A classical degree-theoretic treatment of the sorites paradox : master's thesis in philosophy

Abstract

Since 1970s, degree-of-truth theory has been proposed as a solution to the Sorites paradox. However, one perennial attack to degree-of-truth theory is that its logic - fuzzy logic - is non-classical. Inspired by Gödel (1933), I attempt to better degree-of-truth theory by classicalizing it. That is, I attempt to give an interpretation of fuzzy logic within classical logic enriched by degree operators {⚪, ◔, ◑, ◕, ⚫} - “it is of no/low/moderate/high/full degree that …”. Intuitively, degree-of-truth is classicalized as classical bivalent truth-value and a largely independent notion of degrees. A formal semantics of this enriched classical logic is presented, from which two semantic consequences are derived. The two semantic consequences are applied to analyse the (in)validity of the Sorites argument. There are two results: 1. the validity of the standard Sorites argument is reasserted, 2. a new argument for the invalidity of the degreed version of the Sorites argument is presented.