I. Introduction

In the present paper, I examine Nathan Salmon’s solution to the problem of trivialization, as it arises for conceptions of general term rigidity that construe it as identity of designation across possible worlds; and, in the process of doing so, I will also address some more general issues pertaining to the nature and semantic role of predicative expressions, something that is required if our discussion is to be based on sound ground. Before taking up these topics, anyway, let me first introduce some background considerations that will be useful for understanding what the problem Salmon tries to solve consists in, and the significance of his proposal.

As is well known, the two theses that some singular terms, paradigmatically names, are rigid designators, and that some predicative expressions, particularly natural kind ones, could also be taken as rigid, originate in Kripke’s introduction of the notion of rigidity in Naming and Necessity (^{Kripke 1980}). But, although the meaning of the first of these two theses has usually been taken to be relatively clear and straightforward, and its truth has almost universally been taken for granted, the second thesis, the one about natural kind terms, is more problematic because it is not very clear what its precise meaning could be: in effect, it is uncertain whether the notion of rigidity applies to predicative expressions in the first place and, if so, how it should be understood.¹ There is a problem here because, on the one hand, what Kripke defines is not just “rigidity” alone, but “rigid designator”, thereby implying that being a designator is a necessary condition for being rigid; but, on the other hand, it is not clear to what extent, and in what sense, predicative expressions could be taken to designate anything.

One can find in the literature on this issue at least two prima facie equally plausible proposals about how to understand predicate rigidity (and, in connection with it, predicate designation): on the one hand, there is a group of proposals that could be described as sameness of designation views, according to which a predicative expression is rigid if and only if it designates the same appropriate entity (a property or a kind) in every possible world, and it is non-rigid otherwise (this is the group to which Salmon’s proposal belongs)²; on the other hand, there is another group of proposals, the so called essentialist views, according to which a predicative expression will be considered rigid if and only if it behaves as if it expressed a property that is essential to anything that instantiates it, namely, if and only if, if the expression applies to (or designates) a particular object in some world, it applies to it in every possible world (in which it exists though some varieties of the notion drop this last constraint).³ We see, then, that each of these ways of construing the notion of rigidity takes different semantic relations, among those connecting general terms with non-linguistic items, as the relevant relation of designation with respect to which the notion is to be defined: in the first case, the privileged relation is the one taking place between a term and the property it expresses; in the other case, the privileged relation is that between the term and each of the individuals it is true of.

In any case, it should be noted that the trivialization problem mentioned at the beginning of this paper only raises a serious problem for “sameness of designation” proposals. In effect, it can be very plausibly assumed that the notion of rigidity, as the essentialists understand it, is not trivial, as not all predicates (at least prima facie) seem to stand for properties that are essential to anything that instantiates them (unless, of course, one adhered to the not very Kripkean metaphysical conception that all properties of particulars are essential to them). On the other hand, if the sameness of designation view amounts to the thesis that every predicative expression designates the property which it expresses, then it is plausible to suppose that, for any such expression, it designates that property rigidly: if “is blue” designates being blue, then it would seem that it designates that property with respect to every possible world; but then it is also reasonable to suppose that the same would happen with “is a bachelor”, which would rigidly designate being a bachelor, and with the (for some philosophers non-rigid) “is the colour of the sky”, which would (rigidly) designate the property of being of the same colour as the sky.

In what follows, I will first examine the considerations presented by Salmon in order to defend his view from the charge of trivialization, and will later try to single out the underlying assumptions that, in my view, explain why his argument doesn’t work. The consideration of these deeper assumptions, in particular of what it means for a term to be predicative, will have as a result that, nonetheless, some of Salmon’s examples, but only a few of them, are indeed non-rigid. Finally, I will give some reasons why this result might not be, anyway, such good news for the identity of designation theorist as it may at first sight seem to be.

2. Salmons's Proposal

As has been the case with other authors defending the sameness of designation view from the charge of trivialization, such as LaPorte, Linsky, López de Sa and Martí and Martinez, Salmon’s strategy also consists in trying to show that there are some expressions that are, at the same time, both general terms and non-rigid. I will consider in this section the arguments by means of which he tries to show, in the second section of his 2005, that one example, “the colour of the sky”, which it seems we could take as his “official” example, has both of these characteristics.

