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Wittgenstein on the Infinity of Primes

Timm Lampert∗

History and Philosophy of Logic 29 (1):63-81 (2008)

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Wittgenstein on Mathematical Meaningfulness, Decidability, and Application.Victor Rodych - 1997 - Notre Dame Journal of Formal Logic 38 (2):195-224.details From 1929 through 1944, Wittgenstein endeavors to clarify mathematical meaningfulness by showing how (algorithmically decidable) mathematical propositions, which lack contingent "sense," have mathematical sense in contrast to all infinitistic "mathematical" expressions. In the middle period (1929-34), Wittgenstein adopts strong formalism and argues that mathematical calculi are formal inventions in which meaningfulness and "truth" are entirely intrasystemic and epistemological affairs. In his later period (1937-44), Wittgenstein resolves the conflict between his intermediate strong formalism and his criticism of set theory by requiring (...) Download Export citation Bookmark 18 citations
Wittgenstein on irrationals and algorithmic decidability.Victor Rodych - 1999 - Synthese 118 (2):279-304.details Download Export citation Bookmark 15 citations
(1 other version)Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.details Download Export citation Bookmark 70 citations
Wittgenstein, finitism, and the foundations of mathematics.Mathieu Marion - 1998 - New York: Oxford University Press.details This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Download Export citation Bookmark 38 citations
Wittgenstein’s Constructivization of Euler’s Proof of the Infinity of Primes.Paolo Mancosu & Mathieu Marion - 2003 - Vienna Circle Institute Yearbook 10:171-188.details We will discuss a mathematical proof found in Wittgenstein’s Nachlass, a constructive version of Euler’s proof of the infinity of prime numbers. Although it does not amount to much, this proof allows us to see that Wittgenstein had at least some mathematical skills. At the very last, the proof shows that Wittgenstein was concerned with mathematical practice and it also gives further evidence in support of the claim that, after all, he held a constructivist stance, at least during the transitional (...) Download Export citation Bookmark 6 citations
Wittgenstein, Finitism, and the Foundations of Mathematics.Paolo Mancosu - 2001 - Philosophical Review 110 (2):286.details It is reported that in reply to John Wisdom’s request in 1944 to provide a dictionary entry describing his philosophy, Wittgenstein wrote only one sentence: “He has concerned himself principally with questions about the foundations of mathematics”. However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called transitional phase. Marion’s book represents a giant leap forward in this direction. In the (...) Download Export citation Bookmark 17 citations
(2 other versions)Wittgenstein's Philosophy of Mathematics.Pasquale Frascolla - 1994 - Mind 108 (429):159-162.details Download Export citation Bookmark 26 citations
Wittgenstein, Finitism, and the Foundations of Mathematics.Mathieu Marion - 1998 - Studia Logica 66 (3):432-434.details Download Export citation Bookmark 36 citations

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