December 07, 2006

Accidental Properties and Transworld Identity

The problem of temporary intrinsics, as is well known, has its modal analog---the problem of accidental intrinsics. But each of these problems cuts much deeper than their names suggest. I query whether the deeper problems have a response in the literature.

Here's the initial temporal problem. At one time Brit is bent (because sitting). Later she is straight (because standing). Is this a violation of Leibniz's Law? A well rehearsed endurantist answer is NO. We simply index to times. Brit has both the property being bent at time t and the property being straight at t+1. No contradiction here. Lewis' objection to the fix is that so called intrinsic properties (such as being straight or bent) are now treated as relational since indexed to time. In sum, there are no temporary intrinsics.

The modal analog, the problem of accidental intrinsics, arises in critique of transworld identity---the view that objects may exist in more than one possible world. In the actual world Brit is 5'10''. In other merely possible worlds she is taller. The transworlder will insist that there is no violation of Leibniz's law. Brit has both the property having height 5'10'' in the actual world and the property having height n, where n>5'10'' in world w2. No contradiction here. Again, the reply to the fix is that our intrinsic properties have suddenly become relational.

But isn't the problem with this fix to transworld identity much more general than stated? Indexing to worlds robs objects of their accidental properties (intrinsic and relational). For if an object's properties (and relations) are indexed to worlds, then the object has them necessarily. In every possible world it is true that in w1 Brit is 5'10'' (is a philosopher, lives in St Louis, etc.). The problem with indexing to worlds is then not simply a problem for accidental intrinsics, but a problem for accidental properties and relations more generally. (Analogously, the problem of temporary intrinsics underwrites a problem for temporary properties and relations more generally. No properties are temporal! A fortiori none of them are temporary intrinsics.)

8 comments:

Lee Walters said...

Sounds like an argument for presentism and modalism. Brit is straight and was bent, Brit is a philosopher but could have been an accountant. No violations of LL. Can retain temporary and accidental properties with ~Always (p) and ~Necessarily (p).

I am not suggesting this is a problem-free panacea.

E.J.G. said...

I can only comment the "modal" part of the problem raised here, and have no pretension to offer a solution. But from the standpoint of the modal language, indexes (which can be introduced in the [formal] object language as "nominals", giving rise to so-called "hybrid languages") can be given two readings: one (analogous to) de dicto:

(1) [at world w] Necessarily (A has property P)

and another (analogous to) de re:

(2) Necessarily [at world w] (A has property P)

(Where A is assumed, for the sake of the argument, to be a rigid designator, so that we have at least some invariance, see later.) (1) simply states (in the enriched object language) the locality of the modal claim; while (2) is (harmlessly) true at every world w is accessible from, i.e. the following sentence:

(2') [at world w'] Necessarily [at world w] (A has property P)

is true at every world w'.

Suppose now that we want to express statements about the contingent property Q of A (I refrain from saying simply "accidental" because there are, according to Aristotle, "necessary accidents", and the identification forced by modern modal idiom between the necessary and the essential is unsatisfactory at best); the problem here is the scope of the negation operator: assuming that it holds that:

(3) [at world w] not-Necessarily (A has property Q)

it does not hold that:

(4) not-Necessarily [at world w] (A has property P)

My point is the following: "pushing" the index in the object language makes (3) true and (4) false, hence (3) fully compatible with (2). Indexing does not anymore "rob" A of its contingent properties. But it cannot be retained as a way of "fixing" Leibniz's Law violation.

Mike said...

Hi Joe-

Suppose all accidential properties are world-indexed. In that case, for accidental property P, and world w, x is P-in-w only if x is P-in-w in every world in which x exists. Similarly for temporal intrinsics. How does this entail that there are no accidental properties? The property P still seems accidental since though (w')(x is P-in-w in w'), it is nonetheless true that (Ew')~(x is P-in-w')

E.J.G. said...