Salmon’s evidence for his view that the expression is a non-rigid general term is based on its behaviour in the first two premises of the following argument (that I will call “Argument (A)”):

According to Salmon, “the colour of the sky” has the value of a general term in (A1) because it occupies there a position completely analogous to the one that “blue” occupies in (A3), which is clearly a general term position (given that “blue” combines there with the “is” of predication to form a predicate, something that our author takes as “‘criterial’ of the distinction between singular and general terms” (2005, p. 123)). On the other hand, he also considers that term to be “manifestly non-rigid” (p. 122). This gets further support, moreover, from the fact that, on the one hand, the (allegedly second order) identity expressed by (A2) is only contingently true (as a result of which at least one of the terms involved in the identity should be non-rigid, “the colour of the sky” being the most obvious candidate); and that, on the other, given that (A3) seems to follow from (A1) and (A2) by Leibniz’s Law, it seems reasonable to suppose that the two tokens of “the colour of the sky” appearing there (the one after the “is” of predication in the first premise, the other after the “is” of identity in the second one) are instances of the same type, so that the properties that can be ascribed to that type, given the way in which it appears in one of the premises, can be held to belong to it in all its appearances.

I’m really not convinced by Salmon’s argument. On the one hand, it seems to me that, for Argument (A)’s validity to lend support to his view, it should be formally such that, just as it is, its conclusion should follow from its premises through a straightforward application of Leibniz’s Law, or Substitution of Equality. In my view, though, even if argument (A) is indeed valid, in the intuitive sense that it is impossible for its conclusion to be false in case its premises are true, it is not clear that it has the form required for Leibniz’s Law to apply to it directly, as Salmon’s view requires. For consider the following argument:

It is clear that (B3) could not be false if (B1) and (B2) are true, and that therefore the argument is valid in the intuitive sense mentioned above; but it does not follow from this, of course, that the argument is formally such as to yield, just as it is, the conclusion through an application of Leibniz’s Law: in order to achieve this, a certain connection must be established between “is wise” and “has wisdom” (for instance, following Salmon’s suggestion, through a corresponding “meaning postulate” to the effect that anything is wise iff it has wisdom). In any case, what I would like to stress here is that the intuitive validity of the argument, which can be conceded, cannot be seen as lending support to any conclusion as to the formal connections between, and the specific syntactic and logical profiles of, expressions such as “the virtue Socrates was most famous for” and “wise”. If this is so in this case, it seems reasonable to suppose that the same might happen, mutatis mutandis, in relation to the occurrences of “the colour of the sky” in Salmon’s (A).

On the other hand, and independently of the validity of the argument as a whole, doubts could also be raised concerning the reasons Salmon gives for his particular way of treating “blue” and “the colour of the sky” in each of the sentences making up (A) in particular, it seems to me that there are strong reasons to reject his view that both terms belong to the same formal category in each of their two appearances in the argument. I would rather like to argue that, while “blue” is clearly a general term in (A3), it is, on the contrary, a singular term in (A2), namely, just a name of the colour, which in that context it simply designates without ascribing it to any object. And something similar may be said of “the colour of the sky”, for similar reasons.

Before considering the status of these terms in any more detail, it will be convenient to try to get clearer about some notions that will be important in the discussion, namely, those of general term (or of a general term position), of a first or second order term, and of a predicative expression. As regards the first of these notions, we should remark that the issue of whether an expression is a general term, or of whether it occupies a general term position in a sentence, concerns primarily the level of (what we may call) a surface structure analysis of sentences, a level of analysis that should begin by the elucidation of what ^{Delia Graff Fara (2001)} has called the “argument structure” of a sentence (namely, the level concerned with sorting out the expressions that occupy argument positions, and those that do not), but that also includes distinguishing structures, and the suitable components to fill such structures, within those main constituents; in the particular case that interests us here, that of general terms, it seems that an expression should count as a general term if it combines with the “is” of predication to form monadic predicates.⁴ On the other hand, being first or second order seems to correspond to a different level of analysis, namely, that of the representation of a sentence’s truth conditions in a formal language whose syntactic categories are intended to reflect corresponding ontological categories; so that a referring expression would be first order if it designates an individual, and second order if it designates a property of individuals, and so on (this level of analysis would correspond to that of logical form, on some understanding of “logical form”).⁵ The notion of a predicative expression, finally, is rather more difficult to apprehend because it appears, with equal right, in both levels of analysis distinguished above; there seems to be a core idea in the notion, anyway (as we already hinted at in fn. 1 above), namely, that what makes a term predicative is that it is used not just to designate an item, but, characteristically, to ascribe it (potentially) to a plurality of other items (of an appropriate kind). As I have just said, this notion may be used in relation to both levels of analysis mentioned above: both some ordinary language expressions, distinguished by their behaviour at surface level, and some expressions of formalized languages, may be described as predicative. But while whole predicates would count as predicative on both levels, things appear different as regards general terms (or their formal counterparts), something that will be relevant in the discussion to follow: while both the predicates of ordinary language, and the general terms from which they are formed, may be characterized as having a predicative nature (both “wise” and “is wise” are such that, by their very nature, they may be ascribed to different particulars, contrasting, at this level, with referential expressions, which are those that occupy argument positions) only “is wise”, among the corresponding expressions in Salmon’s formalism, could be so characterised: according to his view, “wise” by itself apparently only designates the property of being wise.⁶

