On Paradoxes Connected with the Vagueness of Concepts

Abstract

All empirical concepts belonging to natural language are vague. The vagueness of empirical discourse is a source of many semantical problems which have been known since ancient times. One of those problems concerns the so called sorites paradoxes. This article is an attempt to show that the paradoxes are either invalid or unsound inferences. Since classical logic is useless for semantical analysis of such inferences, the article makes use of the Belnap four-valued logic based on the bilattice FOUR. Belnap's logic is the base logic for defining a nonmonotonic consequence relation which prefers models with classical valuations among all valuations of the four-valued logic whenever it is possible. The approach outlined in this article is intuitive, and has more advantages than the supervaluational approach.