I'll risk a comment on Mike's. Assume (as he does) standard modal predicate logic semantics (i.e. Kripkean, with constants as rigid designators). Then P-in-w is, if I understand Mike correctly, accidental for a (assuming that a is P-in-w) if there is a world w' such that a is not in the domain of w'. In this case, identity is itself accidental for a, though necessary. So, if it happens that a is undefined at some world w', then any a's w-property (or any of a's "other-world" indexed property) is both accidental and necessary. Equivalently P-in-w is accidental for a iff identity for a is (unless one puts some restriction on the application of the term "accidental" to relations in general, or to identity in particular).

Apart from the fact that Mike's proposal offers a reductio argument for the identification of "necessary" with "essential" (at least in varying domains, and on an arguable construal of "accidental"), it seems a very problematic way to rescue the claim that there are accidental properties. For either we assume varying domains, and thus, for individuals not present at every world, every world-indexed property is both accidental and necessary; or we assume constant domains, and every world-indexed property is necessary and not accidental.

Joe said...

Hey, thanks for all the interesting comments.

To E.J.'s latest comment. I thought Mike meant to express the contingency thus: Not every world w in which a exists is such that a is P in w.

E.J.G. said...

Thanks for the precision, Joe: in this case I missed the point. But if existence in w and inclusion in the domain of w do differ, isn't then existence reintroduced as a (first-order) predicate? And if this is the case, then the clause for evaluating in any world w' "a is P-in-w" depends on the truth value of "a Exists-in-w' ". This would lead to some complication (though re-introduction of an existence predicate makes sense in constant domains containing merely possible individuals). I'd like to have Mike's comments on this.

joe said...

There is a common thread through some of the initial comments. I believe it goes like this. Suppose in w1 that s is P. Then it will be true of course that, in every world, s is P-in-w1. However, the contingency in question may be expressed by adding that not every world w is such that s is P-in-w.

This is very interesting, but as E.J.G. noted, it will not help the transworlder who indexes to avert the argument from Leibniz's Law. Which contingent property is attributed to s?

“Not every world w is such that s is P-in-w” ?

tells us something about the modal status of P, namely that it is not instantiated by s in every world (in which s exists). But it is precisely P that the indexer denies is instantiated by our subject (lest we face off with Leibniz). So if we want to say that s has a property contingently, then the expression of contingency must be about a property that s is said to have ---for the indexer that won’t be P but P-in-w1, where ‘w1’ is a name.

Mike said...

EJG, let me see whether I can address some of your comments. You say,

. . . the clause for evaluating in any world w' "a is P-in-w" depends on the truth value of "a Exists-in-w' ". This would lead to some complication (though re-introduction of an existence predicate makes sense in constant domains containing merely possible individuals). I'd like to have Mike's comments on this.

I'm not sure why the evaluation of 'a is P-in-w' depends on introducing an existence predicate. Certainly, I think, worlds in which "a" doesn't exist are worlds in which 'a is P-in-w' is false, and also worlds in which 'a = a' is false. Since they entail the generalizations respectively to (Ex)(x is P-in-w') and (Ex)(x = a). But that does not require the introduction of some special existence predicate. For this reason I was unsure about Joe's claim (initial post) that,

Indexing to worlds robs objects of their accidental properties (intrinsic and relational). For if an object's properties (and relations) are indexed to worlds, then the object has them necessarily. In every possible world it is true that in w1 Brit is 5'10'' (is a philosopher, lives in St Louis, etc.).

I don't think it is true in every possible world that 'Brit is 5'10" in w1', since there are worlds in which Brit doesn't exist and so does not have that property (or any other). What holds in every possible world is that ''Brit is 5'10"' is true-in-w''. I'm guessing the idea is that Brit has that property essentially, which seems right to me. But there should be a way to preserve the contingency of that property. It's a very interesting question. Here is one (very tentative) suggestion. Call a world-indexed property 'P-in-w' contingent* only if ~[]((a is P-in-w)-> Pa). It does have the odd consequence some world-indexed properties are essential and contingent*.