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Análisis filosófico

versión On-line ISSN 1851-9636

Anal. filos. vol.29 no.2 Ciudad Autónoma de Buenos Aires nov. 2009



Second Symposium. General terms: The rigid/non-rigid distinction

Introduction: General term rigidity and Devitt's rigid appliers*

Ezequiel Zerbudis

Universidad de Buenos Aires - ANPCyT - GAF


In this essay, I present a problem that originates in Kripke's contention, in Naming and Necessity, that natural kind terms are rigid, namely, the problem of how to understand the notion of rigidity when it is applied to general terms. I also give an account, in a principled way, of the main theoretical options that seem to be available to solve that problem, and sketch the main features of Michael Devitt's proposal against that background.

KEY WORDS: General term; Designation; Rigidity; Essence.


En este trabajo, hago una presentación de un problema que Kripke deja planteado al sostener, en El nombrar y la necesidad, que los términos de género natural son rígidos, a saber, el de cómo debería ser entendida la noción de rigidez cuando ésta es aplicada a los términos generales. Asimismo, trazo un panorama de las distintas opciones teóricas disponibles, y presento las tesis centrales de la propuesta de Michael Devitt a la luz de este marco.

PALABRAS CLAVE: Término general; Designación; Rigidez; Esencia.

1. In this introduction, I would like to present the general background against which the discussion that will take up in the following pages is to be understood. I will try to do so by presenting the main features of Devitt's conception of Rigid Application, which will be the main topic of these discussions, and by placing it in the context of the other proposals that have been presented to try to solve the same problem it tries to solve, namely, that of making sense of Kripke's contention, made in the third of the lectures that were to become Naming and Necessity, that not only proper names, but also some general terms, in particular natural kind ones, should be taken to be rigid (cf. Kripke 1980, pp. 115-140, and particularly p. 136, where he explicitly affirms of some natural kind terms that they are rigid).
As is widely known, and I have already suggested, this Kripkean contention has been thought, ever since he first presented it, to be problematic. And it seems that one of the main reasons why commentators have thought so lies in the fact that it is not clear how to put the two following features together: on the one hand, the fact that the definition of the notion of rigidity originally given by Kripke seems to involve, in an essential way, the notion of designation; on the other hand, the fact that natural kind terms are usually taken to be predicative expressions (that is, either predicates or general terms), and that it is not at all clear whether, and in what sense, the notion of designation could be used to characterize their behaviour.
That the notion of designation is essential to the original definition of rigidity may be seen from the fact that what Kripke defines is, indeed, the notion of a rigid designator:

Let's call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case (1980, p. 48).

This being so, the first issue that we must face in order to examine whether, and how, the notion of rigidity can be extended to predicative expressions consists in trying to determine whether, and in what sense, the notion of designation can be used to characterize the semantic behaviour of such expressions.1 The reason why this is somewhat problematic is closely related to the fact that there seem to be at least two different kinds of relation to non-linguistic items that general terms Could be said to stand in, both of which could be considered as semantically relevant designation relations: on the one hand, (1) there is the relation to the properties that they are supposed to express and ascribe to the individuals they are applied to; on the other hand, (2) there is the relation to the individuals that these expressions are applied to truly. Moreover, those individuals can be taken (2a) to form a set, that is, they can be thought of as a single individual constituting the extension of the general term, or (2b) as just as many separate individuals the predicate is true of. So, for instance, if we take the predicative expression 'red' as an example, we might say (1) that it expresses the property of being red, (2a) that it has as its extension the set of red things, and (2b) that it is true of each of the particular red individuals.
Now, it is possible to understand the different proposals that have been made in the literature concerning how to extend Kripke's notion of rigidity to general terms as arising from favouring one or the other of those semantic relations as the notion of designation relevant for an evaluation of their rigidity. It is reasonable to expect to find, accordingly, three different proposals corresponding to the three semantic relations we have distinguished above. And indeed we find, in the first place, some authors that defend a view, the so-called identity of designation view, which ascribes rigidity (or non-rigidity) to predicative expressions by examining the way they relate to the properties that they are supposed to express and that, according to the upholders of the proposal, they should also be taken to designate (cf. the relation (1) we introduced above).2 According to this kind of proposal, then, a general term is characterized as rigid if and only if it expresses (or designates) the same property in all possible worlds. A second proposal that has been defended in the literature evaluates the rigidity (or non-rigidity) of a predicative expression by examining the relation that obtains between the term and each of the individuals it applies to (cf. the relation (2b) we introduced above). According to this kind of proposal, which can be characterized as the essentialist view, a predicative expression is to be considered as rigid in case it applies to an object as though it expressed an essential property of that object, that is, in case it applies to it in all the counterfactual situations in which it exists (we will see a more formal characterization of this  requirement below).3 Besides, what we have said above seems to make room for a third kind of proposal, namely, one that ascribes rigidity (or non-rigidity) to predicative expressions by examining the relations that such terms have to their extensions (considered as sets). But this last position has been very early dismissed as a non-starter, and for obvious reasons: no general term, but those for kinds of necessary existents, would come out rigid on that account, as the extension of most general terms varies from world to world; accordingly, we may safely leave that option aside. Finally, we could discern in the relevant literature a further position that consists in simply denying that the notion of rigidity can have any meaningful application to general terms, either because there would seem to be no way of deciding which of the above-mentioned proposals should be regarded as the genuine extension of rigidity, or because it is thought that all of them are objectionable on other grounds (for instance, because they fail to make a theoretically interesting, non-trivial, distinction).4

