SIMPOSIUM

General term rigidity as identity of designation:
Some comments on Devitt's criticisms^*

Eleonora Orlando

Universidad de Buenos Aires - CONICET - GAF
e_orlando@fibertel.com.ar

Abstract

In his paper "Rigid Application", Michael Devitt defends a particular version of the socalled 'essentialist conception' of rigidity for general terms, according to which rigid general terms are rigid appliers, namely, terms that if they apply to an object in any possible world then they apply to that object in every possible in which the object exists. Devitt thinks that the thereby defined notion of rigidity makes for an adequate extension to general terms of Kripke's notion, originally defined for singular ones, inasmuch as it serves to accomplish its same primary task: namely, "to distinguish terms that are not covered by a description theory from ones that are". He then criticizes the alternative conception of rigidity for general terms as identity of designation -specifically, LaPorte´s (2000) version- on the basis of its entanglement with some controversial metaphysical theses regarding the existence of universals -including a commitment to a selective realism concerning them. In this paper, I try to defend the identity of designation conception from his criticisms: with this aim, I propose a version different from LaPorte's, and claim it to be the best one to accomplish the above-mentioned primary semantic task, namely, the one of showing that some general terms, just like most ordinary names, cannot be accounted for in descriptive terms.

KEY WORDS: General term; Rigidity; Designation; Non-descriptiveness.

Resumen

En su artículo "Rigid Application", Michael Devitt defiende una versión particular de la llamada 'concepción esencialista' de la rigidez para términos generales, según la cual los términos generales rígidos son aplicadores rígidos, esto es, términos que si se aplican a un objeto en algún mundo posible, se aplican a ese objeto en todos los mundos posibles en los que existe. Devitt considera que tal noción de rigidez constituye una adecuada extensión del concepto kripkeano, definido originalmente para términos singulares, en la medida en que permite cumplir la misma función semántica fundamental que aquél: distinguir a los términos que pueden ser explicados mediante una teoría descriptivista de aquéllos para los cuales eso no es posible. De este modo, critica la concepción alternativa de la rigidez para términos generales, basada en la idea de identidad de designación -en la versión de LaPorte (2000)-, a la cual acusa de estar comprometida con discutibles tesis metafísicas, incluido un realismo selectivo acerca de los universales. En este trabajo, me propongo defender a esta concepción de sus críticas, para lo cual presento una versión de la misma diferente de la de LaPorte. En mi opinión, la versión propuesta supera además a la definición de rigidez ofrecida por Devitt en el logro de su objetivo principal, a saber, mostrar que algunos términos generales, al igual que la mayor parte de los nombres ordinarios, no pueden ser explicados en términos descriptivistas.

PALABRAS CLAVE: Términos generales; Rigidez; Designación; No descriptividad.

As stated in the previous introduction, in his paper "Rigid Application", Michael Devitt defends a version of the so-called 'essentialist conception' of rigidity for general terms. In general, that conception takes rigid general terms to be essentialist ones, namely, terms that express essential properties of an object or properties that an object has in all the possible worlds in which it exists. The particular version defended by Devitt conceives of rigid general terms as rigidappliers, where "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 in which the object exists" (Devitt 2005, p. 146). According to him, the thereby defined notion of rigidity makes for an adequate extension to general terms of Kripke´s notion, originally defined for singular ones, inasmuch as it serves to accomplish its same primary task: namely, "to distinguish terms that are not covered by a description theory from ones that are". Moreover, he criticizes the alternative conception of rigidity for general terms as identity of designation -specifically, LaPorte's (2000) version- on the basis of its entanglement with some controversial metaphysical theses regarding the existence of universals, including a commitment to a selective realism concerning them. In this paper, I will try to defend the identity of designation conception from his criticisms: with this aim, I propose a version different from LaPorte's, and claim it to be the best one to accomplish the above-mentioned primary semantic task, namely, the one of showing that some general terms, just like most ordinary names, cannot be accounted for in descriptive terms.
The structure will be the following one. In the first part, I'll offer an argument in favor of the rigid/no-rigid distinction that makes it manifest its relation to the non-descriptive/descriptive one. In the second part, I show that the proposed definition of general term rigidity can overcome the trivialization problem without appealing to selective realism-contrarily to Devitt's opinion. Finally, I argue that the proposed definition is in better condition than essentialism to satisfy what I agree with Devitt to consider its primary task, namely, distinguishing terms that are not covered by a description theory from ones that are.

