On Kripke's "Identity and Necessity"

In this blog post, I will like to consider the implications (if any) of the intelligibility of the following scenario for Kripke’s claim that identity statements involving rigid designators are necessarily true.  Suppose that the Messenger space probe were to send back pictures revealing that “Venus” is actually a binary planetary system—two planets orbiting around a common gravitational midpoint.  Moreover, as luck would have it, when viewed from the northern hemisphere on any given morning, one of the twin-planets (let’s call it V1) would stand perfectly in front of the other (let’s call the second V2), so that only V1 could be seen.  But in the evening, the planets would switch positions so that V2 would obscure V1 such that only the former would be visible.  The upshot of this is that the heavenly body that was visible (from Greece or Italy) in the morning and that was “tagged” with the name Phosphorus would actually be distinct from the heavenly body seen in the evening and which was “tagged” with the name Hesperus.  Now such a scenario is clearly fictional and may, given what we know about the laws of planetary motion, even be physically impossible.  However, it certainly strikes me as intelligible and I wish to consider what follows (in anything) from the simple fact that it is intelligible. 

Suppose, after considering the above scenario, I were to say something to the effect: “If Phosphorus and Hesperus turned out to be different heavenly bodies, then Kripke would be left without a cogent illustration for his identity thesis.”  Presumably, Kripke would hold that it is impossible for the antecedent of the above counterfactual statement to be true.  Moreover, the kind of impossibility that Kripke would have in mind would be logical and not merely physical.  In brief, Kripke holds that both names, Phosphorus and Hesperus, are rigid designators.  Even so, this does not impugn the intelligibility of anything said thus far since we do often employ counterfactuals in which the antecedent is logically impossible (such as in reductio arguments). 

In Kripke’s version of the Phosphorus-Hesperus scenario, the gravitational influence of a passing comet causes Venus to be moved from its normal position and Mars to take its place.  He then suggests that under such circumstances, the thing to say would not be that Phosphorus is not Hesperus (i.e., the two names designate different heavenly bodies), but that Phosphorus has been moved so that it no longer occupies its normal position in the night sky.  Now, it does not seem to me that this reply works in the case as I have described it.  This is because in the binary-planet case we are not simply imagining a case in which another heavenly body, say Mars, is occupying the position we once thought was occupied by Venus.  Rather, we are imagining a case in which what we took to be a single object, Venus, actually turns out to be two distinct objects.  What would Kripke say in response to the above example?

In attempting to answer this question it may be helpful to consider the following question:  “In the aforementioned counterfactual, which of the two heavenly bodies, V1 or V2, should we identify with Venus?”  Given the parity between the two cases (we can suppose that in astronomical observations V1 was identified as Venus just as often as V2) it would seem arbitrary to say that one, and not the other, ought to be identified with Venus.  Since both could not be Venus (personally I’m not convinced of this, but it seems like the position that Kripke would hold) then the only available option would be to say that neither heavenly bodies are to be identified with Venus.  If this is right, then the proper name “Venus” would cease to refer to anything.  (This conclusion seems to jive with Russell’s requirement for successful reference.)

Let us suppose that in the binary-planet example, the proper name “Venus” ceases to refer.  What about the status of the proper names “Phosphorus” and “Hesperus”?  Stated in the terminology of possible worlds, a rigid designator is defined as one that designates the same thing in all possible worlds in which it designates.  Suppose that the names “Phosphorus” and “Hesperus” are both rigid designators, and that “Phosphorus is Hesperus.”  (Strictly speaking, there is no need for imagination here, since this is what Kripke takes to be the case in the actual world.)  Since they are rigid, they each designate the same thing in all possible worlds in which they both designate. That is to say that “Phosphorus is Hesperus” is true in all possible worlds in which “Phosphorus” and “Hesperus” both designate, and hence that “Phosphorus exists & Hesperus exists → Phosphorus = Hesperus” is true in all possible worlds, and is therefore necessarily true.  This, according to Kripke, is all we mean when we say that “Phosphorus = Hesperus” is a necessary truth. 

In my binary-planet example, the antecedent of the conditional (Phosphorus exists & Hesperus exists) is true and the consequent (Phosphorus = Hesperus) is false.  It therefore appears to represent a counterexample to Kripke’s claim that Hesperus and Phosphorus are rigid designators.  Now, I have already conceded that the situation described in the antecedent may be impossible.  Moreover, perhaps Kripke should be interpreted as allowing that even a rigid designator may designate different things in impossible worlds.  If so, then perhaps there is also an expectation on Kripke’s part, that we restrict ourselves to counterfactuals with possible antecedents whenever we unpack the definition of rigid designator in terms of possible worlds. 

However, on pain of circularity, such a move seems illegitimate at this stage.  Kripke is supposed to be offering us an argument for necessity of identity from his definition of rigid designation.  But if Kripke’s definition of rigid designation already required us to omit impossible worlds, it would be to argue for the conclusion that a certain identity is necessary from the starting assumption that the identity failing to hold is impossible.  But that would be to settle before hand the position one wished to achieve by argument.  If Kripke’s argument is to be cogent, it must be possible to begin with the initial supposition that the antecedent it possible.  Then if the argument is successful, we would be led to reject our initial supposition.  But once we grant that the antecedent is possible (i.e., that Phosphorus is not Hesperus), it is not clear that any argument can be given to show that the possibility that has been assumed for the sake of argument should be rejected.  In sum, without some independent argument showing that the binary-planet counterfactual, in which the names “Phosphorus” and “Hesperus” designate different objects, is impossible, it is not clear that Kripke’s argument that the names are rigid designators gets off the ground.