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- Neil Tennant (2008). Carnap, Gödel, and the Analyticity of Arithmetic. Philosophia Mathematica 16 (1):100-112.Michael Friedman maintains that Carnap did not fully appreciate the impact of Gödel's first incompleteness theorem on the prospect for a purely syntactic definition of analyticity that would render arithmetic analytically true. This paper argues against this claim. It also challenges a common presumption on the part of defenders of Carnap, in their diagnosis of the force of Gödel's own critique of Carnap in his Gibbs Lecture. The author is grateful to Michael Friedman for valuable comments. Part of the research towards this paper was carried out while the author was a Visiting Fellow at the Center for Philosophy of Science at the University of Pittsburgh. The paper was presented to the Center's Fellowship Reunion Conference in Athens in 1992. It was committed for publication in the Proceedings of that conference, but those Proceedings never appeared. By the time it became evident that they would never appear, both the hard copy and the source file had been mislaid. The hard copy re-surfaced in 2007. The literature on this topic since 1992 appears to leave some space for the ideas and arguments presented here. Although the paper has been updated in light of the more recent literature, its basic thesis, presented in 1992, remains the same. Only 3 is new, questioning a basic presumption made by more recent commentators in their presentation of Gödel's criticism of Carnap in his Gibbs Lecture. For helpful comments on the current version, the author is indebted to Robert Kraut, Stewart Shapiro, and Adam Podlaskowski. CiteULike Connotea Del.icio.us What's this?Reading list | Discuss | Edit | Categorize |My bibliography
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| | Scholar | At my library | More options ... Recently O'Grady argued that Quine's "Two Dogmas" misses its mark when Carnap's use of the analyticity distinction is understood in the light of his deflationism. While in substantial agreement with the stress on Carnap's deflationism, I argue that O'Grady is not sufficiently sensitive to the difference between using the analyticity distinction to support deflationism, and taking a deflationary attitude towards the distinction itself; the latter being much more controversial. Being sensitive to this difference, and viewing Quine as having reason to insist on a non-arbitrary analyticity distinction, we see that "Two Dogmas" makes direct contact with Carnap's deflationism. We must look beyond "Two Dogmas" to Quine's other critiques of analyticity to understand why the arbitrariness of the distinction threatens to undermine or overextend Carnap's deflationism, collapsing it into a view much like Quine's. Quine is then seen to achieve many of Carnap's ends, with the important exception of deflationism.
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| | Other links: blackwell-synergy.com jstor.org dx.doi.org | Scholar | At my library | More options ... Recently O’Grady argued that Quine’s “Two Dogmas” misses its mark when Carnap’s use of the analyticity distinction is understood in the light of his deflationism. While in substantial agreement with the stress on Carnap’s deflationism, I argue that O’Grady is not sufficiently sensitive to the difference between using the analyticity distinction to support deflationism, and taking a deflationary attitude towards the distinction itself; the latter being much more controversial. Being sensitive to this difference, and viewing Quine as having reason to insist on a non-arbitrary analyticity distinction, we see that “Two Dogmas” makes direct contact with Carnap’s deflationism. We must look beyond “Two Dogmas” to Quine’s other critiques of analyticity to understand why the arbitrariness of the distinction threatens to undermine or overextend Carnap’s deflationism, collapsing it into a view much like Quine’s. Quine is then seen to achieve many of Carnap’s ends, with the important exception of deflationism.
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| | Other links: blackwell-synergy.com jstor.org dx.doi.org | Scholar | At my library | More options ... This paper is a reexamination of Two Dogmas in the light of Quine's ongoing debate with Carnap over analyticity. It shows, first, that analytic is a technical term within Carnap's epistemology. As such it is intelligible, and Carnap's position can meet Quine's objections. Second, it shows that the core of Quine's objection is that he (Quine) has an alternative epistemology to advance, one which appears to make no room for analyticity. Finally, the paper shows that Quine's alternative epistemology is itself open to very serious objections. Quine is not thereby refuted, but neither can Carnap's analyticity be dismissed as dogma.
