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The later Wittgenstein’s guide to contradictions

Persichetti, Alessio (2019) The later Wittgenstein’s guide to contradictions. [Preprint]

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Abstract

This paper portrays the later Wittgenstein’s conception of contradictions and his therapeutic approach to them. I will focus on and give relevance to the Lectures on the Foundations of Mathematics, plus the Remarks on the Foundations of Mathematics. First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: a rejection of the debate about realism and anti-realism in mathematics; and Wittgenstein’s endorsement of logical pluralism. Then, I will explain Wittgenstein’s therapeutic approach towards contradictions, and why it means that a contradiction is not a problem for logic and mathematics. Rather, contradictions are problematic when we do not know what to infer from them. Once a meaning is established through a new rule of inference, the contradiction becomes a usable expression like many others in our inferential apparatus. Thus, the apparent problem is dissolved. Finally, I will take three examples of dissolved contradictions from Wittgenstein to clarify further his notion. I will conclude considering why his position on contradictions led him to clash with Alan Turing, and whether the latter was convinced by the Wittgensteinian proposal.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Persichetti, Alessio0000-0001-8081-5469
Keywords: Wittgenstein, Logic, Contradiction, Mathematics, Alan Turing, Rules, Paraconsistent Logic
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
General Issues > Realism/Anti-realism
Depositing User: Mr Alessio Persichetti
Date Deposited: 06 Jul 2019 11:09
Last Modified: 06 Jul 2019 11:09
Item ID: 16188
Journal or Publication Title: Synthese
Official URL: http://doi.org/10.1007/s11229-019-02310-w
DOI or Unique Handle: 10.1007/s11229-019-02310-w
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
General Issues > Realism/Anti-realism
Date: 2019
ISSN: 0039-7857
URI: http://philsci-archive.pitt.edu/id/eprint/16188

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