1. An Argument for the Identity of Designation Conception

As is known, the rigid/non-rigid distinction is usually ascribed the theoretical task of accounting for certain closely interrelated phenomena concerning the use of singular terms, among which the difference in our intuitive interpretation and evaluation of statements containing names and descriptions relatively to counterfactual circumstances plays a prominent role. In terms of an example, on the one hand, we intuitively take

(1) Aristotle wrote many philosophy books

to be a statement about Aristotle, even with respect to a counterfactual world in which Aristotle died at the age of 4 and someone else taught Alexander the Great and wrote many philosophy books, and we intuitively evaluate it as false with respect to that world; on the other hand, we intuitively think that

(2) The teacher of Alexander the Great wrote many philosophy books

may be a statement about not Aristotle but whoever happened to teach Alexander the Great and write many philosophy books at the world in question, and we intuitively accept that it should be evaluated as true with respect to it -if the person in question in fact did write many philosophy books at the world at stake.¹ In my view, this intuitive difference can be taken to be the premise of an inference to the best explanation whose conclusion is the semantic distinction between rigid and non-rigid designators -according to which, as is also known from Kripke's work, names fall on the rigid side whereas descriptions -at least, on their narrowscope interpretation and if they do not pick out their objects by properties that the objects necessarily satisfy uniquely, namely, if they are not de facto rigid- fall on the non-rigid one.² Now, my present point is that there is an analogous difference in our intuitive interpretation and evaluation, relatively to counterfactual circumstances, of statements containing different kinds of general terms.
As an instance, on the one hand, we intuitively take

(3) There are red apples

to be a statement about red apples, even with respect to a counterfactual world in which, due to a special atmospheric phenomenon, things have stopped looking red to us, and we intuitively evaluate it as false with respect to that world; on the other hand, we intuitively think that

(4) There are apples that are Lucio's favorite color³

may be a statement about not red apples but apples of whatever color happened to be preferred by Lucio at the world in question: for instance, relatively to a world in which Lucio prefers green to red, (4) is intuitively interpreted as a statement about green apples and evaluated as true with respect to it. To put it in other words, in the case of (3), we intuitively think that it ascribes a certain attribute to apples, namely, being red, relatively to both the described counterfactual circumstances and the actual world; in contrast, in the case of (4), we intuitively think that, relatively to the above-mentioned circumstances, it serves to ascribe the attribute of being green to apples, whereas relatively to the actual world it serves to ascribe them the attribute of being red, namely, a different one in each case, given that Lucio's color preferences vary across worlds.⁴
Therefore, through an inference to the best explanation, it is possible to establish the claim that there is a corresponding semantic distinction concerning general terms, according to which there are certain general terms that are related to the same properties or attributes of things both in the actual world and in counterfactual circumstances, whereas thereare others that are not. Inasmuch as the former allow us just to track the same property in all possible worlds, they can be considered to be rigid, whereas the latter, allowing us to pick out a different property in each possible world, can be taken to be non-rigid.
As I mentioned before, there are other, closely related phenomena, concerning our use of singular terms, which are usually accounted for in terms of the rigid/non-rigid distinction as well. One of them is the difference in our intuitive interpretation and evaluation of certain pairs of statements containing modal operators. To put an example, on the one hand, we intuitively take

(5) It might have been the case that Aristotle did not teach Alexander the Great

to be a statement about Aristotle and evaluate it as true; on the other hand,

(6) It might have been the case that the teacher of Alexander the Great did not teach Alexander the Great

can be intuitively taken to be a statement about whoever might have taught Alexander the Great -certainly, somebody different from Aristotle- and evaluated as false -since the person in question could not help having the property of having taught Alexander the Great-; in other words, (6), in contrast with (5), has a possible false reading.⁵ Therefore, the rigid/nonrigid distinction among singular terms may also be inferred as the best explanation of this kind of phenomenon.
Now, it is interesting to note that a similar point holds for general terms. In terms of our previous example, it should be noticed that

(7) It might have been the case that red apples were not apples of Lucio's favorite color

is intuitively interpreted as a statement about red apples and evaluated as true, on the basis of the possible existence of worlds in which red, contrarily to what happens in the actual world, is not Lucio's favorite color; on the other hand,