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| | Other links: jstor.org | Scholar | At my library | More options ... Quine’s paper “Two Dogmas of Empiricism” is famous for its attack on analyticity and the analytic/synthetic distinction. But there is an element of Quine’s attack that should strike one as extremely puzzling, namely his objection to Carnap’s account of analyticity. For it appears that, if this objection works, it will not only do away with analyticity, it will also do away with other semantic notions, notions that (or so one would have thought) Quine does not want to do away with, in particular, it will also do away with truth. I shall argue that there is, indeed, no way for Quine to protect truth against the type of argument he himself advanced in “Two Dogmas” against Carnap’s notion of analyticity. If he wants to keep his argument, Quine has to discard truth along with analyticity. At the end of the paper I suggest an interpretation of Quine on which he can be seen as having done just that.
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| | Other links: philosophy.nd.edu jstor.org | Scholar | At my library | More options ... Gödel began his 1951 Gibbs Lecture by stating: “Research in the foundations of mathematics during the past few decades has produced some results which seem to me of interest, not only in themselves, but also with regard to their implications for the traditional philosophical problems about the nature of mathematics.” (Gödel 1951) Gödel is referring here especially to his own incompleteness theorems (Gödel 1931). Gödel’s first incompleteness theorem (as improved by Rosser (1936)) says that for any consistent formalized system F, which contains elementary arithmetic, there exists a sentence GF of the language of the system which is true but unprovable in that system. Gödel’s second incompleteness theorem states that no consistent formal system can prove its own consistency.
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| | Scholar | At my library | More options ... Machine generated contents note: Part I. General: 1. The Gödel editorial project: a synopsis Solomon Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr., and Cheryl A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical tradition Jeremy Avigad; 4. Only two letters: the correspondence between Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism W. W. Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G. Simpson; 8. On the outside looking in: a caution about conservativeness John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro Kanamori; 10. Generalizations of Gödel's universe of constructible sets Sy-David Friedman; 11. On the question of absolute undecidability Peter Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe and when did he believe it? Martin Davis; 13. On Gödel's way in: the influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual realism Donald A. Martin.
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| | Scholar | At my library | More options ... In this paper all the “acting” philosophers play their classical role: Gödel is present with his incompleteness theorems. Carnap is present with the positivist view of unity of science, and specifically with the thesis about a universal language. Finally, Popper tries to refute Carnap’s thesis with the help of Gödel’s. Unfortunately this debate did not take place in real, only one claim and reponse was made in Shilpp’s volume. I attempt to clarify this question in the present paper. The main focus is on Carnap’s view. I will show that it is possible to hold a thesis about a possible universal language if this is meant in a weaker sense: as a syntactical framework. The concept of “language” in Carnap’s view is also examined, and I come to the conclusion that it was used both in a wider and both in a narrower meaning. I also try to clarify this conceptual issue.
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| | Scholar | More options ... Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the conventionalist point of view in mathematics. When one reads carefully Gödel's text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnap's solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the Fregean heritage. We stress the way both of them try to answer, from different Fregean perspectives, to the question of the nature of logic and mathematics in knowledge.
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| | Other links: jstor.org | Scholar | At my library | More options ... Kurt Gödel criticizes Rudolf Carnap's conventionalism on the grounds that it relies on an empiricist admissibility condition, which, if applied, runs afoul of his second incompleteness theorem. Thomas Ricketts and Michael Friedman respond to Gödel's critique by denying that Carnap is committed to Gödel's admissibility criterion; in effect, they are denying that Carnap is committed to any empirical constraint in the application of his principle of tolerance. I argue in response that Carnap is indeed committed to an empirical requirement vis‐à‐vis tolerance, a fact that becomes clear upon closer scrutiny of Carnap's relevant writings. *Received July 2009; revised January 2010. †To contact the author, please write to: Department of Philosophy, University of Saskatchewan, 9 Campus Drive, Saskatoon, SK S7N 5A5, Canada; e‐mail: r.hudson@usask.ca.
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| | Other links: journals.uchicago.edu dx.doi.org | Scholar | At my library | More options ... Discussion of Neil Tennant, Carnap, gödel, and the analyticity of arithmetic
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