Abstract
What does it mean for a general term to be rigid? It is argued by some that if we take general terms to designate their extensions, then almost no empirical general term will turn out to be rigid; and if we take them to designate some abstract entity, such as a kind, then it turns out that almost all general terms will be rigid. Various authors who pursue this line of reasoning have attempted to capture Kripke’s intent by defining a rigid general term as one that applies to the objects in its extension essentially. I argue that this account is significantly mistaken for various reasons: it conflates a metaphysical notion (essentialism) with a semantic one (rigidity); it fails to countenance the fact that any term can be introduced into a language by stipulating that it be a rigid designator; it limits the extension of rigid terms so much that terms such as ‘meter’, ‘rectangle’, ‘truth’, etc. do not turn out to be rigid, when they obviously are; and it wrongly concentrates on the predicative use of a general term in applying a certain test offered by Kripke to determine whether a term is rigid.
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Notes
An early advocate of this view is Cook (1980). He argues that the term ‘cat’ designates each and every cat, making the term world-relative, but nonetheless it is rigid given that any individual cat in a world is a cat in any other world in which it exists. More recently Devitt (2005) has revived this view by introducing the notion of “rigid application”. Since I wish to separate issues concerning essentialism from that of rigidity, I take Devitt’s terminology to be misleading, and thus I prefer to call such predicates “essential predicates”. Cordy (2004), on the other hand, finds Cook’s account insufficient. He distinguishes between three types of rigidity, and claims that for a general term to be “fully rigid” it must meet two conditions, one of which is what he calls the “extension condition” (p. 251) which implies that the term serves as an essential predicate. So despite the fact that he does not subscribe to EVR, he takes the essentiality of a predicate to be a necessary (but not sufficient) condition for its being fully rigid. Since on my view for a general term to be rigid, it is neither necessary nor sufficient for it to be an essential predicate, my argument has bearing on his account as well. Soames (2002, pp. 250–259) considers this account and then rejects it.
Soames (2002, p. 259) claims that there are terms such as ‘hotter than’ which would be expected to be rigid, that do not apply to its objects essentially. As I argue in the text, this is just the tip of the iceberg; in fact there are many other terms that do not turn out to be rigid on EVR, some of which Kripke explicitly claims to be so.
Some hold that two general terms can never be flanked with the identity sign. On this view ‘water is H2O’ is a universally quantified sentence, stating that the two concepts are co-extensional. This, I believe, is not Kripke’s position. The issue becomes most explicit within the discussions on the mind–body problem. The famous Identity Theory is so-called not because its advocates think that mental state terms are co-extensional with certain brain-state terms, but rather because they hold that a mental state is identical with a brain state, i.e. they are one and the same thing. That is why their theory deserves that name. So when Kripke criticizes versions of the Identity Theory by arguing that a statement such as “pain is the stimulation of C-fibers” cannot be contingently true if both terms are rigid, he interprets the sentence to be expressing an identity statement, not a universal quantification.
I am not suggesting that the collection of molecules is identical with the tiger; that would violate the principle of the Indisernibility of Identicals. Rather what I claim is that the collection of molecules has the property of being (or constituting) a tiger, or simply that the term ‘tiger’ when used as a predicate applies to the collection of molecules.
Kripke’s discussion of the meter case may confuse certain readers. At times he uses “is” of identity (e.g. ‘the length of S is a meter’) and at other times the “is” of predication (e.g. ‘S is a meter long’). That he takes the former use as involving the “is” of identity is evident in a passage where he prefers to explicitly use the identity sign ‘=’ (Kripke 1980, p. 135). For his purposes this does not seem to matter, for either sentence could be used as an example of the contingent a priori, but for my purpose in the text the distinction of course is vital.
I take it that when we talk about a general term applying to an object, what we mean is that the object falls under the extension of the term. But when the general term is used as a name of an abstract entity, then it is quite misleading to say that the term “applies” to it: the term ‘meter’ applies to the stick, but it would be misleading to say that it applies to a certain length. Rather I prefer to say that it “designates” the length and “applies” to the stick.
As it will become clearer later, in order for an adjective such as “small” to be a rigid designator, we have to bring it to the subject position and use italicization so that the term designates a certain size rigidly. Whether adjectives are also rigid when they occupy the predicate position is a different issue, which I leave as an open question.
Kripke states the test in a slightly different way: if a sentence in the form ‘t might not have been t’ is such that the two readings we get by giving the modal operator wide and narrow scope yields different truth values, then the term t is not rigid, otherwise it is. (See Kripke 1980, p. 12n, and p. 62, especially n. 25). If we simplify this, we get the result that the sentence is false (when the modal operator is given narrow scope) in case the term is rigid, but true when it is not.
Though he does not explicitly talk about this ambiguity, Soames seems to think that Kripke was not clear on which reading is intended. (See Soames 2002, p. 253.) The only textual evidence that Soames cites that seem to indicate the reading that the EVR advocates favor involves Kripke’s discussion of the term ‘pain’. I believe the reason why Kripke may appear as if he is not clear on which reading is intended is because he takes the term ‘pain’ to be both rigid and essential. The fact that Kripke gives the term ‘meter’ as an example of a rigid designator should be sufficient to conclude which reading he had intended.
See Salmon (2005, p. 121), where in response to Soames, he says “Soames’s discussion suffers from a failure to distinguish sharply between a general term like ‘tiger’ and its corresponding predicate ‘is a tiger’”.
An exception to this could perhaps be Fregean concepts, which according to Frege can not be referred to by a singular term.
Though it would be wrong to conclude that it does no work at all. If predicates in general turn out to be rigid designators, that should say something philosophically important about our use of language.
