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Developments in Logic: Carnap, Gödel, and Tarski

In Michael Beaney (ed.), Oxford Handbook of the History of Analytic Philosophy. Oxford: Oxford University Press. pp. 546-571 (2013)

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  1. Carnap’s dream: Gödel, Wittgenstein, and Logical, Syntax.S. Awodey & A. W. Carus - 2007 - Synthese 159 (1):23-45.
    In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...)
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  • What is Cantor's Continuum Problem?Kurt Gödel - 1947 - The American Mathematical Monthly 54 (9):515--525.
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  • The concept of logical consequence.John Etchemendy - 1990 - Cambridge: Harvard University Press.
    Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.
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  • Der wahrheitsbegriff in den formalisierten sprachen.Alfred Tarski - 1935 - Studia Philosophica 1:261--405.
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  • Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.K. Gödel - 1931 - Monatshefte für Mathematik 38 (1):173--198.
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  • What is Cantor's Continuum Problem?Kurt Gödel - 1983 - In Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings (2nd Edition). Cambridge: Cambridge University Press. pp. 470-485.
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