(8) It might have been the case that apples of Lucio's favorite color were not apples of Lucio's favorite color

can be intuitively interpreted as a statement about apples of whatever color happens to be preferred by Lucio at a certain world -certainly, of a color such as green, namely, a color different from red, the one that he actually prefers-, and, inasmuch as those apples could not help being of whatever color happens to be preferred by Lucio at the world in question, the statement will be considered false.⁶ Consequently, it is also possible to infer the rigid/non-rigid distinction among general terms as the best explanation of this kind of difference.
The close relationship between the two illustrated phenomena should be clear enough: interpreting and evaluating 'Aristotle did not teach Alexander the Great' relatively to a counterfactual world in which Aristotle died at the age of 4 amounts to interpreting and evaluating 'It might have been the case that Aristotle did not teach Alexander the Great' or 'Aristotle might not have taught Alexander the Great'. Likewise, interpreting and evaluating 'Red apples are not apples of Lucio's favorite color' relatively to a counterfactual world in which Lucio prefers green to red amounts to interpreting and evaluating 'It might have been the case that red apples were not apples of Lucio's favorite color' or 'Red apples might not have been apples of Lucio's favorite color'.⁷

In sum, the difference in the intuitive interpretation and evaluation, relatively to counterfactual circumstances, of statements containing different kinds of singular and general terms is hereby taken to be both (i) the premise of an inference to the best explanation whose conclusion is the theoretical rigid/non-rigid distinction, and, accordingly, (ii) an intuitive test for theoretically classifying certain expressions -'Aristotle', 'red'- as rigid and certain others -'the teacher of Alexander the Great', 'Lucio's favorite color', in predicative use, as exemplified above- as non-rigid.
Moreover, as must be remembered, the difference at stake has been exploited in Kripke's modal argument against description theories of meaning for names. To put it in a nutshell, ordinary names are -de iure or semantically- rigid designators, whereas ordinary definite descriptions are non-rigid ones; consequently, it makes no sense to try to explain, as intended by description theories, the meaning of names in terms of associated descriptions. It is thus clear that, according to Kripke, singular terms are classified as rigid or non-rigid, at least partly, on the basis of their non-descriptive or descriptive character respectively. Likewise, the difference revealed by the above-mentioned intuitions concerning general terms may be regarded as grounded on the absence or presence of a descriptive component in the expressions respectively involved. In other words, following Kripke, general terms can also be classified as rigid or non-rigid, at least partly, on the basis of their non-descriptive or descriptive character respectively.⁸ It might be thus possible to distinguish the rigid referential general terms -such as 'red'- from the non-rigid descriptive ones -such as 'Lucio's favorite color'.

Some clarificatory points are in order.
First of all, as before mentioned, some authors have objected to Kripke's modal argument against description theories (Sosa 2001).
According to this critical perspective, the rigidity of names is compatible with their being semantically equivalent to (wide-scope interpreted) descriptions. At this point, I would like to remain neutral on whether Kripke's argument is a sound one or not: my present point is that on the assumption that it works for singular terms, a parallel argument can be built up for general ones.
Secondly, another important aspect must be pointed out: in saying that, according to Kripke, non-descriptiveness is what grounds rigidity, I am restricting the claim to ordinary names and usual kind terms. I do not intend to deny that Kripke has clearly acknowledged that there are other sources of rigidity for singular terms, such as the presence of a rigidifying operator -'the actual president of the USA'-, the existence of essentialist descriptions -such as 'the product of the union of ovule X and spermatozoid Y'- or descriptions taking wide scope over modal operators -as may be the case with (6) above-, but those are sources of rigidity for descriptions, not for names: in their case, the source of rigidity is, according to Kripke, their non-descriptive character.
Likewise, it is clear that there are other sources of rigidity for general terms, such as the presence of a rigidifying operator -'Lucio's actual favorite color'-, the existence of essentialist descriptive terms -such as 'sample of the substance with atomic number 79'- or descriptive kind terms taking wide scope over modal operators -as may be the case with (8) above. But those are sources of rigidity for descriptive kind terms, not for referential ones: in their case, the source of rigidity is their nondescriptive character.

To summarize the present section, our intuitions concerning both (i) our interpretation and evaluation of statements containing general terms relatively to counterfactual circumstances and (ii) our interpretation and evaluation of modal statements containing them can be taken to ground a theoretical classification of such terms into rigid and non-rigidones -analogous to the famous classification concerning singular terms. Moreover, the classification in question can be regarded as grounded, as proposed by Kripke as far as singular terms were concerned, on their respective non-descriptive and descriptive character. According to this, whereas among singular terms we can distinguish the rigid names from the non-rigid (ordinary) descriptions, among general ones we might distinguish the rigid referential from the non-rigid (ordinary) descriptive kind terms.

