On Singular Propositions

Abstract

A designator a of an object x is rigid in Kripke's sense if and only if (i) for every possible world w, if x exists in w, then a designates x with respect to w and (ii) there is no possible world with respect to which a designates something other than x. Alternatively, but to the same effect, a is rigid just in case neither the sentence:a might have existed and not have been anor the sentence:Something other than a might have been ahas an interpretation on which it is true. This alternative seems to me preferable: the concept of designation with respect to a world is difficult and occasions certain problems (about which something will be said later), but these problems do not arise on this explanation.