An interesting example of a rigidifying device is Frege’s ungerade operator. A contingent sentence non-rigidly designates a truth value, but when it enters into an oblique context, the reference-shifting ungerade operator makes the sentence rigidly refer to the thought that it expresses.
As I understand him, Salmon (2005) subscribes to this view.
This, I believe, is Frege’s view. Under Frege’s system a sentence in the simple subject-predicate form ‘a is F’ has two referring terms (not three), the subject term ‘a’ and the predicate term ‘__is F’ (including the gap). The predicate term refers to a concept (a function from objects to truth values) in virtue of the fact that it expresses a sense (which is also a function from singular senses to thoughts). So I believe that the general term ‘F’ is not a referring expression within the predicate for Frege. Furthermore it appears that properties are simply concepts on Frege’s view.
There may be contexts in which we use the term ‘bachelors’ in the subject position non-rigidly: If I say “bachelors are uniting to revolt against marriage”, I may wish to talk about a scattered collection of males, making the term non-rigid. I am inclined to think that in this case the term ‘bachelors’ neither designates a marital status, nor can be cashed out in terms of the predicate ‘is a bachelor’.
The further fact that ‘bachelors might not have been bachelors’ expresses a true statement when the modal operator is given narrow scope, says nothing about the rigidity status of the term ‘bachelorhood’, nor about the predicate ‘is a bachelor’. It only shows that the predicate ‘is a bachelor’ is not an essential predicate. If one takes this predicate to designate the property of being a bachelor, then it surely designates the same property in all possible worlds. But it would still be true to say that people who have this property might not have had this property. So the truth of ‘bachelors might not have been bachelors’ shows nothing about the rigidity status of the predicate ‘is a bachelor’.
This is Quine’s position in his Word and Object (Chapter III).
A good example is the way in which the term ‘helium’ was introduced: Pierre Jansen first found a bright yellow line in the spectrum of the light emitted by the solar chromosphere, which he thought to be a sodium line. Later the chemist Edward Frankland and the astronomer Joseph Lockyer concluded that the element was not sodium, but some other element that was not discovered on earth, and gave it the name ‘helios’, the Greek word for sun, which later turned into ‘helium’ Only afterwards did William Ramsey discover the existence of helium on earth. If this is historically accurate, then I believe that it should be correct to say that Lockyer and Frankland introduced the general term ‘helium’ not by ostension, but rather by fixing its reference by a description such as ‘the element that is causing the bright yellow light in the spectrum’. It seems clear to me that the description is non-rigid but the term ‘helium’ is rigid, which is good enough to conclude that they are not synonymous. Perhaps EVR could account for this, but that is because ‘is helium’ is an essential predicate. But quite clearly if we take any general term introduced by description that does not serve as a en essential predicate (such as ‘meter’), then no such account follows from EVR.
I am not suggesting that for every identity statement we derive its necessity or contingency by appealing to our intuitions concerning the rigidity of the terms within it. At times it may be just the other way around. Nonetheless it is an important theoretical fact that follows from Kripke’s view that there is a logical equivalence between “‘a’ and ‘b’ are rigid designators”, and “‘a = b’ is necessary, if true”.
There are also cases in which some may have no clear intuitions concerning the rigidity of the terms involved in an identity statement, nor about whether the statement is necessary or not. Examples concerning type-type identity statements used in the mind/body debate perhaps are as such. With respect to the sentence “pain is the stimulation of C-fibers” for instance, intuitions may diverge, but that is not to say that the notion of rigidity does no theoretical work in such cases. It puts the burden on those who argue that such sentences are contingently true—for example functionalists—, to account for the fact that at least one of the terms must then be non-rigid.
In his criticism of La Porte, this I believe is what Devitt has in mind: “The nominalist denies that kind terms designate any universals either rigidly or nonrigidly because she denies that there are any universals. So a proposal like La Porte’s fails to yield a distinction between rigid and nonrigid kind terms that is any use to the nominalist. Yet if there is a useful semantic distinction to be made here we might hope that it would be one that a nominalist could use.” (Devitt 2005, p. 143) Obviously, though it is addressed to La Porte, the criticism is a very general one against any account of rigidity based on abstract entities.
References
Cook, M. (1980). If ‘cat’ is a rigid designator, what does it designate? Philosophical Studies, 37, 61–64.
Cordy, B. S. (2004). Necessity and rigidly designating kind terms. Philosophical Studies, 119, 243–264.
Devitt, M. (2005). Rigid application. Philosophical Studies, 125, 139–165.
Kripke, S. A. (1980). Naming and necessity. Cambridge: Harvard University Press.
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Salmon, N. (1980). Reference and essence. Princeton: Princeton University Press.
Salmon, N. (2005). Are general terms rigid? Linguistics and Philosophy, 28, 117–134.
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Schwartz, S. P. (2002). Kinds, general terms, and rigidity: A reply to La Porte. Philosophical Studies, 109, 265–277.
Soames, S. (2002). Beyond rigidity: The unfinished semantic agenda of naming and necessity. New York: Oxford University Press.
Acknowledgements
I am grateful to Stephen Voss for his valuable comments on an earlier version of this paper. I would like to thank my graduate students in my Philosophical Logic seminar at Bogazici University for their support, as well as an anonymous referee for Philosophical Studies for his/her valuable suggestions that have significantly improved the text.
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Inan, I. Rigid general terms and essential predicates. Philos Stud 140, 213–228 (2008). https://doi.org/10.1007/s11098-007-9138-4
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DOI: https://doi.org/10.1007/s11098-007-9138-4