The Review of Symbolic Logic

Research Article

INTRANSITIVITY AND VAGUENESS

JOSEPH Y. HALPERNa1 c1

a1 Computer Science Department, Cornell University

Abstract

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox.

(Received November 13 2006)

Correspondence:

c1 COMPUTER SCIENCE DEPARTMENT CORNELL UNIVERSITY ITHACA, NY 14853 E-mail: halpern@cs.cornell.edu