First-order logic and vagueness

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’).

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