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First-order logic and vagueness
December 19, 2019 @ 10:00 am - 12:00 pm
Speaker: Marian Calborean (University of Bucharest)
Abstract: The Sorites paradox is usually studied as a propositional paradox. However, the general form of the Sorites is second-order, with three main features. It doesn’t contain any arbitrary parameters. It can be used to generate the propositional Sorites by appropriate replacement of the second-order premise with arbitrary clauses. Finally, it is generally nonfirstorderizable, relying on the notion of transitive closure of a relation. However, it can be expressed in FOL with a finite upper bound on the elements of the relation. This leads to a definition of vagueness in classical FOL, using the interplay between a total preorder and a monadic predicate. A notational extension of FOL will introduce a vague structure formed by the predicate (e.g.tall), the broad predicate (e.g. broadly tall) and the strict predicate (e.g. strictly tall). It allows the failure of a weak non-contradiction (e.g. ‘Some men are both broadly tall and broadly short’), the failure of a weak LEM (e.g. ‘Some men are neither strictly tall nor strictly short`), and the truth of a non-paradoxical tolerance (e.g. ‘If a person of n cm is strictly tall, a person of n-1 cm is broadly tall’).
 P. Cobreros, P. Egré, D. Ripley, R, Van Rooij, Tolerant, Classical, Strict, Journal of Philosophical Logic 41 (2019), 347-385.
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 U. Keller, Some remarks on the definability of transitive closure in first-order logic and Datalog, Internal report, Digital Enterprise Research Institute (DERI), University of Innsbruck, 2004.
 K.G. Lucey, he ancestral relation without classes, Notre Dame Journal of Formal Logic 20 (1979), 281-284.