Wittgenstein, Peirce, and Paradoxes of Mathematical Proof

Analytic Philosophy (forthcoming)

Authors
Sergiy Koshkin
University of Houston - Downtown
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.
Keywords Wittgenstein  Peirce  Scandal of deduction  logical omniscience  corollarial theorematic distinction  semantic information  conservative extension  epistemic logic
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DOI 10.1111/phib.12177
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