Three-valued semantic pluralism

a defense of a three-valued solution to the sorites paradox

Wen-fang Wang

pp. 4441-4476

in: Wiebe van der Hoek, Wesley H. Holliday, Wen-fang Wang (eds), Logic, rationality and interaction (LORI-5), Synthese 195 (10), 2018.

Abstract

Disagreeing with most authors on vagueness, the author proposes a solution that he calls ‘three-valued semantic pluralism’ to the age-old sorites paradox. In essence, it is a three-valued semantics for a first-order vague language with identity with the additional suggestion that a vague language has more than one correct interpretation. Unlike the traditional three-valued approach to a vague language, three-valued semantic pluralism can accommodate the phenomenon of higher-order vagueness and the phenomenon of penumbral connection when equipped with ‘suitable conditionals’. The author also shows that three-valued semantic pluralism is a natural consequence of a restricted form of the Tolerance principle ((hbox {T}_R)) and a few related ideas, and argues that ((hbox {T}_R)) is well-motivated by considerations about how we learn, teach, and use vague predicates.