How do these different notions relate to one another? Salmon’s view seems to be that there is a structural match between ordinary language expressions, analysed at the level of surface structure, and their formal counterparts, analysed at the level of logical form (at least if the formalization is carried out with enough detail), and that second order referential expressions, just because of being second order, may play in the formalization the role of general terms.⁷ It seems to me, on the contrary, that ordinary language general terms, such as “blue” as it appears in (A3), are not referential expressions, that is, they are not expressions whose only semantic task consists in picking out an entity (of whatever kind) as a suitable object of discourse. I am not denying, in saying this, that general terms somehow pick out properties that play a role in an assessment of the expression’s semantic contribution; I think that this is so, but I also think that the expression’s contribution to a sentence’s meaning goes beyond that, as such expressions seem to have what we could call “ascriptive force” by themselves otherwise the explanation of a certain range of phenomena involving these terms would be rather strained. I shall not attempt to provide here a full defence of this view; but I shall offer, anyway, the following remarks to motivate it. Consider, first, “bare” uses of such terms, as when one exclaims “Disgusting!” when, say, reacting to someone’s behaviour; it seems that in these cases we clearly ascribe the property of being disgusting to such behaviour, even without the copula.⁸ On the other hand, we also characterize people and objects by using predicative expressions outside the sentence predicate, as when we say “Poor Pete lost all his money in the races”. Moreover, it would be difficult to understand why it would be natural to say that “My true love’s blue eyes are blue” is analytic, in the traditional sense according to which the predicate says (at least part of) what the subject term already said about its denotation, if the first “blue” weren’t already ascribing being blue to my true love’s eyes. And, finally, the traditional idea that the “is” of predication does not make a substantial (but just a formal) contribution to a sentence’s meaning would be equally difficult to account for.⁹

After these preliminary clarifications, let’s go back now to the analysis of the relevant examples.

3. Salmon’s Other Examples and Genuine Second Order Descriptions

Something similar to what we have found concerning “the colour of the sky” is also to be found, in my view, in most of the other examples of (allegedly) non-rigid predicative expressions presented by Salmon, such as “Henry’s favourite beverage” and “the chemical compound composed of two parts hydrogen, one part oxygen”. Indeed, it is not clear whether any of these ever appear in genuine predicative positions. For instance, a sentence such as “This is Henry’s favourite beverage”, uttered, say, in front of a can of beer, is most naturally understood, I think, not as ascribing a property to a particular amount of liquid referred to by “this”, but, on the contrary, as asserting the identity between the kind referred to by the indexical (arguably, (a specific kind of) beer) and the kind designated by “Henry’s favourite beverage”, a phrase which, as “the colour of the sky”, is most naturally taken in that context as a singular term.¹⁷

Be that as it may, it seems that we face a different situation in relation to another of the examples that he discusses, namely, with “what I am” as it appears in (H):¹⁸

(H) What I am is nauseous.

It seems to me that, contrary to what is the case, as we argued, in statements such as (A2) and (B2), this is a genuine second order identity sentence, and, in particular, that “what I am” is, in general but also in this context, a predicative expression.¹⁹ The reasons for thinking so could be expressed as follows: on the one hand, “nauseous” can only be construed as a general term, that is, as an expression typically used to ascribe properties (instead of being used to refer to them); but, on the other hand, the “is” that appears in (H) could not be understood as the “is” of predication (it does not combine with “nauseous” to form a predicate ascribing the property of being nauseous to the referent of “what I am”), but as the sign of (here: second order, or general term) identity. And, finally, “what I am” also functions typically, and perhaps exclusively, as a predicative expression, as, for example, in (I):

(I) He was what I am (sc. nauseous).

