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>Indistinguishability doesn't entail identity. Of course it does, by Voevodsky's Univalence Axiom ;-). >One obvious way to show this is to note that only the latter is a transitive relation. In other words, if A = B and B = C, then A = C; but if A is indistinguishable from B and B is indistinguishable from C, it doesn't follow that A is indistinguishable from C. In this case, you seem to be envisioning A, B, and C as points along a spectrum, and talking about ways to classify them as separate from each-other, in which we can classify {A, B}->+1 or {B, C}->+1, but {A, C}->-1 always holds. That's fine, but when we say indistinguishable in the p-zombie argument, we're talking about a physical isomorphism, which doesn't really allow for the kinds of games you can get away with when classifying sections of spectrum. |
I think this was a joke, right? Just asking because it's hard to tell sometimes on the internet. I didn't see how VUA was particularly relevant but I may be missing something.
It is question-begging in this context to assert that the existence of a physical isomorphism between A and B entails that A and B are identical, since precisely the question at issue in the case of P-zombies is whether or not that's the case.
I took OP to be making an attempt to avoid begging the question by arguing that in general, indistinguishability in a certain very broad sense entails identity, so that without question-beggingly assuming that the existence of a physical isomorphism entails identity, we could non-question-beggingly argue from indistinguishability to identity. In other words, rather than arguing that P-zombies couldn't differ in any way from us because they're physically identical to us (which just begs the question), the argument would be that they couldn't differ in any way from us because they're indistinguishable from us.