Historical Development of Fuzzy Logic and Theories of Language

Abstract

The purpose of this research is two-fold. The first goal is to study the relationship between the ordinary or natural languages which we use for communication (such as English) and the standard logical languages and elementary set theory. We examine how, with the advent of mathematical logic, formal systems diverged from actual language usage. We examine the historical and philosophical roots of the idea that human classification schemes are "infected" with vagueness and that the classical systems do not provide an adequate model of the way in which people use language. Consequently, we argue that new mathematical models are necessary. Thus, our second goal is to provide an exposition of one of those new mathematical models, fuzzy set theory. The exposition is suitable for students who have completed an elementary survey course in the foundations of mathematics.