Wednesday, February 06, 2008

Relative identity at a time

Working at the ancestral home of relative identity, I feel the need to say something about it. The relative identity theorist says that we can’t speak of x and y being identical simpliciter but only identical relative to a sortal, and that while x and y might be the same F they might not be the same G. So, for example, while the foetus in 1979 might be the same biological organism as that typing this blog post, it is not, perhaps, the same person.

Something I was reading recently suggested the following argument against relative identity. The cases that are remotely plausible as being cases of relative identity are (like the one above) cases of identity across time. There are no plausible cases of relative identity at a time. But if that’s the case, we should think that identity at a time is absolute. In which case we shouldn’t think that the relation that is holding across time and is sortal relative is identity at all. And so we don’t really have relative identity: we’ve just got no cases of identity across time, but with a surrogate relation that holds between entities across time and is like identity in some respects but which is sortal relative.

I guess I think that’s a good argument against relative identity if the premise is correct, but I’m not convinced that there aren’t cases of relative identity at a time that are just as plausible as the cases of relative identity across time.

Before I give my case, consider the following situation. Suppose there is a sculptor, Bob. Bob takes a lump of clay at t1 – call it CLAY - and makes it into a statue of a man at t2 – call it STATUE. We have the familiar question as to the relationship between CLAY and STATUE. Some will say that STATUE is a proper temporal part of the CLAY, some that it is distinct but constituted by CLAY. The relative identity theorist, as I understand her, thinks she has a simpler story: STATUE is the same lump of clay as CLAY, but not the same statue (since CLAY is not a statue, and x and y are only the same F if they are both Fs). But that is relative identity across time, of course, not at a time. We don’t get relative identity at a time on this story: STATUE is both the same statue and the same lump as STATUE, and CLAY is the same lump as CLAY, and it doesn’t make sense to either say or deny that CLAY is the same statue as CLAY, since it isn’t a statue.

Now suppose another sculptor, Sara, made a different statue from a different lump. Sara’s sculpture is an intrinsic duplicate of Bob’s sculpture (STATUE), but while Bob’s sculpture is of a man, Sara’s sculpture is of a lump of clay shaped like a man. Sara’s sculpture has aesthetic properties that Bob’s sculpture lacks: her work is a comment on the very nature of art and representation. You can imagine her sipping Merlot out of a teacup and proclaiming the impossibility of separating the signifier from the signified, or something.

Now suppose there is a third sculptor, Jacob, who decided to kill two birds with the one stone and sculpt two statues from the one lump of clay: a statue of a man and a statue of a lump of clay shaped like a man. We know they are two, because they differ in their aesthetic properties. At a single time t after the sculpting is complete, then, there is the lump of clay, LUMP, the statue of a man, MAN, and the statue of the lump of clay shaped like a man, LUMP-MAN. MAN is the same lump of clay as LUMP, and LUMP-MAN is the same lump of clay as LUMP. It seems to follow that MAN is the same lump of clay as LUMP-MAN. Now, the logic of relative identity is somewhat up for grabs, but x is the same F as y and y is the same F as z seem to entail that x is the same F as z. Counterexamples to transitivity should only arise when there’s a change in sortal. And in any case, it’s independently plausible that MAN is the same lump of clay as LUMP-MAN, since there’s only one lump of clay in the vicinity. But MAN is not the same statue as LUMP-MAN – they are distinct statues, for they have different aesthetic properties. So MAN and LUMP-MAN are, at one time t, the same lump of clay but different statues. So we have relative identity at a time.

Now of course there are loads of things we could say without invoking relative identity, such as that the one lump constitutes two statues at this time, or (my preference) that you can’t conclude that there are two statues from a difference in aesthetic properties. But that’s not the point. There’s always an absolutist story one can tell when the relativist would tell a relativist story; my claim is only that this case of relative identity at a time is just as plausible as the alleged cases of relative identity across time, in which case the above argument against relative identity is unsound, and doesn’t give us reason to accept absolutism. (Common sense on the other hand . . . )

8 comments:

Geoff said...

Great post! It's not so easy to combine philosophy and blog but you do it well. Is there any significant difference between the LUMP-MAN/MAN case and a single individual holding two different posts within an institution (say) - each post granting different powers? Ben is identical with King but not with General, so at one time, t, King and General are the same person, but different posts.

Jason T said...

