Kripke Rigidity versus Kaplan Rigidity

Abstract

In a recent article in Mind A. D. Smith suggests that much of the confusion and misunderstanding concerning issues that arise from Saul Kripke's claim that proper names are rigid designators can be cleared up once it is determined exactly what his notion of rigidity is. Like Smith I believe that it is important to pay close attention to the concept of rigidity. My aim in this paper, however, is to put a rather different slant on the sort of issues he considers, since a number of philosophers, following the lead of David Kaplan, have pointed out that two distinct definitions of rigidity can be found in Kripke's Naming and Necessity. (I shall refer to these as Kaplan rigidity and Kripke rigidity.) The trend has been to argue that Kaplan rigidity is the requisite sense of the notion for properly understanding Kripke's views concerning proper names. Although I will not contest the claim that Kripke's notion of rigidity is ambiguous, I will show that the attempt to understand rigidity in terms of Kaplan rigidity fails. Finally, I will sketch out a solution to the kind of problem that started this trend. The term 'rigid designator', as originally introduced by Saul Kripke, was meant to characterize an expression that designates the same thing with respect to every possible world in which that thing exists and designates nothing with respect to possible worlds in which that thing does not exist. (I shall hereafter refer to this sense of rigidity as Kripke rigidity.) This definition is given, unequivocally, by Kripke in 'Identity and Necessity' (p. 146), and seems clearly to be the understand? ing of the concept that was uppermost in Kripke's mind in Naming and Necessity (pp. 48-9). Other philosophers such as Leonard Linsky and Hilary Putnam have characterized rigidity in a slightly different way. Linsky, for example, calls a term rigid if it denotes the same thing in every possible world where it denotes anything at all. It is unlikely, however, that either Linsky or Putnam intended to give a de? finition of'rigid designator' that diverged in any significant way from the one given by Kripke. David Kaplan in his unpublished monograph Demonstratives has, how? ever, given a definition of rigidity that does differ significantly from the one cited. According to Kaplan there is a second definition of'rigid designator' to be found in Naming and Necessity which closely conforms to his own understanding of what it is for a term to be 'directly referential'. An expression is a 'rigid designator' in this sense if it designates the same thing in every possible world whether the thing 'exists' in that world or not. (I shall hereafter refer to this sense of rigidity as Kaplan rigidity.) In his monograph Kaplan goes on to suggest that Kripke may have been confused and misdescribed his own concept. According to Kaplan, not only did Kripke, in spite of the textual evidence, intend this second understanding of rigidity, but it is actually required in order to consistently represent an individual's contingency. Kaplan does agree with Kripke that proper names are rigid designators, but only in the sense that they are Kaplan rigid and not Kripke rigid.