Some thoughts on identity

What makes something the same as something else?

It is obvious that two identical twins are not truly identical, because they do not, and cannot, inhabit the same space at the same time. But is “inhabiting the same space at the same time” a necessary or sufficient condition for identicalness? Suppose instead that I speak only of myself. Am I identical to the me of one second ago? It strikes me that this cannot be the case, simply because I can speak of the two selves as though separate, and not talk meaninglessly. (If I assign two names to the same object, then I can talk meaningfully, but only on the context of the object rather than the object itself.) This is of course more amplified over a greater distance in time. A second person who has seen me both as a baby and at present can speak of the two as if completely different people, and make perfect sense. Apart from this, there is no logical reason for physical continuity between time. If anything, it seems far likelier, given the constant state of motion that the universe finds itself in, that nothing stays the same from any moment to the next. The computer scientist Steve Grand has said that, due to the constant flow of matter in the universe, nobody is composed of exactly the same atoms throughout their whole life. From this, one can at least assume that we cannot assume that we are composed of the same atoms (or electrons, or quarks, or superstrings, of the same charge or spin) at any time as at another time, and that therefore none of us is identical with our past or future selves.

This seems (and indeed, is) perfectly compatible with the idea of identicalness being “inhabiting the same space at the same time”. However it is clear that this can only refer to physical objects, and identity presumably refers to anything ontologically possible. If we look at logical constructs such as numbers, we see that they do not satisfy the above definition, but we have no problem speaking of identity with regards to them. “1” is identical to “1” regardless of what time it is. (And of course, “1” is the same no matter where you are, but the number itself cannot change location.) The same applies, I think, to any a priori concept we might think of—the laws of logic, pure mathematics, and so on.

All talk of identity with regards to physical objects, indeed any a posteriori concept, seems doomed to failure. No physical object is identical to anything other than itself at only one (and the same) moment in time, since all objects are in a constant state of change. More abstract, non-physical a posteriori ideas are clearly just as liable to change. “Democracy”, “law”, and “Shakespeare” are examples of this (though it is arguable in the cases of democracy and law that it is only the manifestations rather than the ideas in themselves that are subject to change). Only a priori ideas appear to be identical in their respective incarnations throughout all time. Perhaps this is because they subsist rather than exist: anything that exists is in some sense a function of space and time.

Indeed, this might even be a reasonably good definition of a priori ideas: “any idea which remains identical with ‘itself’ throughout all time”.