary language, it
is possible to express a scientific theory (with all of its observable consequences) without
having to require any t-vocabulary. There is no “surplus meaning” problem since there are no
theoretical terms to speak of that are not fully interpreted (since a complete translation is
untenable). The reinvention of the Ramsey-sentence by Carnap makes good sense under
Friedman’s structuralist motivations for Carnap’s Aufbau system. The Ramsey-approach is a
result of Carnap’s explicationary approach to scientific theories.
3. The Ramsey-Language Proposal
The Carnap of 19588 and 19649 proposed and elaborated an extension of the ordinary
observation language LO to the Ramsey-language LR. Unlike LO, LR is sufficiently powerful to
express what has come to be known as the Ramsey-sentence of a theory. Not only does LR
entails VO (o-terms and o-predicates) and elementary logic/mathematics, it contains essentially
“the whole of mathematics” (Carnap 253), including very complicated logic. Being an extension
8
Carnap, Rudolf. “Beobactungssprache und Theoretische Sprache.” Dialectica, (1958); reprinted with introduction
by Ed. Stathis Psillos. “Rudolf Carnap’s ‘Theoretical Concepts in Science’.” (2000), pp. 162. Carnap uses Ramsey’s
“device”—the Ramsey-sentence of a theory—in order to define analytic truths (in the broad sense) not only for
the LO but also LT as well.
9
Carnap, Rudolf. “The Ramsey Sentence.” The Philosophical Foundations of Physics: An Introduction to the
Philosophy of Science. Basic Books, Inc., (1966), reprinted in Ed. Martin Gardner’s An Introduction to the
Philosophy of Science. Dover Edition, (1974), pp. 252. By “observational language” Carnap is speaking about a
language entailing o-terms and o-predicates with elementary logic and mathematics.
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of the LO, LR has no VT (t-terms and t-predicates). By conceptually engineering LR, Carnap is able
to formulate Ramsey-sentences of theories which in turn shows that there can be ways of
speaking—which in this case is a very complicated and inconvenient—that entail all observable
consequences of theories without the use of VT. What is important is that it is possible to
construct a language in which a well-formed sentence (Ramsey-sentence of a theory) captures
all observable consequences of that theory. Whether such a construction of a language is
practically inconvenient is not relevant. The formulation of a Ramsey-sentence makes it obvious
that the question of whether so-and-so t-terms (for example, ‘proton’) or such-and-such tpredicates (for example, ‘charge’ in the theoretical sense) has empirical meaning is no longer
problematic. It is not a problem because the question disappears altogether since in LR there is
no t-talk to begin with. If Carnap is successful in reinventing a suitable Ramsey device to express
the content of scientific theories without resorting to t-discourse, then the Aufbau problem of
“surplus meaning” would be no problem. But not only this; for Carnap, it is only through the
Ramsey approach that the meaningfulness of t-discourse is supposed to be achieved in a
semantical framework where there is a strict distinction between analytic and synthetic
truths.10 In other words, his proposed Ramsification of theories solves the problem of defining
analytic-truths (in the broad sense) as well.
In Carnap’s proposed two-model language of science, a scientific theory consists of all
logical consequences of the conjunction of t-postulates and c-postulates. C-postulates result in
the derivation of correspondence rules—a name that Carnap prefers over P. W. Bridgman’s
10
Morman, Thomas. “The Structure of Scientific Theories in Logical Empiricism.” Ed. Alan Richardson,
Ed. Thomas Uebel. The Cambridge Companion to Logical Empiricism (2007), pp. 153-154.
