Synthese 198 (4):3783-3799 (2019)

Alessio Persichetti
University of Aberdeen
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.
Keywords Wittgenstein  Logic  Contradictions  Alan Turing  Mathematics  Paraconsistent Logic
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DOI 10.1007/s11229-019-02310-w
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References found in this work BETA

In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
Beyond the Limits of Thought.Graham Priest - 1995 - Philosophy 71 (276):308-310.
Beyond the Limits of Thought.Graham Priest - 1999 - Philosophical Quarterly 49 (194):121-125.

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