Intransitivity and Vagueness

TL;DR

This paper demonstrates that by carefully modeling uncertainty perception and reporting, indistinguishability can be treated as an equivalence relation, and proposes a logic of vagueness that addresses classical paradoxes like the sorites paradox.

Contribution

It introduces a model that resolves intransitivity issues in indistinguishability and develops a logic of vagueness that tackles longstanding philosophical problems.

Findings

Indistinguishability can be modeled as transitive with proper assumptions.

The proposed logic of vagueness addresses the sorites paradox effectively.

Modeling perception and reporting clarifies intransitivity issues.

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.