That's a very bad argument. Indistinguishability doesn't entail identity. 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.
Yes, I know. Indistinguishability in that sense is not a transitive relation. Imagine e.g. that we have detectors which can distinguish As from Cs, but no detectors which can distinguish As from Bs or Bs from Cs. There is no contradiction in that scenario. In contrast, there is no consistent scenario in which A = B and B = C but A != C.
Imagine that we have bunch of As, Bs and Cs in one place. Start testing every one against another. You'll quickly discover two groups - An A tests positive with other As and Bs, but tests negative with Cs. A C tests negative with As, but tests positive with Bs and other Cs. B is the one that tests positive with everything.
Here, I distinguished them all. Doesn't that contradict your argument about indistinguishability not being transitive in general?
Yeah, that strategy would work in the scenario I sketched, but it's easy to change it so that you couldn't do that. Just say we have As, Bs, Cs and Ds and that all pairings are indistinguishable except As with Ds.
But at this point I have to ask, how do you define identity? I'm pretty sure that I could use the strategy I outlined above to separate our objects into three groups - As, Ds and the rest. So how do you define that Bs are not Cs, if there is no possible way for telling the difference?
I'd define identity as the smallest relation holding between all things and themselves.
If you want, you can redefine identity in terms of some notion of indistinguishability, but then you'll end up with the odd consequence that identity is not transitive. In other words, you'd have to say that if A is identical to B, B is identical to C, and C is identical to D, it doesn't necessarily follow that A is identical to D.
There are even semi-realistic examples of this, I think. Suppose that two physical quantities X and Y are indistinguishable by any physically possible test if the difference between X and Y < 3. Then i(1, 2), i(2,3), i(3,4), but clearly not i(1,4).
I'll have to think a bit more about this. Thanks for all those scenarios and making my brain do some work :).
So at this point I'm not sure if your example is, or is not an issue for a working definition of identity. To circle back to p-zombies, as far as I understand, they are not supposed to be distinguishable from non-p-zombies by any possible means, which includes testing everything against everything.
What if I define the identity test I(a,b) in this way: I(a,b) ↔ ∀i : i(a,b), where i(a,b) is an "indistinguishable" test? This should establish a useful definition of identity that works according to my scenario, and also your last example unless you limit the domain of X and Y to integers from 1 to 4. But in this last case there's absolutely no way to tell there's a difference between 2 and 3, so they may as well be just considered as one thing.
As I said, I need to think this through a bit more, but what my intuition is telling me right now is that the very point of having a thing called "identity" is to use it to distinguish between things - if two things are identical under any possible test, there's no point in not thinking about them as one thing.
>But in this last case there's absolutely no way to tell there's a difference between 2 and 3, so they may as well be just considered as one thing.
Yes, that's the point. But then you lose the transitivity property, since although 2 and 3 are indistinguishable, 3 and 4 are indistinguishable, and 4 and 5 are indistinguishable, 2 and 5 are not. So the kind of operational definition of identity you have in mind yields a relation that's so radically unlike the standard characterization of the identity relation that I don't see any reason to call it "identity" at all.
Here's one way of drawing this out. Suppose that X linearly increases from 2 to 5 over a period of 3 seconds. Do we really want to say that there was no change in the value of X between t=0 and t=1, no change between t=1 and t=2, no change between t=2 and t=3, and yet a change between t=0 and t=3? (?!)
As far as I understand you, you have some kind of positivist skepticism about non-operationalizable notions, and so you want to come up with some kind of stand-in for identity which can play largely the same role in philosophical/scientific discourse as the ordinary, non-operationalizable notion of identity. That's a coherent project, but it rests on assumptions that anyone who's interested in P-zombies is likely to reject.
> Here's one way of drawing this out. Suppose that X linearly increases from 2 to 5 over a period of 3 seconds. Do we really want to say that there was no change in the value of X between t=0 and t=1, no change between t=1 and t=2, no change between t=2 and t=3, and yet a change between t=0 and t=3? (?!)
