Research Group
in Analytic Philosophy

Abstract

The tolerance principle, according to which vague concepts are not sensitive to sufficiently small changes, seems very intuitive. Yet, accepting the tolerance principle, apparently, leads to the Sorites paradox within the realm of classical logic. To deal with the Sorites paradox, in many theories of vagueness the tolerance principle is rejected and a weaker version of it is proposed.  In this talk I will take a look at the tolerance principle from a topoogical point of view. First, I will give some common formulations of the tolerance principle and the Sorites Paradox. Then, after introducing basic topological notions, I will show in what way vague predicates are tolerant to sufficiently small changes. Based on the work of Ian Rumfitt (2015), “The Boundary Stones of Thought: An Essay in the Philosophy of Logic”, I propose a weak version of the tolerance principle that does not lead to the Sorites paradox in classical logic. I follow Rumfitt in that vague concepts, which are structured around typical cases (prototypes), are boundaryless.  In order to get to a more suitable formulation of the tolerance principle, I will focus on the similarity relation that is often considered as an indistinguishability relation. The similarity relation plays an important role in the formulation of the tolerance principle and the Sorites Paradox. Two adjacent elements in a sorites series are indistinguishable (similar) with respect to a certain concept. Given the crucial role of the similarity relation, I will give different formulations of the similarity relation that might be suggested by Rumfitt. None of them, it will be argued, are appropriate if we consider the similarity relation between two elements of the sorites series as an indistinguishability relation. Finally, I define the indistinguishability relation in a topological space and formulate a weak version of the tolerance principle.