I suspect that most theories of diachronic personal identity—the exceptions being the soul, further-unanalyzable-fact and no-diachronic-identity theories—have to admit of cases where there is a person in ten years who is only vaguely identical with me where it is definite that he exists and is a person. (Think of cases where people split, parts of brains get put in other heads, memories get recombined, etc.) Vague identity is a known problem given the indiscernibility of identicals (a problem one can get out of by abandoning classical logic—a heavy price to pay to avoid the three exceptional theories). But now consider the following way of making the problem vivid:
- In ten years there will be an x who definitely suffers pain but who is only vaguely identical with me. (Premise for reductio)
- Necessarily, for any given kind and intensity P of pain, if x and y have the same exactly alike, it is definitely intrinsically less bad for x that she only only vaguely suffers P than it is for y that she definitely suffers P. (Premise)
- Therefore, what will happen in ten years is definitely less bad for me than for x. (By 1 and 2)
- If y suffers from something definitely less bad than x (on some particular occasion), then x and y definitely differ in their properties. (Premise)
- If x and y definitely differ in their properties, then x and y are definitely non-identical. (Premise)
- Therefore I am definitely not x. Which contradicts (1).
I am thinking that (2) is the thing for the opponent to challenge. Maybe (2) slips between intuitions about vagueness in the pain (a vague pain is intrinsically less bad than a definite pain) and intuitions about attribution of the pain. But I think (2) is pretty plausible even if one thinks about this. Suppose that over then next 40 years we have a sequence of persons, x1,x2,...,x40, with the last one being definitely not identical with me, and with each only somewhat identical with the previous. It seems clear that I should not be concerned at all in a self-centered way about pains to x40, and that I should be less and less concerned as one goes down the sequence. And it seems that (2) is the best explanation here.
A different way out is to insist that whenever x and y are vaguely non-identical, it is only vaguely true that x and y are non-identical. I think one would end up with a view on which we have vagueness all the way down, so it's only vaguely true that it's vaguely truth that ... x is me (for any finite number of vaguelies). But I don't find this plausible. For one, it seems to me that if one has a sequence like the above one, at some point it should be non-vaguely true that there is only vague identity. For another, presumably it is only vaguely true that it's vaguely true that ... x is not me. But in the latter case, intuitively, x is very close to definitely being not me. And that should be enough for (2).
Quite possibly the previous two paragraphs beg the question against the defender of vague identity. As may the first premise of the following argument, which is nonetheless fun:
- If you're vaguely in excruciating pain, definitely you are at least in a somewhat bad state. (Premise)
- If you are definitely in at least a somewhat bad state, you are definitely in existence. (Premise)
- If vague identity is possible, then it is possible that you are only vaguely x at t and x is definitely in excruciating pain at t and you definitely are not identical with anybody at t other than x. (Premise)
- Suppose vague identity is possible. (Premise for reductio)
- It is possible that you are only vaguely x at t, and are definitely at least in a somewhat bad state at t, and you definitely are not identical with anybody at t other than x. (By (7)-(10))
- It is possible that you are only vaguely x at t, and definitely exist at t, and definitely are not identical with anybody at t other than x. (By (8) and (11))
- Necessarily, if you definitely exist at t and definitely are not identical with anybody at t other than x, then you are definitely x at t. (Premise)
- (12) and (13) contradict one another. So we reject (10).