On the other hand, it seems that (H) is only contingently true (or false, as the case may be), given that I might have been something other than nauseous in the circumstances in which (H) was uttered, which by itself is enough to show that at least one of the two terms appearing in the identity is non-rigid; and, moreover, “what I am” seems the obvious candidate to be construed as the non-rigid term much more so, at any rate, than “nauseous” is.

If things are so, then, it seems that there are after all expressions that could be characterized as second order descriptions and that are, at the same time, both general terms and non-rigid, as a consequence of which the notion of general term rigidity would indeed turn out to be non-trivial. So that, after all, it seems that the materials for a solution to the trivialization problem were already available in Salmon’s paper, only that it is a solution slightly different from the one he explicitly endorsed there. It may be urged, however, that even if this different solution can withstand the difficulties raised above for the proposal based on examples such as “the colour of the sky”, there might still be some other objections that would be effective against the non-rigid, general term status of “what I am” and similar expressions. In the rest of this section, I consider a couple of such objections; in the end, it seems to me that all of them are faulty, and that the prima facie non-rigid general term character of these expressions could still be maintained after closer scrutiny.

What considerations could be adduced in favour of the view that examples like “what I am” do not after all undermine the general assumption that all predicative expressions are rigid? I can only think of the following three:

(i) A first such consideration would consist in supposing that a sentence like (H) is nothing other than a stylistic variation (or superficial transformation) of a canonical predication such as (K):

(K) I am nauseous.

Indeed, if this is correct, (H) could then be considered as having the same logical form as (K) (a form which, moreover, one has to assume to be accurately mirrored by the argument structure of (K)). On the other hand, given that “nauseous” is the only genuine general term in (K), and that it is an admittedly rigid general term, an example such as (H) would therefore not involve any threat to the idea that all general terms are rigid.

I don’t think that this strategy really succeeds. In the first place, notions such as that of (logical) form (or of representational structure) are notoriously dependent on the theoretical function they are expected to play. In this sense, it is clear that, for some purposes, (H) could be considered as having the same form or the same underlying structure that (K) has. But it should now be remembered that the phenomenon we are focusing on is a rather superficial one, that is, one that mainly concerns the surface structure of sentences, and that therefore, for our purposes, the fact that two sentences such as, say, “John is wise” and “John instantiates wisdom” are necessarily equivalent is no evidence that they have the same form in the relevant sense. This has direct application to our cases (H) and (K): from the fact that they are equivalent, and that “nauseous” appears predicatively in the latter (that is, in a non-argument position), it doesn’t follow that it must also appear predicatively in the former; on the contrary, precisely the fact that in the former “nauseous” appears in an argument position must be taken as a reason to take (H) to have a different form from (K).

(ii) A second reason that could be given in order to avoid the conclusion that some predicative expressions are non-rigid would consist in supposing that (H) should be construed as really expressing a metalinguistic statement, along the lines of (L):

(L) “Nauseous” may be used to complete the open formula “I am…" adequately.

I think that this proposal should be rejected for a number of reasons. First of all, we have the problems pertaining to the relations between logical equivalence and logical form that we already considered in relation to the previous proposal, something which applies here even more strongly because in this case the relevant sentences are not necessarily equivalent. But this proposal faces also a more specific problem, namely, that there simply seems to be no independent reason for accepting the metalinguistic reading as the standard, or even as an acceptable, reading of our sentence (H), over and above the circumstance that such a construal would allow us to keep the thesis that all predicative expressions are rigid. In fact, if (L) were the standard reading of sentences such as (H), one would expect that, if this is due to the fact that (H) is a pseudo-cleft sentence, (N) should then express the standard reading of (M):

(M) What I bought is a house.

(N) “A house” could be used to complete the open formula “I bought…” adequately.

But I cannot see any reason why one should believe that these sentences should be understood in this way; clearly, (M) is about some concrete thing that its utterer bought, presumably a house, but it is not about “a house”. Moreover, there seems to be no indication in the example that one could take as suggesting a metalinguistic construal, such as explicit mention of expressions or the use of predicates that could only apply to expressions, something which also applies to our initial example (H); it seems to follow, then, that this reading would be as little plausible in the latter case as in the former.

It is important to emphasize, again, that the only reason in favour of this construal seems to be the desire to safeguard the (initially intuitive enough) general assumption that only singular terms could occupy argument positions. But given that an example such as “what I am” behaves as a non-rigid general term is expected to behave, and that it can actually occupy what cannot be understood but as second order argument positions, the sensible policy seems to be simply to abandon the general rule as inadequate. Failing this, there is no genuine reason, then, to adopt the metalinguistic proposal.