2. The Trivialization Problem: a Non-Metaphysical Solution

It has been objected that 'Lucio's favorite color' can be taken to designate in each world the property of being of whatever color happens to be preferred by Lucio at the world in question, namely, one and the same property in all worlds. Since this can be generalized, the upshot is that, on the identity of designation approach, all general terms turn out to be rigid, what seems to deprive the notion of rigidity of any theoretical interest. This is known as 'the trivialization problem'. Now, inasmuch as the present proposal is a particular version of that general approach, it may appear to be threatened by the above-mentioned problem: to put it in terms of our example, why not think that a so-called 'descriptive general term' such as 'Lucio's favorite color' is rigid insofar as it is semantically related to the property of being of whatever color happens to be preferred by Lucio in all the worlds?⁹
Now, according to Devitt, the problem at stake can only be solved by adopting a selective realism, namely, a metaphysical position that is committed to the existence of some properties -the sparse or natural ones-, like being red, but not others -the abundant or non-natural ones-, like being of whatever color happens to be preferred by Lucio.¹⁰ This is clearly stated in the following fragment against LaPorte's version of the identity of designation conception:

This proposal avoids trivializing rigidity by claiming that some kind terms like 'beverage my uncle requests at Super Bowl parties' are not rigid. But what is the basis for this claim? Suppose that among the kinds there is not only the soda kind but also the different beveragemy-uncle-requests-at-Super-Bowl-parties kind (which happens to be coextensive with the soda kind in the actual world). For short, call this kind "BMURASP." Then, in the actual world, 'beverage my uncle requests at Super Bowl parties' would not designate the soda kind because the soda kind happens to satisfy a particular description. Rather it would designate the BMURASP kind. Indeed it would designate the BMURASP kind in all possible worlds: it would be rigid. So the semantic issue of whether this term is rigid comes down to the issue of whether the BMURASP kind exists and is distinct from the soda kind. A totally "unselective realist" about "universals" -roughly, a universal for every predicate- will think that there is indeed a distinct BMURASP kind with the result that the term is rigid after all. LaPorte's claim that the term is not rigid requires a "selective realism" that rules out the existence of the distinct BMURASP kind. So the choice between these claims comes down to a controversial metaphysical issue in the theory of universals. LaPorte's proposal seems to leave the rigidity issue with no substance beyond this metaphysical issue.¹¹

First of all, there is no need for LaPorte -or any other supporter of the identity of designation conception- to conceive of properties in terms of universals: there are other available options as far as the nature of properties is concerned -more specifically, he may defend the theory of tropes or a version of nominalism, such as resemblance nominalism. Secondly, am I committed to the selective realist kind of solution? In what follows, I will try to show that the particular version of the identity of designation conception that I want to defend can give a different, nonmetaphysical answer to the trivialization problem. ^12-13 In arguing for this, I will appeal to a distinction made by Perry concerning singular terms (Perry 2001), belonging, as is known, in the direct reference tradition.¹⁴ My main point will be the following one: if Perry's distinction can do its job with respect to singular terms, a parallel distinction can be taken to do a similar job concerning general ones. In other words, I think that, on the assumption that Perry's distinction can be taken to introduce a correct and significant distinction among singular terms, an analogous one among general terms could be put forward. The viability of my non-metaphysical solution is dependent on that assumption.
As is known, according to Perry, taking into account their respective mechanisms of designation, grammatically singular terms can be classified into two different groups: the naming expressions and the denoting ones (Perry 2001, pp. 30-31). On the one hand, names are naming expressions: they directly name individuals; on the other, descriptions are denoting expressions: they denote individuals by means of expressing/connoting properties uniquely belonging to them, namely, identifying conditions.^15-16 Therefore, a name is in principle related to just the individual being named, whereas a description is related to two kinds of entities by means of two kinds of relations: the property being expressed and the individual being denoted. Therefore, designation is hereby taken to be a generic relation for singular terms: different kinds of singular terms hold more specific relations to different aspects of reality -in particular, names name individuals, whereas descriptions both express/connote properties and denote individuals. Moreover, the former are rigid, whereas the latter are usually -aside from the special cases mentioned before- non-rigid.
Now, on a parallel to the distinction between mechanisms of  designation concerning singular terms, I would like to distinguish mechanisms of expression concerning general ones. Taking those mechanisms into account, a referential general term may be said to (directly) name a property, whereas a descriptive one may be considered to denote a property by means of expressing/connoting a different, more complex one. Consequently, expression is hereby taken to be a generic relation for general terms: different kinds of general terms hold more specific relations to different aspects of reality.
Likewise, as we have seen in the previous section, on the one hand, referential general terms are rigid; hence, a rigid general term is one that directly names the property it expresses, the only one it is related to in all worlds. In terms of our example, 'red' is related just to the property of being red in all possible worlds, and can be thus said to directly name it in all of them. On the other hand, descriptive general terms are usually -again, aside from the special cases above mentioned- non-rigid. More specifically, I will call them functional-descriptive ones, inasmuch as I take them to abbreviate the description of a certain function or functional property -the property expressed in all the possible worlds-, which is realized by different basic properties at each world -the property denoted in each of them-. Regarding functional properties I could subscribe to what Schnieder has to say about what he mostly describes as relational ones:

