Intensionality and the gödel theorems

Philosophical Studies 48 (3):337--51 (1985)
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Abstract

Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness of the standard extensional semantics for mathematics. In this paper I investigate some implications of the Gödel Second Incompleteness Theorem for these positions. I argue that the realm of mathematics, proof theory in particular, has been a breeding ground for intensionality and that satisfactory intensional semantic theories are implicit in certain rigorous technical accounts.

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David D. Auerbach
North Carolina State University

Citations of this work

Self-reference in arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
Hilbert's program then and now.Richard Zach - 2006 - In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 411–447.
On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
How to Say Things with Formalisms.David Auerbach - 1992 - In Michael Detlefsen (ed.), Proof, Logic, and Formalization. Routledge. pp. 77--93.
On the Depth of Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Philosophia Mathematica.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
Elementary logic.Benson Mates - 1965 - New York,: Oxford University Press.
Undecidable theories.Alfred Tarski - 1953 - Amsterdam,: North-Holland Pub. Co.. Edited by Andrzej Mostowski & Raphael M. Robinson.

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