Journal article
TRACTARIAN LOGICISM: OPERATIONS, NUMBERS, INDUCTION
The review of symbolic logic, Vol.14(4), pp.973-1010
12/01/2021
DOI: 10.1017/S1755020320000350
Abstract
In his Tractatus, Wittgenstein maintained that arithmetic consists of equations arrived at by the practice of calculating outcomes of operations Omega(n)((xi) over bar) 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 theTractarian logicist interpretation that theN-operator N((xi) over bar) and recursively defined arithmetic operators Omega(n)((xi) over bar) 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.
Details
- Title: Subtitle
- TRACTARIAN LOGICISM: OPERATIONS, NUMBERS, INDUCTION
- Creators
- Gregory Landini - Univ Iowa, Iowa City, IA 52241 USA
- Resource Type
- Journal article
- Publication Details
- The review of symbolic logic, Vol.14(4), pp.973-1010
- Publisher
- Cambridge Univ Press
- DOI
- 10.1017/S1755020320000350
- ISSN
- 1755-0203
- eISSN
- 1755-0211
- Number of pages
- 38
- Language
- English
- Date published
- 12/01/2021
- Academic Unit
- Philosophy
- Record Identifier
- 9984397201802771
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