Indiscriminability as Indiscernibility by Default

Most solutions to the sorites reject its major premise, i.e. the quantified conditional ∀i(P(ai) → P(-auth-temp_i+)). This rejection appears to imply a discrimination between two elements that are supposed to be indiscriminable. Thus, the puzzle of the sorites involves in a fundamental way the notion of indiscriminability. This paper analyzes this relation and formalizes it, in a way that makes the rejection of the major premise more palatable. The intuitive idea is that we consider two elements indiscriminable by default, i.e. unless we know some information that discriminates between them. Specifically, following Rough Set Theory, two elements are defined to be indiscernible if they agree on the vague property in question. Then, a is defined to be indiscriminable from b if a is indiscernible by default from b. That is to say, a is indiscriminable from b if it is consistent to assume that a and b agree on the relevant vague property. Indiscernibility by default is formalized with the use of Default Logic, and is shown to have intuitively desirable properties: it is entailed by equality, is reflexive and symmetric. And while the relation is neither transitive nor substitutive, it is "almost" substitutive. This definition of indiscriminability is incorporated into three major theories of vagueness, namely the supervaluationist, epistemic, and contextualist views. Each one of these theories is reduced to a different strategy dealing with multiple extensions in Default Logic, and the rejection of the major premise is shown to follow naturally. Thus, while the proposed notion of indiscriminability does not solve the sorites by itself, it does make the unintuitive conclusion of many of its proposed solutions-the rejection of the major premise-a bit easier to accept.