[...] we may say that these properties possess a varying basis; with respect to different possible worlds there are different properties such that in virtue of possessing them, an object possesses the relational property.¹⁷

This makes sufficiently clear that functional properties are not properties of properties but properties of objects, with the peculiarity that they are properties that objects have in virtue of having other, more basic properties: to give an example, my car has the property of being of whatever color happens to be preferred by Lucio because it has the property of being red -and not the other way around.
I would then say that 'Lucio's favorite color' expresses one and the same functional property, namely, being of whatever color happens to be preferred by Lucio, in all worlds, whereas it denotes a different color property in each one, namely, the one playing the function of being significant in Lucio's aesthetic and emotional life at the world in question -in the actual world, the property of being red. Likewise, 'the liquid that fills the lakes and rivers' expresses the functional property of being a sample of the liquid that fills the lakes and rivers in all worlds, while denoting a different natural property in each one, namely, the one playing the function of filling the lakes and rivers at the world in question -in the actual world, the property of being water. In a close analogy with a description, which is related to two kinds of entities -an individual and a property- by means of two kinds of relations, a descriptive general term is thus related to two kinds of properties by means of two kinds of relations: the functional property it expresses in all worlds and the different, basicproperties it denotes in each one.^18-19
It is worth emphasizing that saying that 'red' designates rigidly what 'Lucio's favorite color' designates non-rigidly is, from my perspective, just a shorthand for saying what I would rather express in the following terms: 'red' names or refer to the property that 'Lucio's favorite color' denotes, that is, being red. The claim does not imply that both terms are related just to one property: 'Lucio's favorite color' is also related, by means of the expression/connotation relation, to another property, namely, the property of being of whatever color happens to be preferred by Lucio. Therefore, my position does not involve an identification of the properties of being red and being of whatever color happens to be preferred by Lucio.²⁰
The above-mentioned non-metaphysical solution to the trivialization problem is thus pretty straightforward: 'Lucio's favorite color' expresses the functional property of being of whatever color happens to be preferred by Lucio in all the worlds but cannot be considered to name it, because it denotes a different color property in each world, namely, the specific color that happens to be preferred by Lucio at the world at stake. It is this second feature -and not the alleged non-existence of the property of being of whatever color happens to be preferred by Lucio- that makes it non-rigid.²¹ Once again, the present proposal not only does not exclude but is perfectly compatible with an ontological commitment to the existence of what have been called 'abundant' or 'non-natural' properties -such as the property of being of whatever color happens to be preferred by Lucio.
It is important to bear in mind that to solve the trivialization problem it is enough to count on at least some non-rigid terms: the problem is solved by any position, like the present one, entailing that descriptive general terms are non-rigid. In other words, the trivialization problem should be clearly distinguished from the overgeneralization one, namely, the problem involved by any theory entailing that there are more rigid general terms than the ones originally identified by Kripke as such: the natural kind ones. Another question is thus whether the present account turns out to be undermined by that problem, a clear different one.
My first point against Devitt can be thus put in the following terms: it does not seem to be the case that a supporter of any version of the identity of designation conception has to either concede that the notion of rigidity is trivial as far as general terms are concerned or subscribe to a selective realism -according to which the properties that exist are just the natural or sparse ones.