(iii) A third way in which one could try to resist the conclusion that some predicative expressions are non-rigid would consist in holding that, even though in some contexts, as that exemplified by (H), in which it appears in an argument place, a general term such as “what I am” is indeed non-rigid, terms of that kind will nevertheless always be rigid when they appear in genuine predicative positions, such as in (O):

(O) He finally became what he had never been before (sc. happy/ a respected person).

The idea would be that “what he had never been before”, as it appears in (O), should not be understood as designating, as suggested by the expressions given between brackets, different properties in different circumstances (such as the properties of being happy or of being a respected person), but that, on the contrary, it should be taken as designating, instead, the same property across all possible worlds in this case, this property rigidly designated would be something like being what S had never been before t (where “S” and “t” are schematic letters that designate, rigidly, for every particular utterance, the speaker and time of the utterance of a token of the predicative expression in (O)).

What kind of considerations could help us decide between these two contrasting interpretations? I believe that the issue is of such a nature that it is difficult even to think of giving a conclusive answer. But, in my view, the evidence available suggests that the non-rigid interpretation is the right one.

First of all, it would seem that, in relation to this particular example, we can present a formally valid argument, based on Leibniz’s Law, of the kind that Salmon was looking for when he produced argument (A). Argument (P) would be such an argument:

It seems to me that we do not find here the problems that we met with when discussing argument (A), and that there seems to be nothing to suggest, as was the case in relation to that argument, that this one is not complete as it is. If things are so, then, one had better conclude that “what I am” is a non-rigid general term in both cases -as the contingent character of (P2) attests.

Moreover, the expressions between parentheses with which (O) ends seem to suggest that expressions of the kind of “what I am” are usually intended as replaceable by some other, more specific ones, which would, so to speak, give the “solutions” to the puzzles implicit in such assertions (which correspond to questions that the speaker anticipates the audience are implicitly asking themselves). That is, it is as though the utterer specifically used, at least in some cases, a deliberately roundabout manner to refer to a definite property he could have referred to in a much more straightforward way so that, in the case of (O), he should be taken as designating, according to what happens in the different worlds (and different contexts), the properties of being happy, or of being a respected person. And, as I said, it is clear that things are so at least in some cases and that is all we need here.²⁰

4. Conclusions

We have examined, then, in the first place, the arguments by means of which Nathan Salmon has tried to show that predicative expressions are not trivially rigid, and we have found them partially unsatisfactory. He argues in favour of the non-trivial character of his preferred notion of rigidity by presenting some examples of (allegedly) non-rigid general terms, but we have found that the reasons he has given for thinking that many of them, including the paradigmatic “the colour of the sky”, are such are unconvincing. On the other hand, we have found that one of his examples, and many similar ones that could be formed in the same way, are indeed, arguably, non-rigid, although for reasons somewhat different from those Salmon gives. So that it would seem that the notion of general term rigidity is not trivial, after all.

Let me finally say a word on the relevance of the preceding discussion for Kripke’s thesis that natural kind terms are rigid, and more broadly for the project of using the notion of rigidity to make a significant distinction among general terms. Contrary to most of the authors who argue that there are some non-rigid predicative expressions, I don’t think that the notion of rigidity as identity of designation, even if non-trivial, constitutes an adequate extension, applicable to predicative expressions, of the original notion of rigidity that Kripke defined for singular terms. I think so because, on the one hand, it is clear that the kind of expression found to be non-rigid is so marginal among general terms, and involves descriptive resources of so limited a nature, that it could hardly play the role of an adequate foil to Kripke’s rigid natural kind terms; and, on the other hand, but relatedly, because being non-trivial is only a first, necessary condition, for any notion of predicate rigidity to count as an adequate extension of the singular term notion and, it seems to me, the sameness of designation view fails to satisfy some other important desiderata mainly, that natural kind terms should be, if not the only rigid terms, at least paradigmatically such in ways in which other terms are not; and that rigidity should validate the necessitations of true identification sentences, which I assume should be construed as universally quantified biconditionals (cf. ^{Soames 2002}, p. 263, for a statement of similar desiderata). It seems to me, indeed, that there is really no adequate extension of the notion of rigidity to general terms if the notion is to do most of the theoretical work it did in the case of singular terms. But it lies outside the scope of the present paper to try to argue in favour of these theses in any more detail.²¹