2. The proposal that Devitt presented in his (2005) paper "Rigid Application" belongs in the group of the essentialist views. As we said earlier, the intuitive idea behind those proposals is that a rigid predicative expression should be understood as an essentialist one, that is, as an expression that behaves as if it stood for a property that is essential to anything that has it. But Devitt seems to prefer to avoid the talk of properties, let alone essential ones. For him, a general term (the kind of predicative expression for which he defines the notion) is to count as rigid if it is a rigid applier, a notion he defines as follows:

[A] general term F is a rigid applier if and only if it is such that if it applies to an object in any possible world, then it applies to that object in every possible world in which the object exists (2005, p. 146).

In the paper, Devitt tries to defend his view against two objections raised against it by Schwartz (2002). The first one amounts to the claim that any notion of rigidity that fails to distinguish natural kind terms from all other general terms should be considered as theoretically useless; the second is that a proposal such as Devitt's fails in fact to distinguish between natural kind terms and all other general terms.
With regard to the first charge, Devitt thinks that it is a mistake to suppose that the main work of a rigidity distinction should be that of providing a principled way of distinguishing between natural kind terms and all other general terms. He urges us instead to take a look at the more clear case of singular terms to see what kind of work the notion of rigidity does for them, and suggests as a methodological criterion that any acceptable extension of rigidity to general terms should be one that played an analogous role. Devitt then finds that there is, on the one hand, some "primary work" that the notion of rigidity does for singular terms, which consists in "identifying terms that are not synonymous with descriptions and hence refuting description theories of meaning for those terms" (2005, p. 144). On the other hand, he finds that there are four pieces of "secondary work" that the notion of rigidity is expected to perform, namely, explaining four different contrasts that are found in the modal behaviour of those terms. The contrasts that are to be explained by rigidity are the following: the fact that, while the truth of a sentence with a name in subject position depends, in different possible worlds, on what happens with a single object in all of them (namely, that rigidly designated by the name), the truth of a sentence with a description in subject position may depend on what happens with different objects in different worlds; the fact that, while a sentence like 'The last great philosopher of Antiquity might not have been the last great philosopher of Antiquity' has a true reading, this is not so with 'Aristotle might not have been Aristotle'; the fact that, while 'It might have been the case that the last great philosopher of Antiquity was not a philosopher' has two non-equivalent readings (depending on the relative scope of the modal operator and the first description), this is not so if the first description is replaced by 'Aristotle'; and finally, the fact that, while true identity sentences between rigid names are necessary, this is not so with identities that include non-rigid singular terms.
As we said, Devitt thinks that it would certainly constitute a good reason to accept a specific notion of rigidity for general terms if its adoption enabled us to explain some phenomena that take place in the case of those terms (namely, some contrasts between natural and nominal kind terms) just as the adoption of a notion of rigidity for singular terms did enable us to explain some allegedly parallel phenomena taking place in the case of them (namely, some contrasts between names and descriptions). And he thinks moreover that his preferred account of rigidity is in fact successful as regards this requirement, except for the fact that it cannot perform the last of the four explanatory tasks which are the general term analogues of those we already mentioned concerning singular terms. For instance, in relation to the primary work, he says that, while 'gold' does not fail to apply to actual pieces of gold with respect to counterfactual situations in which they exist but have a different appearance, the typical descriptive predicates true of pieces of gold in the actual world could in some cases fail to do so -therefore showing that the term and the description aren't synonymous. Besides, he presents some other examples to show that his account of rigidity also explains the phenomena alluded to in the first three pieces of secondary work. I will like to point out that, although Devitt is right that his preferred view only fails concerning the necessitation of true identification statements, it seems to me that he has somehow downgraded this failure: from my perspective, the phenomenon of the necessitations seems significant to Kripke's whole project and may deserve to be given more weight.5
We could take the second criticism made by Schwartz, as I think Devitt himself does in the paper, as saying that, no matter what we end up thinking concerning the theoretical work that a rigidity distinction should be able to perform, Devitt's proposal fails concerning the demand, that it would be reasonable to make on independent grounds, to the effect that rigid general terms should (approximately) coincide with the class of natural kind terms (what I will call the condition of extensional adequacy). I will not deal with this problem in any detail here because I will do so below, in my contribution to the present symposium, but I would like to draw attention to the fact that, contrary to what some other authors have done, namely, refusing to accept as valid the very condition of extensional adequacy,6 Devitt addresses the objection and tries to defend his view against it, thereby apparently assuming that the satisfaction of the condition should be taken, if not as mandatory, at least as desirable for any conception of rigidity for general terms.


