Showing, Analysis and the Truth-Functionality of Logical Necessity in Wittgenstein's Tractatus

Author: Cheung L.K.C.

Source: Synthese, Volume 139, Number 1, March 2004 , pp. 81-105(25)

Publisher: Springer

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Abstract:

This paper aims to explain how the Tractatus attempts to unify logic by deriving the truth-functionality of logical necessity from the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying of what is intrinsic to an expression (or a symbol). Then I argue that, according to the Tractatus, the thesis that a proposition shows its sense implies the determinacy of sense, the possibility of the complete elimination of non-primitive symbols, the analyticity thesis and the strong analyticity thesis. The picture theory emerges as what provides the only acceptable account of an elementary proposition, subject to the constraint that a proposition must show its sense. The picture theory and the analyticity thesis then entail the contingency thesis (that an elementary proposition is contingent) and the independence thesis (that elementary propositions are mutually logically independent) which, together with the strong analyticity thesis, imply that all logical propositions are tautologies.

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:SYNT.0000021309.60256.8e

Affiliations: 1: Department of Religion and Philosophy Hong Kong Baptist University Kowloon Tong Hong Kong, Email: kccheung@hkbu.edu.hk

Publication date: 2004-03-01