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.
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.