3. On the Theoretical Purpose of General Term Rigidity

I shall argue that the above-mentioned definition provides us with a concept of rigidity for general terms that serves what I agree with Devitt to regard as the main theoretical purpose that such concept must serve, namely, "to distinguish kind terms that are not covered by a description theory from ones that are". Consequently, although I agree with Devitt on the main theoretical purpose that the concept is supposed to serve, I don't agree with him in thinking that the purpose in question can only be served by subscribing to an essentialist conception. Moreover, I think that the explanation of why the above-defined concept achieves its basic objective is clearer than the one provided by Devitt to the effect that his essentialist concept does it.
Now, on the proposed account, general terms are classified into rigid and non-rigid on the basis of the absence or presence, respectively, of a descriptive component. To be more specific, general terms are classified as rigid and non-rigid on the basis of the differences in our intuitive interpretation and evaluation, relatively to counterfactual circumstances, of statements containing them, and such differences are in turn grounded on the absence or presence of a descriptive component in the terms respectively involved. Accordingly, as we have seen, the rigid terms turn out to be the referential ones, whereas the non-rigid terms turn out to be the (functional-) descriptive ones. As should be then clear, the criterion involved allows us to say that rigid general terms, precisely because they are non-descriptive ones, cannot be covered by a description theory, whereas non-rigid ones, in as far as they are descriptive, are suitable for being explained by a theory of the likes. This is exactly the theoretical objective that the notion of rigidity for general terms was asked to achieve in the first place, namely, distinguishing terms that are not covered by a description theory from ones that are.
On the other hand, as before mentioned, from the standpoint of Devitt's essentialist conception, general terms are classified into rigid and non-rigid depending on whether they express, respectively, essential and accidental properties of an object; accordingly, rigid general terms are essentialist terms, whereas non-rigid general terms are non-essentialist ones. More strictly, insofar as Devitt is fond of neither properties nor property-talk, he prefers to state the position as specified above: rigid general terms are rigid appliers, namely, terms that apply to objects in all the worlds in which they exist (if they apply to them in any world). In both cases, the idea is that a rigid term is related to a feature that an object could not help having unless it ceased to be the object it is.
It is worth noticing, though, that there does not seem to be any clear reason why the essentialist or non-essentialist character of a general term should have any conceptual relation to - let alone determine- its aptitude for being explained in terms of a description theory. In terms of some examples, a general term may be an essentialist one -hence, rigid, according to essentialism- and be nonetheless explainable by a description theory, as is the case with 'rational animal' and 'different from Plato'; conversely, a general term may be a non-essentialist one -hence, non-rigid, according to essentialism- and be nonetheless not explainable by a description theory, as is the case with 'red'. This is as it should be, since there does not seem to be any reason to expect, on the one hand, essentiality to be conceptually related to non-descriptiveness, and, on the other hand, non-essentiality, to descriptiveness.
It is also interesting to notice that a general term such as 'sample of the product of the union of ovule X and spermatozoid Y' turns out to be rigid on both the essentialist and the identity of designation accounts, but for different reasons. From the perspective of the essentialist conception, it is rigid because it expresses an essential property of an individual so that the term applies to her in all the worlds in which she exists (if in any); on the present approach, it is an exceptionally rigid descriptive general term: not only does it express the same functional property in all worlds -namely, being a sample of the product of the union of ovule X and spermatozoid Y- but it also denotes the same basic property -namely, being a certain person, such as, for instance, being Queen Elizabeth I- in all of them.²² As I said before, the existence of essentialist descriptive terms is a source of rigidity for descriptive kind terms, which are usually non-rigid. Likewise, 'water' turns out to be rigid on both accounts, for clearly different reasons. The essentialist takes it to be rigid inasmuch as it expresses an essential property of a sample, namely, being water: as said before, no sample of water can cease to be water without thereby ceasing to exist as the sample it is. On the approach here defended, 'water' is rigid because it is semantically related to one and the same basic property, being water, in all possible worlds, so that it can be taken to directly name or refer to it in all of them.
Let's take stock of my second point against Devitt's stance on the matter. I think that, contrarily to what he thinks, a concept of rigidity defined in terms of the identity of the property named or referred to in all the possible worlds can achieve the main theoretical purpose agreed on for such a concept, namely, distinguishing the general terms that are covered by a description theory from the ones that are not. Moreover, I think that the aim in question is clearly achieved by the concept hereby proposed, since it allows us to identify the subset of rigid terms with the non-descriptive ones and the subset of non-rigid terms with the descriptive ones. In contrast, it is not so clear that it can be achieved by a concept, such as Devitt's, involving the identification of the subset of rigid general terms with the essentialist ones and the subset of non-rigid terms with the non-essentialist ones.

Notes

* I want to thank Max Freund, Dan López de Sa, Gonzalo Rodriguez-Pereyra, Benjamin Schnieder and Ezequiel Zerbudis for their very helpful comments to different versions of the present paper. Special thanks are due to Michael Devitt, for his careful reading, his detailed and interesting comments and his encouraging attitude. Funding for the research done has been provided by both the PIP 204, subsidized by the CONICET, and the UBACyT F 123, subsidized by the University of Buenos Aires.

1 By 'intuitive interpretation and evaluation' I mean the competent speaker's judgments about the content of statements belonging in the language in which she is competent, as much as her intuitive assignments of truth-values to such statements.