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‘operational rules’ or Norman R. Campbell’s ‘dictionary rules’11—which are mixed sentences
entailing both o-and-t-terms. These mixed sentences serve as rules that connect the sentences
involving VT with sentences involving VO and provide a partial interpretation to sentences
occurring in VT. This is because the sentences of VO are confirmable through experience. The
more the correspondence rules, the more the t-discourse is interpreted, but no number of crules is sufficient to result in a complete interpretation of t-discourse. This is why the problem
of “surplus meaning” as discussed in the previous section resulted. The logical conjunction of tand-c-postulates in effect entail all observable consequences that a theory could have. Say a
theory has n-theoretical terms and m-correspondence postulates, then a theory would simply
be expressed as T&C <-> [(T1&T2…Tn-1&Tn) & (C1&C2…Cm-1&Cm)]. Given C-postulates contain tterms and o-terms, such a theory expanded to entail t-classes (for example, a class of all
protons) and t-predicates can be represented as follows:

Theory = Def. TC(t1,t2,…,tn;o1,o2,...,om)
Without realizing Carnap reinvented the Ramsey-approach to scientific theories by
proposing existentialized forms of theories.12 To get a Ramsey-sentence of a theory TC, first, we
replace all t-terms with corresponding u-variables to get a propositional function (or open
ended formula). Secondly, to convert the propositional function containing variables u1,..,un to a
11
Carnap, Rudolf. “Correspondence Rules.” The Philosophical Foundations of Physics: An Introduction to the
Philosophy of Science (1966). Reprinted in Ed. Martin Gardner’ An Introduction to the Philosophy of Science
(1974), pp. 233.
12
“Beobactungssprache und Theoretische Sprache.” (1958). Reprinted with introduction by Ed. Stathis Psillos.
“Rudolf Carnap’s ‘Theoretical Concepts in Science’.” (2000), pp. 153. Psillos presents Carnap’s letter to Hemple in
which Carnap clearly indicates that it was only after reading Hemple’s ‘The Theoretician’s Dilemma’ that he
realized that a Ramsey device was already invented by Ramsey in his ‘Theories’ (1929) paper.
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sentence having a truth-value, we bind the open-ended formula by adding existential quantifier
∃u1…∃un to the formula. Through this Ramsey device, Carnap is able to provide an incomplete
rational reconstruction of TC as a Ramsey-sentence. The Ramsey-sentence of TC is expressible
as follows:

Ramsey-sentence of a theory
TC = Def. RTC: (∃u1)(∃u2)…(∃un)TC(u1,u2,…,un-1,un; o1,o2,…,om)
If RTC is true, then it is empirically adequate in that it entails all the observable
consequences as TC. The difference being that RTC is an existentialized form of TC. As a
result, theoretical terms do not occur in RTC. In place of the t-terms, we now have variables
which do not refer to any t-classes, but only asserts that there are classes that satisfy
certain descriptions. But, for Carnap, the RTC alone is not a useful explication of TC. Ramsey
eliminated t-discourse altogether through his Ramsey process but at the expense of not
capturing our preanalytic intuitions of a successful formulation of the analytic/synthetic
distinction. In order for Carnap to give a more satisfactory rational construction, he
proposed separating the synthetic postulate from its analytic postulate by introducing what
has come to be known as a Carnap-sentence of a theory in addition to RTC. The Carnapsentence is an analytic postulate AT which is represented as the conditional RTC -> TC. It is
easy to see that AT is devoid of empirical content and true unconditionally since all that it
asserts is that “if the Ramsey sentence is true, we must understand the theoretical terms in
such a way that the entire theory is true” (Carnap 270)13. As for the synthetic-postulate FT,
it must capture all observable consequences of TC. The RTC is a suitable candidate since it
13
“Analyticity in a Theoretical Language.” The Philosophical Foundations of Physics: An Introduction to the
Philosophy of Science (1966). Reprinted in Ed. Martin Gardner’ An Introduction to the Philosophy of Science (1974).
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says exactly what TC says without providing any interpretation of t-terms since VT is
absent in RTC to begin with. RTC “has factual content simply because it thereby constrains
the observable phenomena in definite ways” (Friedman 102)14. A theory, for Carnap, then,
is represented as follows:

TC ↔ FT & AT ↔ (RTC ) & (RTC->TC)
The LR (the Ramsey-extension of observation language) is powerful enough to express FT
and AT of TC without naming any t-entities. As a result, Carnap not only does not have to
explain the problem of “surplus meaning” but he also separates TC into its synthetic and
analytic postulates as Ramsey and Carnap sentences respectively speaking.
