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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’).

References:

[1] P. Cobreros, P. Egré, D. Ripley, R, Van Rooij, Tolerant, Classical, Strict, Journal of Philosophical Logic 41 (2019), 347-385.

[2] D. Graff, Shifting Sands: An Interest-Relative Theory of Vagueness, Philosophical Topics 28 (2000), 45-81.

[3] 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.

[4] K.G. Lucey, he ancestral relation without classes, Notre Dame Journal of Formal Logic 20 (1979), 281-284.