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 | ||||||
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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 |
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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 |
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Date: | 2019 | ||||||
ISSN: | 0039-7857 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/16188 |
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