2 If (2) were taken to contain an implicit modal operator -'with respect to the counterfactual world w'-, it should be said that the above-mentioned intuitive interpretation of the statement corresponds just to the narrow-scope reading of the description, namely, to the reading in which it is interpreted as having narrower scope than the modal operator in question. While defending the view that the rigidity of names is compatible with their being semantically equivalent to wide-scope interpreted descriptions, Sosa points out that Russell's theory implies that any sentence containing a definite description and a modal operator has a scope ambiguity, and he argues that on the wide-scope reading of the description -in Russell's terms, when the description has primary occurrence-, it can be taken to work semantically like a name -and be thus as much rigid as a name (Sosa 2001). Now, even if Sosa's argument were sound -and hence names could be considered to be semantically equivalent to wide-scope interpreted descriptions-, Kripke's contrast would still hold between names and narrow-scope interpreted descriptions: the former are rigid expressions whereas the latter are clearly non-rigid ones.

3 A very important clarificatory point: I take general terms to be essentially predicative; accordingly, they should not be confused with their respective nominalizations, nominal forms or canonical designators. The difference at stake in exemplified by the following sentences: 'This apple is red' -predicative use of the general term 'red'- and 'Redness/the property of being red is a color property' -nominalization of the general term 'red', which may result, for instance, either from substituting the adjective for an abstract substantive or by using the words 'the property of...'-. Likewise, it is necessary to distinguish between the uses exemplified by 'There are apples that are Lucio's favorite color' -predicative use of the general term 'Lucio's favorite color'- and 'Lucio's favorite color/the property of being of whatever color happens to be preferred by Lucio is my favorite one' -nominal form of the general term 'Lucio's favorite color'-. Throughout the paper, I will consider that 'Lucio's favorite color' -as it occurs in sentences such as (4)- is to be classified as a general term. For an argument for this position see Salmon (2005). Notice that mass terms, like 'water' and 'the liquid that fills the lakes and rivers', are easily confused with their (respective) canonical designators, which should not be taken to imply that they do not have clear predicative uses -such as the use of 'water' in 'This is water'.

4 As before, on the assumption that (4) contains an implicit modal operator -'with respect to counterfactual world w'-, it should be taken to be ambiguous between a widescope interpretation of the descriptive general term and a narrow-scope one. The abovementioned intuitive interpretation, under which the term turns out to be non-rigid, is meant to capture just the latter reading -but not the former one.

5 Once again, (6) is considered to have a scope-ambiguity: it is false on the narrowscope interpretation of the description -namely when the modal operator has wider scope than the description-, whereas it is true on its wide-scope one -when it has wider scope than the modal operator. It is then the narrow-scope interpretation of descriptions -hereby taken to be an intuitive one- that makes for a clear contrast between them and names.

6 Likewise, we may think that (8) provides us with an example of scope ambiguity: on the one hand, it has a false reading corresponding to the narrow-scope interpretation of the descriptive general term; on the other, it also has a true one based on the wide-scope interpretation of the term in question. Moreover, following Sosa (2001), we might think that on its true reading the descriptive term, that is, 'Lucio's favorite color', is rigid and semantically equivalent to the simple one, namely, 'red' - on the assumption that Lucio prefers, as a matter of fact, red to any other color. I think we should object to this semantic equivalence, though, since we may think that rigid descriptive general terms are not semantically equivalent to rigid non-descriptive ones -as will be argued below, the former are related to two different properties, the property expressed and the property denoted, whereas the latter are related to just one property, the property named or referred to.

7 That is why simple sentences containing singular terms in subject position -such as 'Aristotle did not teach Alexander the Great', or the above 'Aristotle wrote many philosophy books'- can be taken to contain an implicit modal operator, as stated before. The same hold for other simple sentences containing general terms, namely, sentences that are not logically of the subject-predicate form but quantified ones -such as 'Red apples are not apples of Lucio's favorite color', or the previous 'There are red apples'.

8 I think that the ultimate explanation of the difference between rigid and non-rigid terms should appeal to the fact that the former but not the latter are introduced by mere stipulation (and without having in mind the description of a particular and specific function, as is the case with artificial kind terms). In this spirit, I subscribe to Martí's reflections: "The difference between the semantic behaviour of names and definite descriptions is a special case of a more general distinction between simple name-like expressions for which the ultimate explanation of why they apply to something is 'because that´s the way we call it' and expressions whose content determines their domain of application by virtue of the obtaining of certain facts or the satisfaction of certain (necessary or contingent) wordly conditions, a difference that applies to singularand to general terms equally. Thinking in terms of the Putnamian idealized model of introduction of a general term, we can say that someone decided to apply the word 'gold' to the original paradigms. But it is certainly not by decision that 'substance with atomic number 79' and 'wedding-ring material' apply to them. This consideration mirrors Russsell's remarks about 'Scott' and 'the author of Waverley'. [...]" (Martí 2004, pp. 132-133, the first emphasis is mine).

