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Th e simple proposal about rigidity for predicates can be stated thus: a predicate is rigid if its canonical nominalization signifi es the same property across the different possible worlds. I have tried elsewhere to defend such a proposal from the trivialization problem, according to which any predicate whatsoever would turn out to be rigid. Benjamin Schnieder (2005) aims fi rst to rebut my argument that some canonical nominalizations can be fl exible, then to provide fi ve arguments to the eff ect that they are all rigid, and fi nally to propose a general explanation of why they are all rigid. I show fi rst why my argument has not been rebutted, then why Schnieder’s fi ve arguments for their rigidity all fail, and fi nally why the alleged “explanation” cannot be such, as the facts alluded to are neutral with respect to the rigidity or fl exibility of the nominalizations.

I offer an understanding of what it is for a term to be rigid which makes no serious metaphysical commitments to or about identity across possible worlds. What makes a term rigid is not that it 'refers to the same object(property) with respect to all worlds' - rather (roughly) it is that the criteria of application for the term with respect to other worlds, when combined with the criteria of identity associated with the term, ensure that whatever meets the criteria of identity also meets the criteria of application and vice versa - in the simplest case, the criteria of application just are the criteria of identity - but things can be more complex to allow for the necessary a posteriori. This makes rigidity a non-metaphysically loaded semantic matters, and allows us to see that the phenomenon of and involving rigidity - especially the necessary a posteriori - are of no metaphysical significance on their own.

1. Nathan Salmon paper is entitled with a question: are general terms rigid? He asks this question in way of engaging the issue of the extension of the notion of rigidity beyond the domain of singular terms. While singular terms has been the province of most of the discussion of this rigidity since Naming and Necessity, it is well known that Kripke saw the notion extending to at least certain general terms such as terms for natural kinds. Scott Soames has recently weighed in on this issue in the latter chapters of his book Beyond Rigidity. His conclusion is that although there are significant overlaps in the properties of singular and general terms, there is no direct extension of rigidity to the general terms, and that rigid designation is properly applied only to singular terms. Salmon disagrees. His view, based in part of views dating back to his book Reference and Essence, is that there is an extension to be had, one which allows the application of the standard Kripkean characterization of rigidity to be applied to both sorts of terms. Central to his thesis is a claim about the status of certain definite descriptions. In these remarks, I will try to outline the issues to which NS is reacting, and the proposal he posits in response. I will then consider in a more critical light his claim about definite descriptions, bringing to bear considerations of their grammar.

Joseph LaPorte in an article on `Kind and Rigidity'(Philosophical Studies, Volume 97) resurrects an oldsolution to the problem of how to understand the rigidityof kind terms and other general terms. Despite LaPorte'sarguments to the contrary, his solution trivializes thenotion of rigidity when applied to general terms. Hisarguments do lead to an important insight however. Thenotions of rigidity and non-rigidity do not usefullyapply at all to kind or other general terms. Extendingthe notion of rigidity from singular terms such as propernames to general terms such as natural kind terms is amistake.

A widely accepted thesis in the philosophy of language is that natural language proper names are rigid designators, and that they are so de jure, or as a matter of the “semantic rules of the language.” This paper questions this claim, arguing that rigidity cannot be plausibly construed as a property of name types and that the alternative, rigidity construed as a property of tokens, means that they cannot be considered rigid de jure; rigidity in this case must be viewed as a pragmatic and not a semantic property.

The article discusses an idea of how to extend the notion of rigidity to predicates, namely the idea that predicates stand in a certain systematic semantic relation to properties, such that this relation may hold rigidly or nonrigidly. The relation (which I call signification) can be characterised by recourse to canonical property designators which are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification divides into rigid and non-rigid cases will then depend uponwhether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be nonrigid, canonical designators such as having the colour of ripe tomatoes which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented.

Most discussions of Kripke's Naming and Necessity focus either on Kripke's so-called "historical theory of reference" or his thesis that names are rigid designators. But in response to problems of the rigidity thesis Kripke later points out that his thesis about proper names is a stronger one: proper names are de jure rigid. This sets the agenda for my paper. Certain problems raised for Kripke's view show that the notion of de jure rigidity is in need of clarification. I will try to clarify the notion of de jure rigidity by analyzing characterizations of it given in the literature. I will argue in particular that Kripke can count descriptive names as de jure rigid and that the concept of de jure rigidity should not be explained with recourse to the concept of a semantical rule. The second part of the paper is a critical discussion of arguments intended to show that proper names are not de jure rigid. I will show that these arguments are unconvincing by using Dummett's distinction between assertoric content and ingredient sense.

It is generally assumed that rigidity plays a key role in explaining the necessary a posteriori status of identity statements, both between proper names and between natural kind terms. However, while the notion of rigid designation is well defined for singular terms, there is no generally accepted definition of what it is for a general term to be rigid. In this paper I argue that the most common view, according to which rigid general terms are the ones which designate the same kind in all possible worlds, fails to deliver a posteriori necessities. I also present an alternative view, on which the work of explaining a posteriori necessities is not done by rigidity, but by a related metasemantic notion, which I call actuality - dependence.

A paradigmatic case of rigidity for singular terms is that of proper names. And it would seem that a paradigmatic case of rigidity for general terms is that of natural kind terms. However, many philosophers think that rigidity cannot be extended from singular terms to general terms. The reason for this is that rigidity appears to become trivial when such terms are considered: natural kind terms come out as rigid, but so do all other general terms, and in particular all descriptive general terms. This paper offers an account of rigidity for natural kind terms which does not trivialise in this way. On this account, natural kind terms are de jure obstinately rigid designators and other general terms, such as descriptive general terms, are not.

In this paper I discuss two approaches to rigidity. I argue that they differ in the general conception of semantics that each embraces. Moreover, I argue that they differ in how each explains the rigidity of general terms, and in what each presupposes in that explanation.