Second order descriptions and general term rigidity.
| Autor | Zerbudis, Ezequiel |
| Cargo | Art |
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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.
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Salmon'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)"):
(A1) My true love's eyes are the colour of the sky.
(A2) Blue is the colour of the sky.
(A3) My true love's eyes are blue.
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:
(B1) John has the virtue Socrates was most famous for.
(B2) The virtue Socrates was most famous for is wisdom.
(B3) John is wise.
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...
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