Yeah, I get that, but what I meant in my previous comment is that you either limit the domain of t to 0-3 (and X to 2-5) and there is indeed no way to tell the change between t=2 and t=3, or you don't limit yourself to that test and can distinguish the intermedate values by means of the trick I described before. In other words, either you have transitive identity or you have all the reasons to treat non-transitive cases as one (if the identity test is like the one I described in my previous comment).
> positivist skepticism about non-operationalizable notions
I think it's too late in the night for me to understand this, I'll need to come back to it in the morning. Could you ELI5 to me the meaning of "non-operationalizable" in this context?
Again, thanks for making me think and showing me the limits of my understanding.
>Again, thanks for making me think and showing me the limits of my understanding.
Yes this was a fun discussion, thanks.
Your objection stands if you have (and know you have) at least one instance of every value for the quantity. So suppose that we are given a countably infinite set of variables and told that each integer is denoted by at least one of these variables, and then further given a function over pairs of variables f(x,y), such that f(x,y) = 1 if x and y differ by less than 3 and = 0 otherwise. Then, yes, we can figure out which variables are exactly identical to which others.
However, I would regard this as irrelevant scenario in the sense that we could never know, via observation, that we had obtained such a set of variables (even if we allow the possibility of making a countably infinite number of observations). Suppose that we make an infinite series of observations and end up with at least one variable denoting each member of the following set (with the ellipses counting up/down to +/-infinity):
...,0,2,3,4,5,6,7,9,...
In other words, we have variables with every integer value except 1 and 8. Then for any variable x with the value 4 and variable y with the value 5, f(x,z) = f(y,z) for all variables z. In other words, there'll be no way to distinguish 4-valued variables from 5-valued variables. It's only in the case where some oracle tells us that we have a variable for every integer value that we can figure out which variables have exactly the same values as which others.
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.
>Of course it does, by Voevodsky's Univalence Axiom ;-).
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.
This isn't really germane to the p-zombie thought experiment, but:
Indistinguishability does entail identity. If I have a sphere of iron X, and a sphere of iron Y which is atom-for-atom, electron-for-electron, subatomic-particle-for-subatomic-particle identical to sphere X, and I place sphere X in position A, and sphere Y in position B, then they are still distinguishable, because one is in position A and one is in position B.
Basically, I'm not sure what the two of you mean by "the same", but I suspect you're not in agreement on it.
I think we're talking about a sense of indistinguishable/identical for which the two spheres would be indistinguishable/identical, since we're comparing a person to a P-zombie, so it's clear that we're dealing with two different individuals. I think identity in that sense is still transitive on the ordinary understanding. So e.g. if I can show that sphere A has exactly the same physical constitution as sphere B, and that sphere B has exactly the same physical constitution as sphere C, then presumably sphere A must have exactly the same physical constitution as sphere C.
The human and the p-zombie are distinguishable because one is in the zombie universe and one isn't. For the purposes of the experiment, you're not supposed to be able to tell which universe is which by observation of the universe itself (i.e. there is no property of p-zombies that gives them away as p-zombies), but from the outside looking in I guess you have a label for one and a label for the other.
Like I said, it doesn't seem germane to the thought experiment anyway, which doesn't allow for epsilons, at least none that could have a causative effect on anything. Like, if you have universe A with no consciousness, and universe B with orange-flavored consciousness, and universe C with grape-flavored consciousness, and finally universe D with cherry-flavored consciousness, and none of them are distinguishable from the others except for universe A and universe D, then you're violating the terms of the thought experiment because you have two supposedly physically identical universes which are nonetheless distinguishable by dint of their underlying consciousness substrates (or lack thereof).
Anyway you're right, it is a weak argument, but only because it doesn't go far enough in outlining why p-zombies are ridiculous (which, IMO, the argument I presented instead, does).
Identity isn't what we're measuring here, it's "humanness" or "consciousness" -- things that are behaviorally distinguishable. Up to an abstract categorical similarity.
Thus they only need to be indistinguishable up to some feature of similarity that allows them to be classified in the same group. That's why, for example, we don't have to worry about "A is the same as B except that it is 2 meters to the left."
OP was saying that P-zombies are "the same" as us in virtue of being indistinguishable from us. I was just pointing out that this inference doesn't go through, since two non-identical things can be indistinguishable.
