Philosophical Studies 48 (3):337--51 (1985)
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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References found in this work BETA
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
The Unprovability of Consistency: An Essay in Modal Logic.George Boolos - 1979 - Cambridge University Press.
Citations of this work BETA
Self-Reference in Arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
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