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Analytic Philosophy

Wittgenstein, Peirce, and Paradoxes of Mathematical Proof

Profile image of Sergiy KoshkinSergiy Koshkin

Analytic Philosophy

https://doi.org/10.1111/PHIB.12177
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23 pages

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Abstract

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning.

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References (42)

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  2. Relationship between Peirce's and late Wittgenstein's positions is complicated. "Mean- ing is use" is reminiscent of the pragmatic maxim (but qualified as "sometimes, but not al- ways"), and "a way of grasping a rule that is not an interpretation" is akin to Peirce's habit change analysis. However, a detailed examination of the available evidence in (Boncom- pagni, 2016, Ch.1) concludes that "Wittgenstein expresses a basically negative attitude towards pragmatism as a Weltanschauung, but acknowledges affinities with pragmatism as a method". It is known that Wittgenstein read James extensively, and spent a year (1929) working with Ramsey, who developed his own version of semantic pragmatism based on Peirce's early works (Marion, 2012). Boncompagni speculates that Wittgenstein read Peirce's collection Chance, Love, and Logic, Ramsey's source, some time after 1929. Ramsey was also a precursor of epistemic logic, with key ideas developed around 1929.
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