Reply to Ramachandran.
How does Ramachandran set up his deeper problem? In Gallois (1993) I offer the following necessary and sufficient condition for a term restrictedly rigidly designating:
RDC#: ([unkeyable]d) ([unkeyable]x) ([unkeyable]W) [d rigidly designates x in world W [unkeyable] ([unkeyable]y) ([unkeyable]W') (d designates y in W' [right arrow] ([unkeyable]z) (in W: x=z [and] in z=y))]. As Ramachandran correctly observes, in the light of (RDC#) I am committed to:
(CC) A term's restrictedly rigidly designating (RR-designating) an object x is compatible with it designating an object y in a world W where x exists but is distinct from y. Ramachandran (1993) contends that the following is a consequence of (CC):
... the necessary (contingent) truth of a sentence of the form "[alpha] is identical with [beta]", where "[alpha]", and "[beta]" are RRDs of objects x and y respectively, does not require the necessary (contingent) identity of x and y. Why does Ramachandran think that the above is a consequence of (CC)? If I have understood it correctly his argument goes like this. Suppose:
(1) a is contingently identical with b. We have:
(2) The sentence "a=a" is necessarily true. Since "a" RR designates a, from Leibniz's Law and (1) we have:
(3) Each occurrence of "a" in "a=a" RR designates both a and b. Hence:
(4) a=a" expresses a=b. So, from (1), (2) and (4) it follows that:
(5) The necessarily true identity sentence "a=a" expresses a contingent identity. Now suppose:
(1') "a=b" is contingently true. However from (1) it follows that "a" and "b" both RR desinate a. Hence:
(2') "a=b" expresses a=a. Moreover:
(3') [unkeyable] (a=a) So, from (1'), (2') and (3') it follows that:
(4') The contingently true identity sentence "a=b" expresses a necessary identity. Why should I be reluctant to accept (4')? Ramachandran puts the problem like this:
...if, as I have argued, the contingent truth of a sentence of the form "[alpha] is identical with [beta]" where "[alpha]", and "[beta]" RR-designate x and y respectively, does not require the contingent identity of x and y, how are we to express their contingent identity? The problem is that any candidate sentence involving RRDs one might consider could just as well be said to express (falsely) the contingent identity of x and x. I take it the difficulty is this. Assume that "a=b" is a true unambiguous identity sentence containing the RR-designators "a" and "b". In addition, assume that "a=b" expresses a contingent identity. Since "a=b" is unambiguous it expresses just one thing. The argument from (1') to (4') instructs us that "a=b" expresses the necessary identity a=a. Hence, "a=b" only expresses a necessary identity. So, "a=b" does not express a contingent identity.
A counterpart difficulty is suggested by the argument from (1) to (5). Suppose (3') follows from (1). In that case, "a=b" expresses the necessary identity a=a. Again we may take it that "a=b" expresses just one thing. So, the allegedly contingently true "a=b" only expresses a necessary identity.
For either of these arguments to succeed (3') must be true. (3') features as a crucial premiss in one version of the modal argument for the necessity of identities mentioned earlier. Using the [lambda] notation to form predicates it goes like this:
(1") Suppose a=b
(2") "a=a" is necessarily true.
(3') [unkeyable] (a=a).
(4") ([lambda]x)[[unkeyable](x=a)]b. Together with Leibniz's Law (") and 4") yield: (5") ([lamda]x) [[unkeyable](x=b)]b. which in turn yields:
(6") [unkeyable] (a=b).
What reason is there to think that (3') is true? (Certainly (3') looks incontestable. However, there is a danger of conflating (3') with something that is incontestable. In order to show this I invoke a distinction familiar from discussions of the contingent a priori. Consider the following sentence:
(6) "I am here". Suppose that C is the set of linguistic conventions governing the use of (6) in English. If so, this is true: necessarily any utterance of (6) governed by C expresses a truth. On the other hand, this is not: any utterance of (6) governed by C expresses a necessary truth.
Here is an alternative way of putting the point. (6), as used in English, expresses a truth in any possible situation in which "I" has a referent. However, the following is not true: in any possible situation in which "I" has a referent (6), as used in English, expresses a necessary truth. After all I might not have been here.
Our use of singular terms is governed by the following convention. If a singular term is not being used ambiguously then repeated uses of that singular term in a sentence assign it the same referent. Call this the stability convention. The stability convention ensures that "a=a" expresses a truth in any world in which a exists. The stability convention, whatever "a" refers to in a given world, governed by the stability convention, whatever "a" refers to in a given world, both of its occurrences in "a=a" will have the same referent. However, the stability convention does not ensure that the truth actually expressed by "a=a" is necessary. For that to be so this must be true:
(7) Anything that is actually referred to by "a" is identical with a in any world in which a exists. Of course, to insist on (7) is to beg the question against an advocate of contingent identities.
Is (2) true as Ramachandran contends? Clearly it is if it is taken to mean that "a=a" expresses a truth in any world in which a exists. It is not obviously true if (2) is taken to imply (3'). However, if (2) does not imply (3'), and (3') is false, then the argument from (1)-(5) to the conclusion that "a=b" only expresses a necessary truth collapses. (2) is consistent with "a=b" and "a=a", both expressing only contingent truths. Moreover, if (3') is false the argument from (1') to (4') and the modal argument for the necessity of identities also collapse. Ramachandran's deeper problem is solved.
(2) The reader may he understandably reluctant to treat the stability convention as a convention since it is not optional. What it means for a singular term to be used unambiguously is that repetitions of it should be taken to have the same referent. Even if it is to mis-describe the stability convention to call it a convention that will not affect the points I wish to make.
Gallois, A. 1986: "Rigid Designation and the Contingency of Identity". Mind, 95, 1, pp. 57-76.
--1993: "Ramachandran of Restricting Rigidity". Mind, this issue pp. 151-155.
Kripke, S.: "Identity and Necissity". in Milton K Munitz, ed., Identity and Individuation, New York University Press, 1971.
Ramachandran, M. 1992: "On Restricting Rigidity". Mind, 50, 3, pp. 163-6.
--1993: "Restricted Rigidity: The Deeper Problem". Mind, this issue pp. 157-8.
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|Title Annotation:||Murali Ramachandran, this issue, p. 157, on rigid designation and contingent identity|
|Date:||Jan 1, 1993|
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