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TRACTARIAN LOGICISM: OPERATIONS, NUMBERS, INDUCTION

Published online by Cambridge University Press:  21 October 2020

GREGORY LANDINI
GREGORY LANDINI*
Affiliation:
UNIVERSITY OF IOWAIOWA CITY, IA52241, USAE-mail: [email protected]
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Abstract

In his Tractatus, Wittgenstein maintained that arithmetic consists of equations arrived at by the practice of calculating outcomes of operations $\Omega ^{n}(\bar {\xi })$ defined with the help of numeral exponents. Since $Num$ (x) and quantification over numbers seem ill-formed, Ramsey wrote that the approach is faced with “insuperable difficulties.” This paper takes Wittgenstein to have assumed that his audience would have an understanding of the implicit general rules governing his operations. By employing the Tractarian logicist interpretation that the N-operator $N(\bar {\xi })$ and recursively defined arithmetic operators $\Omega ^{n}(\bar {\xi })$ are not different in kind, we can address Ramsey’s problem. Moreover, we can take important steps toward better understanding how Wittgenstein might have imagined emulating proof by mathematical induction.

Keywords

WittgensteinRamseyRussellmathematical inductionN-operatorTractarian operations
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 4 , December 2021 , pp. 973 - 1010
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Copyright
© Association for Symbolic Logic 2020

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