Notre Dame Journal of Formal Logic

Wittgenstein on Mathematical Meaningfulness, Decidability, and Application

Victor Rodych

Abstract

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

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

Dates
First available in Project Euclid: 12 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039724887

Mathematical Reviews number (MathSciNet)
MR1489410

Digital Object Identifier
doi:10.1305/ndjfl/1039724887

Zentralblatt MATH identifier
0891.00007

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

Citation

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


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