Rigid Designation and Semantic Structure

Forthcoming in " Philosophers' Imprint " Comments to: [email protected] 1. the issue 'Rigid designation' is Kripke's name for a concept that has been in the air at least since the development of quantified modal logics: (a token of 1) a designator is rigid if and only if it designates the same individual in every possible world in which the individual exists. Two seminal conclusions for which Kripke (1971, 1972) argues are that proper names are rigid designators, and that there are some deep semantic affinities between proper names and various sorts of general terms. However, even though he does, at places, explicitly attribute rigidity to certain general terms, 2 Kripke nowhere gives a definition of rigidity that applies to general terms. This presents a challenge: Precisely which general terms ought to be classified as rigid designators? More fundamentally: What should we take the criterion for rigidity to be, for general terms? There exists a considerable sub-literature, stretching back over 35 years, addressed to this challenge. 3 As the notion of rigidity is at the core of the causal-historical theory of reference, and of closely associated, fundamental criticisms of traditional ideas about language, these questions have been thought to have relevance to various debates in contemporary philosophy. 4 Two immediately evident options for extending the notion of rigidity to general terms are, in rough outline: (a) classify a general term as rigid if it designates the same extension in every possible world, and (b) classify a general term as rigid if it designates the same kind (or some such abstract entity—cf. note 5) in every possible world. The problem with (a) is that almost all general terms (including especially all natural kind terms) turn out nonrigid. That is, 2 there might have been more (or less, or different) tigers than there actually are, and so 'tiger' does not designate the same extension across counterfactual situations. Surely, the same is true of 'gold', 'water', and 'pain', of virtually any term that designates contingently existing concrete stuff and things. There is also a quick objection to (b), which many find compelling—i.e., on this approach, rigidity seems to become trivial, as almost all general terms (including the likes of 'bachelor', 'hunter', and 'pencil') come out rigid. The reason is that the conventional link between an expression and its meaning must be held constant across counterfactual situations, if we are to study the modal properties …