The Expressive Power of the N-Operator and the Decidability of Logic in Wittgenstein’s Tractatus

IF 0.5 3区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

History and Philosophy of Logic Pub Date : 2022-04-13 DOI:10.1080/01445340.2022.2056687

Rodrigo Ferreira

引用次数: 0

Abstract

The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein’s reasons for believing that Logic is decidable were purely philosophical and the undecidability result shows that there are aspects of his criticisms of Frege and Russell that become unjustified in light of these results.

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维特根斯坦《论》中N算子的表现力与逻辑的可判定性

本文讨论了论论的警句6.1-6.13与丘奇-图灵定理关于谓词逻辑的可决性是否存在矛盾。我们试图建立以下几点:(i)警句6.1-6.13与丘奇-图灵定理不一致。(ii)由n算子构建的Tractatus的逻辑符号可以(也应该)被解释为相对于一阶公式的表达完备。(iii)维特根斯坦相信逻辑是可决定的理由是纯粹哲学的，而不可决定的结果表明，他对弗雷格和罗素的批评有一些方面在这些结果的基础上变得不合理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

History and Philosophy of Logic 综合性期刊-科学史与科学哲学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： History and Philosophy of Logic contains articles, notes and book reviews dealing with the history and philosophy of logic. ’Logic’ is understood to be any volume of knowledge which was regarded as logic at the time in question. ’History’ refers back to ancient times and also to work in this century; however, the Editor will not accept articles, including review articles, on very recent work on a topic. ’Philosophy’ refers to broad and general questions: specialist articles which are now classed as ’philosophical logic’ will not be published. The Editor will consider articles on the relationship between logic and other branches of knowledge, but the component of logic must be substantial. Topics with no temporal specification are to be interpreted both historically and philosophically. Each topic includes its own metalogic where appropriate.