What you say looks right. But I was a bit surprised that the thing you read suggested there weren't any plausible synchronic relative identity cases: I thought that one of the common applications of relative identity (insofar as anything having to do with relative identity is common at all) was in the problem of the many. Tibbles the cat (who is getting sick and tired of being the subject of so many philosophy examples) might be made up of hunk of matter M, or hunk of matter M* which is just M minus a molecule at the tip of Tibbles' whisker. Then M is the same cat as M* (and both are the same cat as Tibbles), but not the same hunk of matter at M*, and all of this is at a time.

Was the author's thought maybe that the problem of the many case is implausible (in a way that, as it turns out, LUMP-MAN isn't)? This might be right: suppose we endorse the following sortally-relative Leibniz Law principle:

(SRLL) If x is the same F as y, then if P(x), then P(y).

Now Tibbles has a problem. He is the same cat as M, so he is made up of (say) 10^23 molecules. But he's the same cat as M*, so he is made up of (10^23)-1 molecules. So there's no single number of molecules such that Tibbles is made of that many molecules. (Or, if you don't like that example, consider how heavy Tibbles is --- presumably, he should be slightly lighter if he's made up of 10^23-1 molecules than if he's made up of a full 10^23 molecules.)

I was thinking one nice feature of the LUMP-MAN case was that (as far as I can tell, anyway) there are no parallel problems. There's some pressure to say that Tibbles is made up of some number of molecules. But there's no downwards pressure to say, for instance, that since the statue LUMP-MAN is a comment on the very nature of art and representation, so is the lump of clay LUMP. And, at least on a cursory look, I can't think of any properties that we want to inherit *downward* the way we tend to think that number of molecules and/or weight gets inherited upwards.

OK, so bold conjecture time (assuming the above is right, which is a big assumption to swallow): relative identity at-a-time is going to be generally plausible only when we've got multiple F's "at the top" (as it were) that are the *same G*, where G is "below" the Fs in the material-constitution hierarchy. Reason: things higher-up in the hierarchy inherit properties from things below them in a way that the things below don't inherit from things higher up.

Ross Cameron said...

Geoff: the only thing I can think of that might lead you to prefer my case to yours is that you might think the inference from a difference in powers to numerical distinctness was independently dodgy (say because you thought modal predicates were context sensitive) in a way that the inference from a difference in aesthetic qualities to numerical distinctness isn't. (I'm thinking of Fine in recent stuff, who seems to give more weight, when arguing for the non-identity of a thing and its matter, to facts like 'the statue is Romanesque, but the clay isn't' over facts like 'the clay could be squashed but the statue couldn't'. But other than that, the cases look pretty similar to me. Thanks for the extra case.

Jason: The author I was reading was making a pretty throwaway remark on this stuff, so wasn't saying much about it. But everything you said sounded exactly right to me, including the bold conjecture and the reason for it. Really interesting stuff - thanks!

Daniel Elstein said...

I thought that part of the attraction of relative identity (at least to Geach) was that it helped to make sense of the doctrine of the Trinity (i.e. the Son is the same god as the Father, but not the same person). Now I suppose that due to divine atemporality, that isn't exactly relative identity at a time; but it's hardly relative identity across times either. Of course, I'm gratified if you don't think the doctrine of the Trinity is remotely plausible...

More helpfully, could you have examples like teams, which might be less resistable than the pretentious artist case? E.g. the pub pool team is the same group of people as the pub darts team, but it isn't the same team.

Ross Cameron said...

Daniel, why do you think my artist case is pretentious? Hee hee. Ambiguity is funny.

Geach did want to use relative identity for the Trinity, of course, and this might be construed as relative identity at a time. But I guess the thought is that if you're going to appeal to relative identity to convince your opponent that the doctrine of the Trinity is coherent, then you should be able to motivate it independently, in which case you'd better find examples of it other than the Trinity.

I think the case of teams is fine as well - but I can't see why it is less resistable than my case: can you say more?

Daniel Elstein said...

Well, maybe someone would say that that there's only one sculpture, with two modes of presentation. If I draw a duck-rabbit, do I get to say that I've made two drawings? Whereas I'm more inclined to say that there really are two teams. After all, the darts team is gunning for promotion, whereas the pool team stares relegation in the face.

Admittedly, I'm just making a kind of ordinary language argument here, in that we seem happy to talk about multiple teams with the same members, but not about multiple statues made of the same clay. But that's a pretty contingent feature of usage. So maybe I'll change my tune when the Turner prize committee awards the prize for LUMP-MAN. Seriously, it's a lot of money; you should go for it.

Lee W said...

I don't understand why the simple statue case doesn't give relative identity. At t2 you have both STATUE and CLAY and whilst they are the same lump they are not the same statue since, as you say, CLAY is not a statue. But this is an instance of R in Wiggins which is what relative identity is.

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