Document Type

Article

Publication Title

Journal of Philosophical Logic

Publication Date

2-1976

Keywords

vagueness, degrees of truth, sorites arguments, applied logic, model theory

Abstract

Formal mathematical logic is designed to capture the logical form of mathematical statements, all of which employ precisely defined concepts, unlike the concepts found in natural languages, almost all of which are vague. In this paper I argue that in order to more accurately represent the logical form of vague natural language statements, formal logic should employ degrees of truth and falsehood, rather than assuming just the two truth “values” T and F. I explore in detail the most reasonable definitions for basic logical operations in a system that allows for degrees of truth, concluding that one of the multi-valued systems proposed by Lukasiewicz works well. I then apply that system to represent the logical form of the paradox-generating sorites arguments, such as the paradox of the bald man, in which the argument concludes that everyone is bald, if anyone is. My analysis of the sorites arguments shows that these arguments yield false conclusions because their key premise is almost, but not quite, fully true. Along the way, I also point out that seeming contradictions can be as much as half-way true, along with other startling things in the logic of vague statements.

Comments

This is a manuscript of an article first published in Journal of Philosophical Logic.

Download

Share

COinS