9 In LaPorte (2006)'s terms: "Perhaps there are 'unusual kinds', such as the kind species-typically-farmed-for-honey. This is not identical to the honeybee kind because, had some species of honey-thieving ants been farmed for honey more often than honeybees, the metaphysical extension of the honeybee kind would have contained all and only individual honeybees just as it does in fact, but the metaphysical extension of the unusual kind species-typically-farmed-for-honey would have contained some species of ant instead of honeybees. Suppose that there is a kind species-typicallyfarmed- for-honey. Why should not 'the species typically farmed for honey' be said to designate this unusual kind rigidly, rather than, as I would have it, to designate the honeybee kind non-rigidly?" (p. 324, the last emphasis is mine). It should be taken into account that LaPorte has stated his theory in terms of kinds rather than properties, and considers their designators to be not general but singular terms. But it is reasonable to assume that kinds are properties -as acknowledged by LaPorte himself- and that the same problem affects the predicative uses of such terms.

10 The classification of properties into sparse or natural and abundant or non-natural is taken from Lewis (1983).

11 Devitt (2005, p. 141).

12 The present proposal has similarities with the one offered by Martí in her (2004) paper, which does not involve a metaphysical commitment to sparse or genuine properties either (pp. 135-140).

13 LaPorte has also offered an alternative way out of the trivialization problem, though different from the one I will be defending in this paper (2006, section II, pp.324-328).

14 Perry in turn credits Genoveva Martí with it; see Perry (2001) footnote 10, p. 30.

15 As is known, in virtue of their specific kind of contribution to the truth-conditions of the statements in which they occur, definite descriptions are not considered to be semantically -that is, genuinely- singular terms.

16 I set aside the case of empty descriptions, namely, of descriptions that, for different reasons, do not denote any individual.

17 Schnieder (2005, p.13).

18 I prefer to classify properties into basic and functional, rather than classifying them into natural and non-natural/artificial/unusual ones -as done by LaPorte in the article quoted before, pp.325-328- because I think that some functional properties may also be natural ones -such as the above mentioned property of being a sample of the liquid that fills the lakes and rivers.

19 In her (2004) paper, Martí proposes a solution to the trivialization problem by making a similar distinction between the property expressed and the property designated by a general term. A difference between the present account and Martí's is that she conceives of properties in terms of intensions of different levels; according to her, the property expressed by 'Lucio's favorite color' would be a higher level function that assigns to each index a lower level function, the property designated, which in turn assigns to each index a set of things. It is not clear to me whether those abstract functions are considered to have metaphysical counterparts or not; in other terms, whether her proposal involves a metaphysical commitment to the existence of different kinds of properties or not. I tend to think that this is not the case.
On the other hand, I would not say that 'Lucio's favorite color' can be used rigidly to designate the property of being Lucio's favorite color: to me, 'Lucio's favorite color' is a non-rigid designator and cannot be thus used to rigidly designate anything at all. It can only be used to both express the property of being Lucio's favorite color and denote a more basic color property -such as being red-, namely, it can only be used as a nonrigid designator, with the two semantic properties that serve to characterize them. Mutatis mutandi, for 'the property of being Lucio's favorite color': from my perspective, it is one of the nominal forms of 'Lucio's favorite color' and as such it makes the same semantic contribution as the predicative form, through an analogous semantic mechanism, namely, it contributes the functional property it expresses in all worlds and denotes a different basic property in each world -on the assumption that Lucio's color preferences vary across them (see the discussion on page 136 of her article).

20 That may be the case with other versions of the identity of designation conception. See Schnieder's criticisms in his (2005, pp. 7-10). I agree with Schnieder on all his points, but I think that they are irrelevant to my version, which does not have the consequence that he criticizes.

21 Notice that an analogous claim can be held regarding definite descriptions: 'the teacher of Alexander the Great' expresses/connotes the same set of properties, constituted by the property of having taught Alexander and the property of being identical to any other individual who has that property, in all possible worlds, whereas it denotes a different individual in each world. The former feature does not make the description rigid, though, since having that kind of fixed meaning is compatible with having different denotata across the different possible worlds -which is usually thought to constitute its non-rigidity.

22 Even if they are taken to be one and the same property, the important point is that there are two semantic relations involved -the property in question would be both expressed and denoted.

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