I have tried to present here, then, in a brief outline, the main solutions that have been offered to the problem of how to extend the notion of rigidity to predicative expressions, together with the main theses defended by Devitt on the topic. Of course, I could not address most of the many interesting issues he raises in his paper in this introduction; some of them, in any case, will be given some attention in the discussion that follows. But I hope that what I have said is enough to help a reader who is not acquainted with the present debate to better understand the papers that follow.


* I would like to thank Michael Devitt and Eleonora Orlando for comments on an earlier version of the present introduction. Research leading to this paper has been partly funded by the CONICET and the University of Geneva (Coimbra Scholarship).

1 I use 'designation' in a rather broad way, as a word that applies to any kind of semantically relevant relation that might take place between linguistic expressions and appropriate items in the world, while I reserve 'reference' to describe the more specific kind of relation that is supposed to take place between, say, names, on the one hand, and, on the other hand, the objects they stand for. It should be noted here that such a terminology is by no means universally accepted; Devitt himself seems to favour a very different use of the terms, according to which, for instance, 'reference' stands for the more general notion we called 'designation' (cf. Devitt 1998).

2 I shall assume here that kinds are no more than a special class of properties. The most important upholders of identity of designation views include Linsky (1984), LaPorte (2000), Salmon (2005) and López de Sa (2008a, 2008b).

3 Devitt (2005) and Gómez-Torrente (2006) have presented the most fully developed versions of essentialist views of predicative expression rigidity.

4 A prominent sceptic is Soames; see his (2002).

5 Gómez-Torrente (2006) has recently presented a defence of the essentialist proposal in which he tries to show that an essentialist conception of predicate rigidity would be able to explain the necessity of true identification sentences -or, at least, that it could explain such necessities to the same extent than the standard conception of singular term rigidity explains the necessity of true identities.

6 I think here mainly of some identity of designation theorists, such as LaPorte (2000), Salmon (2005) and López de Sa (2008a).


1. Devitt, M. (1998), "Reference", in Craig, E. (ed.), Routledge Encyclopaedia of Philosophy, London, Routledge.        [ Links ]

2. Devitt, M. (2005), "Rigid Application", Philosophical Studies, 125, pp. 139-165.        [ Links ]

3. Gómez-Torrente, M. (2006), "Rigidity and Essentiality", Mind, 115, pp. 227-259.        [ Links ]

4. Kripke, S. (1980), Naming and Necessity, Cambridge, Mass., Harvard University Press.        [ Links ]

5. LaPorte, J. (2000), "Rigidity and Kind", Philosophical Studies, 97, pp. 293-316.        [ Links ]

6. López de Sa, D. (2008a), "The Over-Generalization Problem: Predicates Rigidly Signifying the 'Unnatural'", Synthese, 163, pp. 263-272.        [ Links ]

7. López de Sa, D. (2008b), "Rigidity for Predicates and the Trivialization Problem", Philosophers Imprint, 8, Nº 1.        [ Links ]

8. Linsky, B. (1984), "General Terms as Designators", Pacific Philosophical Quarterly, 65, pp. 259-276.        [ Links ]

9. Salmon, N. (2005), "Are General Terms Rigid?", Linguistics and Philosophy, 28, pp. 117-134.        [ Links ]

10. Schwartz, S. (2002), "Kinds, General Terms and Rigidity: A Reply to LaPorte", Philosophical Studies, 109, pp. 265-277.        [ Links ]

11. Soames, S. (2002), Beyond Rigidity, Oxford, Oxford University Press.        [ Links ]

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