‘Sometime a paradox’, now proof: Yablo is not first order
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Publication:5066800
DOI10.1093/JIGPAL/JZAA051zbMATH Open1497.03023arXiv1908.01496OpenAlexW3095618167MaRDI QIDQ5066800
Author name not available (Why is that?)
Publication date: 30 March 2022
Published in: (Search for Journal in Brave)
Abstract: Paradoxes are interesting puzzles in philosophy and mathematics, and they could be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's paradox turns into a first-order tautology. Russell's paradox, which collapsed Frege's foundational framework, is now a classical theorem in set theory, implying that no set of all sets can exist. Paradoxes can be used in proofs of some other theorems; Liar's paradox has been used in the classical proof of Tarski's theorem on the undefinability of truth in sufficiently rich languages. This paradox (and also Richard's paradox) appears implicitly in G"{o}del's proof of his celebrated first incompleteness theorem. In this paper, we study Yablo's paradox from the viewpoint of first and second order logics. We prove that a formalization of Yablo's paradox (which is second-order in nature) is non-first-order-izable in the sense of George Boolos (1984).
Full work available at URL: https://arxiv.org/abs/1908.01496
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