Notre Dame Journal of Formal Logic

Wittgenstein on Mathematical Meaningfulness, Decidability, and Application

Victor Rodych


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.

Article information

Notre Dame J. Formal Logic, Volume 38, Number 2 (1997), 195-224.

First available in Project Euclid: 12 December 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 00A30: Philosophy of mathematics [See also 03A05]
Secondary: 01A60: 20th century


Rodych, Victor. Wittgenstein on Mathematical Meaningfulness, Decidability, and Application. Notre Dame J. Formal Logic 38 (1997), no. 2, 195--224. doi:10.1305/ndjfl/1039724887.

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