4. The Newman Objection: The problem of Triviality or Incoherence
Roughly speaking, the Newman problem in effect states that any form of pure epistemic
structuralism is either nearly trivial or incoherent. If this is so, then Carnap’s Ramsey proposal of
scientific theories may be susceptible to Newman’s objection. This is because Carnap seems to
fit a form of epistemic structuralism. His account of a theory TC is structuralist since in the RTC
the variables range over logico-mathematical entities. And this is because variables range over
a structure of domain that is isomorphic to natural numbers. It is due to such structural
isomorphism that we can replace talk of t-entities with “numbers, classes of such, classes of
classes” (Carnap 963)15, and so forth. Moreover, his account of a theory TC is also epistemic (as
14
Friedman, Michael. “Carnap’s Philosophical Neutrality Between Realism and Instrumentalism.” Ed. Melanie
Frappier, Ed. Derek H. Brown, Ed. Robert DiSalle. Analysis and Interpretation in the Exact Sciences: Essays in
Honour of William Demopoulos (2012).
15
“Replies and systematic expositions.” P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (1963).
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opposed to ontic) since we only have epistemic access of the world up to structure, for Carnap.
The Newman’s theorem states the following.

Newman’s Theorem: Let S = (U, R1,…,RK) be a structure and V be a set. Suppose
that there is an injection p: U -> V. Then, there exists a structure S’ whose domain
is V and which has a substructure isomorphic to S.16
Newman’s theorem in effect says that at least all pure epistemic structuralisms that arise from
the Ramsey device say nothing whatever beyond the world of observation except imposing a
cardinality constraint. This is because all we need RTC to be true is to assign objects of a domain
to be the values for the variables that satisfy RTC. And this can be done in an artificial and selfserving manner. The only restriction is that the domain needs to be sufficiently large. This is
why RTC is almost trivial. While RTC says that “there are abstracta, classes or properties of this
case, that bear certain systematic relations to a large body of observable goings on” (Creath
60)17, the claim follows as a matter of a priori reasoning and a cardinality of the class under
question. As Votsis notes, “the mere number of members in an aggregate entails that there are
systems of relations definable over those members having a specified structure” (Votsis 881).
RTC
is trivially satisfied given only a cardinality constrain and yet, RTC is derived from AT the
synthetic postulate of TC. This is why the Newman problem makes Carnap’s Ramsey-approach
an inadequate representation of TC. But even if we try to avoid the problem of triviality, we do
so at the cost of incoherency. The only plausible way to restrict triviality is to specify particular
16
Votsis, Ioannis. “Is Structure Not Enough?” (2003), pp. 881. For definitions that lead to the theorem, refer to the
same page.
17
Creath, Richard. “Analyticity in The Theoretical Language: Is a Different Account Really Necessary?” Ed. Richard
Creath. Rudolf Carnap and the Legacy of Logical Empiricism (2012).
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relations that exemplify certain structures. In specifying relations, however, Carnap would no
longer be committed to pure epistemic structuralism. This would be inconsistent with Carnap’s
neutralist approach.
5. Proposal Sketch: Conceptual Reengineering For Carnap’s Ramsey Approach
Given Newman’s objection, I briefly propose that we do not abandon altogether
Carnap’s Ramsey-approach to scientific theories. It seems plausible that a suitable conceptual
modification to Carnap’s proposed reconstruction of scientific theories could remedy or
sidestep altogether the pessimistic force of Newman’s objection with respect to structuralism.
We need not abandon altogether any hopes for a neutralist position in the
realist/instrumentalist controversy; instead, the Ramsey-way may require conceptual
engineering. Given that non-neutralist positions have their own deeply troublesome problems,
it is a good and promising decision to search for a reconceptualization of the Ramsey-approach
given that “Carnap’s and Ramsey’s reconstructions possess not only internal coherence and
elegance, but, more importantly, a degree of philosophical motivation not matched by rival
accounts” (Demopoulos 109)18.
6. Conclusion
In this paper, I showed that Carnap’s reinvention of the Ramsey-sentence for the
purpose of maintaining neutralism in the realism/instrumentalism controversy on scientific
theories is subject to the Newman objection. As such, Carnap’s Ramsey-approach to scientific
theories requires a conceptual modification in order to avoid incoherence or triviality
18
“On the Rational Reconstruction of our Theoretical Knowledge.” Logicism and Its Philosophical Legacy (2013). I
will be attempting a remedy for Newman’s objection for my thesis.
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conditioned on a cardinality restriction. Such a reconceptualization is well motivated given that
the problem of “surplus meaning” and a successful explication of ‘analyticity’ within a
theoretical language are also sufficiently forwarded within Carnap’s program of scientific
philosophy. Otherwise, the Newman problem is a serious problem for Carnap’s Ramsification of
scientific theories.
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