Article ID: CBB312904403

The later Wittgenstein’s guide to contradictions (2021)

unapi

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 (LFM 1976), plus the Remarks on the Foundations of Mathematics (RFM 2001). First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: (a) a rejection of the debate about realism and anti-realism in mathematics; and (b) 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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Authors & Contributors
Loner, David
Zellini, Susanna
Zalabardo, José L.
Nakano, Anderson
Quinon, Paula
McNally, Thomas
Concepts
Philosophy
Mathematics
Logic
Computer science
Computers and computing
Philosophy of science
Time Periods
20th century, early
20th century
19th century
Places
United States
Europe
Great Britain
Institutions
Princeton University
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