From causality to rigidity.
I shall assume what I call "the assumption of interworld reference", that is, that when a name is used in a certain possible world--let's suppose for simplicity that this is the actual world--it may refer to objects also in other possible worlds. Anyone who accepts that names can function as the grammatical subjects of counterfactual conditional sentences such as "Had George Bush born in England, he would not have been the president of the United States", must accept this assumption. This assumption is different from the claim that the objects the name refers to in other possible worlds are identical with the object it refers to in the actual world. I am not assuming this latter claim, of course--assuming it would amount to assuming that names are rigid designators and thus to begging the question. (Note also, that the assumption of inter-world reference does not even presuppose that one object can inhibit different possible worlds. I shall refer to this point below.)
Now the causal relation that determines the name's reference is--like any other causal relation--a non-transworld-relation: there is no causal relation the relata of which are members of different possible worlds. (2) Hence, there cannot be a causal relation between a use of a certain name in one possible world, and an object in another possible world. Such a causal relation cannot therefore determine a name's reference in possible worlds other than the actual one.
This consideration might seem to lead to the conclusion that causal theories of reference for names must be rejected, for it seems to show that no causal theory can explain a name's reference in possible worlds other than the one in which the name is used. But this is not so. The assumption that the causal theory of reference is correct is compatible with the assumption of inter-world reference. Only the conjunction of these two assumptions and a third assumption, namely the one that names may refer to different objects in different possible worlds, is inconsistent. If this third assumption had been correct, we would have had to supplement the causal theory by somehow connecting the actual world's referent with the other possible worlds' referents. In that case reference would be determined by means of a combination of two ways, and we would not have a pure causal theory of reference determination.
If indeed we want a pure causal theory of reference with no supplementation, and we accept the evident assumption of inter-world reference, then adhering to the claim that names are rigid designators is unavoidable. If this claim is true, then the name's referent is picked out only once (in the actual world) for every possible world (the actual as well as the non-actual ones), so no inter-world causal connection is needed to endow it with referents in possible worlds other than the actual one: the causal relation of the actual world performs this task, as the object it picks out is the referent for every possible world.
Kripke's view that names are rigid designators has been part of his case against the description theory of names. In fact, this view opposes a specific component of the description theory, namely the satisfaction model. According to this model, what makes an object in a given possible world the referent of an expression is the fact that this object satisfies in this world a certain condition. (3) The satisfaction model, in itself, is not committed to descriptivism. That is, it is not committed to the idea that a speaker has to (explicitly or implicitly) associate with the name a description that expresses the condition in question. But the satisfaction model is incompatible with a pure causal approach to reference determination, precisely for the reason that a causal relation is a non-trans-world relation. A causal relation can connect the use of a name in one possible world only to an object in the same possible world. The condition of being causally connected to the use of a name is a condition that can be satisfied by an object in the world which this object inhabits only if the object inhabits the same world in which the name is used. The claims that, on the assumption of cross-world reference, the satisfaction model is incompatible with a causal theory of reference and the claim that the causal theory of reference entails the claim that names are rigid designators, are, of course, the two sides of the same coin.
Kripke's specific conception of rigidity presupposes his conception of possible worlds, on which one and the same object can inhabit different possible worlds. David Lewis' conception of possible worlds denies this. (4) But this is not to say that Lewis' counterpart approach leaves no room for inter-world reference of names. It is possible to account for inter-world reference of names in the framework of such an approach in a way that is similar to the way it is possible to account for it in the Kripkean framework. The idea is to take names to be "rigid" designators in essence--to be "Lewisrigid" rather than "Kripke-rigid". That is, whereas "Kripkean rigidity" is the thesis that a name refers to the same object in all possible worlds, "Lewisian rigidity" is the thesis that a name that is used in the actual world refers in any possible world to that object of that possible world that is the counterpart of its actual world's referent. On such a conception too, there is no need to appeal to inter-world causal connection for fixing reference in non-actual worlds. The counterpart relation does the work.
There is, though, a significant difference between the ways in which non-actual worlds' reference is determined in terms of Kripkean rigidity and in terms of Lewisian (counterpart) rigidity. An account in terms of Lewisian (counterpart) rigidity does appeal to a certain connection between the actual world's referent and the other possible worlds' referents. In the framework of a Kripkean approach, on the other hand, no such connection is needed at all, since there are no other referents to be connected to the actual world's referent, as there is no difference in reference among the worlds. This point is sometimes blurred by defining "a rigid designator" (within a Kripkean conception of possible worlds) as one that refers to the same object in every possible world in which this object exists. The impression is thus created that whether or not a rigid designator refers to something in some non-actual possible world depends on the ontological furniture of that world. But according to the interesting sense of rigidity, a rigid designator refers to the same object in every possible world, whether or not this object exists in this possible world. (5) (One possible way to realize this is to notice that we may speak counterfactually of a world in which, say, George Bush does not exist.) Under this sense of 'rigidity', it is clear that it is the referent of the rigid designator in the actual world that may serve as the referent of this designator in other possible worlds, regardless of any characteristic of these worlds, and, a fortiori, regardless of any connection between the actual world's referent and any of these worlds' objects. If names are rigid designators in this sense, then a causal theory of the reference of names does not need any supplementation by assuming such a connection.
In sum, I hope to have shown that given the assumption of inter-world reference of names, the causal theory of reference for names is tenable only if names are rigid designators in either the Kripkean sense or the Lewisian sense. Since that assumption (I believe) is true,--it is a constraint that any theory of the semantics of names must respect, this means that the causal theory of reference for names entails that names are rigid designators in either of those senses. (6)
NOTES AND REFERENCES
(1.) Kripke, S., Naming and Necessity, Blackwell, Oxford, 1980.
(2.) This claim is not in clash with the idea (endorsed by some interpreters of quantum mechanics), that parallel universes causally effect events in our universe, for our world and worlds that allegedly causally interact with it are ex hypothesi part of the same world.
(3). On the satisfaction model see, e.g., John Searle's discussion in his Intentionality: An Essay in Philosophy of Mind, Cambridge University Press, Cambridge, 1983.
(4). See e.g. Lewis, D., "Counterpart Theory and Quantified Modal Logic", in Journal of Philosophy, 65, 1968, pp. 113-126.
(5.) Kripke expressed his commitment to this conception of the rigidity of names. In a private correspondence with Kaplan he denies that he has ever endorsed the first (this correspondence is reported in fn. 8 of the 'Afterthoughts' of Kaplan, D., 1989, "Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and other Indexicals", in Almog, J. et al., Themes from Kaplan, Oxford University Press, Oxford, pp. 481-563) he denies that he has ever endorsed the first.
(6.) I believe that the argument of this paper can be extended so as to apply to natural kind terms, but showing this would have to await another occasion.
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|Publication:||Linguistic and Philosophical Investigations|
|Date:||Jan 1, 2009|
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