Wittgenstein on Mathematical Meaningfulness, Decidability, and Application

Notre Dame Journal of Formal Logic 38 (2):195-224 (1997)
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 that a mathematical calculus (vs. a "sign-game") must have an extrasystemic, real world application, thereby returning to the weak formalism of the Tractatus
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DOI 10.1305/ndjfl/1039724887
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Wittgenstein's Critique of Set Theory.Victor Rodych - 2000 - Southern Journal of Philosophy 38 (2):281-319.
Wittgenstein on Pure and Applied Mathematics.Ryan Dawson - 2014 - Synthese 191 (17):4131-4148.
Gödel's 'Disproof' of the Syntactical Viewpoint.Victor Rodych - 2001 - Southern Journal of Philosophy 39 (4):527-555.

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