Difference and Necessity
Essentialists have found in identity a shining example of their creed. Any object is necessarily identical to itself—how could that not be so? It has even been thought that the necessity of identity can be proved from Leibniz’ Law: given that a is necessarily identical to a and that a is identical to b, it follows that b is also necessarily identical to a. But far less attention has been paid to the modality of difference: if a and b are different objects, is that a necessary fact or a contingent fact? If objects are distinct in the actual world, are they distinct in every possible world? Given that I am actually distinct from Saul Kripke, are there any worlds in which we are identical? Is there any world at which the statement “Colin McGinn is identical to Saul Kripke” is true? We can clearly lack certain of our actual properties in a possible world—neither of us are philosophers in some possible world–but could we lack the property of being numerically distinct? Are there worlds in which London is identical to Paris or the moon is identical to the sun? Could twins be numerically identical in a possible world?
The answer is intuitively obvious: none of these things is possible. If objects are different, they are necessarily different—different in all worlds in which they exist. If a is different from b, this is part of a’s essence—it is essentially different from b. Thus objects have an enormous number of difference essences, as many as there are objects from which they are distinct. They only have one identity essence, viz. identity to themselves, but they have hugely many difference essences, according to all the objects in the universe. In fact, they have infinitely many difference essences, given the infinity of numbers or points in space: I am different from the number two, say, in every possible world, and so for any number. These essences come cheap and plentiful. Furthermore, they are a distinct species of essence, not to be assimilated to the other kinds—origin, composition, etc. Nor are they derivable from the necessity of identity; they cannot be proved from Leibniz’ Law, for one thing. The difference of a given thing from everything else is essential to what it is, as a primitive modal fact. No amount of merging or fusion can make two actually distinct things into the same thing. For instance, you might think two rivers that flow side by side could be one river in a world in which the dry land separating them is removed; but such a world is really one in which a new river exists, not a world that contains the old two rivers joined in a single river. Those actual rivers don’t exist in this possible world; we have fused two rivers into a broader river and eliminated the actual rivers. Physical merging or joining is not two things existing as one, for those things will no longer exist—any more than fission is one object existing as two, and hence not being self-identical. There are no worlds in which McGinn and Kripke both exist and yet are one person—though there is a world in which an individual has characteristics belonging to each of us.
That is all at the level of metaphysical possibility—what could really be. I have said nothing yet about epistemic possibility, and here matters assume a different shape. For it is an epistemic possibility that McGinn and Kripke are the same individual: it might turn out that we are identical—some very elaborate trick has been performed. To take a simpler example, suppose I am dating a woman I believe to be an only child but in fact she has an identical twin. I have been seeing both twins but don’t realize it: I have mistakenly believed of different women that they are one woman. Isn’t it possible that this is true of a great many people I know? I am always assuming identity from one meeting to the next, but in fact there is a plurality—different people where I thought there was one person. We can conjure ample grounds for a skeptical argument here. So it is not an epistemic necessity that what I take to be one individual is really one individual—it might turn out that I know many more people than I realize. Just as you can mistakenly suppose that what is in fact a single object is two, as in a classic Frege case, so you can mistakenly suppose that what are in fact two objects are a single object. Judgments of identity and difference are fallible. But none of this has anything to do with questions of metaphysical necessity: just because one object can be mistaken for two, or two objects mistaken for one, has no bearing on whether identity and difference are metaphysically necessary relations. We should not confuse metaphysical and epistemic questions. How things might turn out is a quite different question from how things could be. It might turn out that there are many things where you thought there was one, or that there is one thing where you thought there were many, but these possibilities don’t show that one thing could be many things or many things one thing.
Frege used identity statements to prove that distinct senses can correspond to the same reference, since this is what explains someone’s inability to know the identity a priori. But an exactly parallel argument leads to the conclusion that there can be many references corresponding to a single sense, namely that a person can think he is referring to one object when he is really referring to two. If I call the woman I am dating “Joan” in the morning and “Joanie” in the evening (she always seems more fun-loving in the evening), I will subscribe to the truth of “Joan is Joanie”, even regarding it as analytic. But given that I am seeing twins and don’t know it, we have to say that I really have two references, while meaning the same by the name. The twins are perceptually presented to me in the same way and I intentionally use the names “Joan” and “Joanie” as synonyms, but I refer to different individuals when I use the name in relation to the women in question. This is a case of sameness of sense combined with difference of reference. To me the statement “Joan is Joanie” is analytic, but the context of use generates distinct references.
The same points apply to natural kinds: people can fail to realize identities and fail to realize differences. You can fail to realize that water is identical to H2O and you can fail to realize that gold is different from copper (you think they are the same metal). Nevertheless, it is part of the essence of water to be H2O and part of the essence of gold to be different from copper. There are no worlds where water is identical to some other chemical compound and no worlds where gold and copper are the same metal (though one metal might be called both “gold” and “copper” in a possible world). If pain is identical to C-fiber firing in this world, then it must be so in all worlds; and if sensations of red and sensations of green are different in this world, then they must be different in all worlds. In order to create pain all God had to do was create C-fiber firing (according to the identity theory); and in order to create gold and copper God must perform two acts of creation—he can’t skip one of these creative acts and more economically create both metals in the form of a single metal. Different things can never be other than different, and identical things can never be other than identical. Hesperus is Phosphorus in every world and Venus is not Mars in every world—despite the fact that both these propositions are not known a priori. Modality behaves in the same way for both identity and difference: the essentialist can also find in difference a shining example of his creed. We find necessity not just in the relation a thing has to itself and to no other thing but also in the relation a thing has to other things and not to itself.