Kripke's two definitions of rigid designation

Abstract

Philosophers, following Kripke, have formulated their notions of rigid designation in two ways. One way focuses on objects and defines a rigid designator as "referring to the object in every possible world in which the object exists" (I will call it 'the first defination').1 The other way focuses on designators and defines a rigid designator as "referring to the same object in every possible world in which the designator refers at all" (I will call it 'the second definition').2 The difference between these two definitions has not gone unnoticed, but to my knowledge the origin of the second definition and the consequences of the inconsistency between these two co-existing definitions have not been carefully explored.3 I shall show that Kripke in Naming and Necessity is accountable for both definitions and he would have to make a hard choice to maintain consistency.