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André Gallois (1998) attempts to defend the occasional identity thesis (OIT), the thesis that objects which are distinct at one time may nonetheless be identical at another time, in the face of two influential lines of argument against it. One argument involves Kripke’s (1971) notion of rigid designation and the other, Leibniz’s law (affirming the indiscernibility of identicals). It is reasonable for advocates of (OIT) to question the picture of rigid designation and the version of Leibniz’s law that these arguments employ, but, the problem is, some form of rigidity is required for one to affirm the occasional identity of objects, and some (restricted) version of Leibniz’s law must be conceded if identity really is involved. Gallois accordingly recommends an account of rigidity and a version of Leibniz’s law to this end.1 We find Gallois’ proposals entirely inadequate to their task. We aim in this paper is to explicate and defend an alternative approach for occasional identity theorists. We do not seek to defend (OIT) per se; our aim, rather, is simply to show that the arguments from rigid designation and Leibniz’s law are inconclusive. Let’s begin with an outline of these arguments.

André Gallois (1998) attempts to defend the occasional identity thesis (OIT), the thesis that objects which are distinct at one time may nonetheless be identical at another time, in the face of two influential lines of argument against it. One argument involves Kripke’s (1971) notion of rigid designation and the other, Leibniz’s law (affirming the indiscernibility of identicals). It is reasonable for advocates of (OIT) to question the picture of rigid designation and the version of Leibniz’s law that these arguments employ, but, the problem is, some form of rigidity is required for one to affirm the occasional identity of objects, and some (restricted) version of Leibniz’s law must be conceded if identity really is involved. Gallois accordingly recommends an account of rigidity and a version of Leibniz’s law to this end.1 We find Gallois’ proposals entirely inadequate to their task. We aim in this paper is to explicate and defend an alternative approach for occasional identity theorists. We do not seek to defend (OIT) per se; our aim, rather, is simply to show that the arguments from rigid designation and Leibniz’s law are inconclusive. Let’s begin with an outline of these arguments.

There is a considerable sub-literature, stretching back over 35 years, addressed to the question: 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? The aim of this paper is to give new grounds for the old view that if a general term designates the same kind in all possible worlds, then it should be classified as a rigid designator. The new grounds in question have to do with excavating the connection between rigid designation and semantic structure. Other original contributions of the present work consist in developing responses to some objections to this approach to rigid designation.

In this paper I argue that questions about the semantics of rigid designation are commonly and illicitly run together with distinct issues, such as questions about the metaphysics of essence and questions about the theoretical legitimacy of the possible-worlds framework. I discuss in depth two case studies of this phenomenon – the first concerns the relation between rigid designation and reference, the second concerns the application of the notion of rigidity to general terms. I end by drawing out some conclusions about the relations between rigid designation, semantic frameworks, reference, and essence.

Few philosophers today doubt the importance of some notion of rigid designation, as suggested by Kripke and Putnam for names and natural kind terms. At the very least, most of us want our theories to be compatible with the most plausible elements of that account. Anaphoric theories of reference have gained some attention lately, but little attention has been given to how they square with rigid designation. Although the differences between anaphoric theories and many interpretations of the New Theory of reference are substantial, I argue that rigid designation and anaphoric theories can be reconciled with one another and in fact complement one another in important ways.

Millikan's nondescriptionist approach applies an account of meaning to concepts in terms of designation. The essentialism that provides the principal grounds for rigid designation, however, receives no empirical support from concepts. Whatever the grounding, this view not only faces the problems of rigid designation in theories of meaning, it also calls for a role for pragmatics more consonant with descriptionist theories of concepts.

In this note I revive a lingering (albeit dormant) account of rigid designation from the pages of Mind with the aim of laying it to rest. Why let a sleeping dog lie when you can put it down? André Gallois (1986) has proposed an account of rigid designators that allegedly squares with Saul Kripke’s (1980) characterisation of them as terms which designate the same object in all possible worlds, but on which, contra Kripke, identity sentences involving rigid designators may be merely contingently true. This suits Gallois, as he finds the notion of contingent identity coherent. Thus, the thrust of Gallois’ thesis is that his account of rigidity is preferable to Kripke’s because his accommodates a coherent metaphysical viewpoint, whereas Kripke’s doesn’t. Gallois has thwarted one unconvincing challenge (see Carter 1987; Gallois 1988) and his account, as yet, remains untainted. But not for long, I hope.1 Let us assume, for the sake of argument, that the notion of contingent identity is coherent, that, in other words, it makes—or can make—sense to say that certain (possible) objects are identical in one world but distinct in another. What I shall argue here is that Gallois’ account of rigidity would prevent us from expressing the contingent nonidentity of objects; if so, this is a significant failing of the account, for, as it will emerge, clearly Gallois is committed to the contingency of non-identity.

Kripke's argument for the rigid designation of natural kind terms is fallacious because he does not distinguish natural kinds from second-order functional properties; by clarifying the concepts of natural kind and functional property, we can show that natural kind terms do designate their referents rigidly, but that functional property terms are not rigid designators. My discussions of functional property will also help dispel the worry about the alleged cases of contingent identity with regard to theoretical statements in science. There is no contingent identity even in the form of second-order logic: Property identity is also a necessary identity. The principle of necessary identity rules relentlessly.