Tuesday, May 15, 2007

Necessity, Contingency, and Essence

Today I gave a brief consideration that could be turned into an argument against the following thesis from Divers (which Divers was just presenting, not defending):

(1) x is essentially F iff for all metaphysically possible worlds w, if x exists in w then x is F in w.

Here is a case (this is from Kit Fine's "Essence and Modality"): the essential properties of an object, in the Aristotelian sense, stem from the nature or identity of that object. Intuitively, it is no part of the nature of Sparky that he is a member of a set. But if he exists at w, then he is a member of a set at w. So by (1), being a member of a set is an essential feature of Sparky. So (1) is false. (I hope it's obvious how to make this argument valid.)

If this is right, then the right-to-left direction of (1) fails, but (2) may still be plausible:

(2) If x is essentially F, then for all metaphysically possible worlds w, x is F in w.

Carl suggested that Ben rejects (1) because of the "existence restriction" in the right-hand side. I take it that Ben instead endorses (3) (?):

(3) x is essentially F iff for all metaphysically possible worlds w, x is F in w.

(I assume Ben holds that objects can have properties at worlds where they are absent? (Homework: State the assumption I am attributing to Ben in a way that does not imply the truth of that assumption.))

So if one accepted both Fine's argument and Ben's point, the (partial) account would be (4):

(4) If x is essentally F, then for all metaphysically possible worlds w, x is F in w.

Joe Salerno at Knowability argues here that there are contingent essential properties. So his view is that (5) is correct:

(5) x is essentially F iff if nothing were F, then x would not exist.

This account has several interesting features. One of them is that the right-hand-side counterfactual conditional is, on his view, not vacuously true if the antecedent is impossible. Any thoughts on which, if any of these accounts, is correct, or on what, if anything, can be added to (2) or (4) to yield a more complete account?


Adam said...

I have two questions and one comment.

First, philosophers sometimes distinguish between qualitative and non-qualitative properties. (i) What is the best way to cash-out this distinction, and (ii) is this distinction relevant to an account of essential properties?

Second, there also appears to be a distinction (made by Plantinga) between the essential properties of an object and the individual essence of an object. Is this distinction important here?

It seems to me like the notion of essential property at work in (2)could be made to work if we have in mind something along the lines of a Plantingian individual essence. This is because Plantinga thinks that individual essences exist necessarily, even if they are not exemplified.

Chris Tillman said...

Well none of this is completely uncontroversial, but I think the best way to distinguish qualitative from non-qualitative properties is in terms of those properties' constituents. The idea is that some predicates include singular terms in their syntax or in their logical form. These predicates express non-qualitative properties.

So 'is left of Adam', on this view, expresses a complex property that has the being-to-the-left-of relation and Adam himself as constituents. Thus that property is non-qualitative.

Examples of purely qualitative properties are slightly trickier. One might think 'is red' expresses only a simple property that lacks individual constituents. But if the logical form of 'is red' is basically that of 'is red at t', and if times are individuals, then 'is red' expresses a non-qualitative relation to a time. But there were a lot of 'if's in there. Even if that view is right, think of the relational constitutents of 'is red' and 'is left of Adam'. These would be purely qualitative relations, presumably.

Essential property vs. individual essence is more controversial. For the purposes of asking "what is the correct account of essential properties" I think we should take a weak characterization as common ground so as not to beg questions between the alternatives on offer. So we may say vaguely, with the likes of Aristotelians, that an essential property of x is a property x has in virtue of x's nature. (This is intentionally vague.)

An individual essence, then, is sometimes taken to be something like a conjunction of essential properties. Alternatively, it is conceived by some as a special sort of property that involves identity. On one view, the individual essence of Adam is the property of being identical to Adam. This is non-qualitative on the foregoing account of the distinction. A third conception, and this seems to be Plantinga's, is that an individual essence is a purely qualitative property that bears some special relation to the non-qualitative individual essence. This non-qualitative property can exist without being exemplified.

(One can see why it may be problematic to hold that the non-qualitative property of being identical to Adam can exist without being exemplified--it seems that in order for it to exist, Adam must exist, since he's part of that property. But on the envisaged view, the property can be around without Adam being around.)

Dan said...

Salerno seems to be talking about a different kind of essence. Certainly not the "springing from one's nature" Aristotelian kind of concept.

There seem to be two intuitive pumps at work. One is from the word "essential" that Salerno is working of of. That is, some property is essential for my existence, I'd die without it.

The other is from Aristotle. I haven't read the original but I think it's origins could be modal. Intuitively, there are some properties I have that must be carried along when considering possibilities about me, if those possibilities are to make sense. For instance, the intuition that humanity is essential to me may be fueled by the fact that such contemplations as "what if I were a tree" seem meaningless or trivial. What if I were a tree? Well, I suppose the same thing if anyone were a tree. This would be part of the motivation for (2) and (4).

As far as sorting out identity, if one feels the need to do this, the second approach seems superior. To make this a little less hand-wavey, maybe I should formulate the idea behind the second notion.

(E) F is essential to x iff when considering a possible scenario, ~Fx makes the identity of x irrellevant to the scenario.

This has problems (for instance, if dan was a tree he wouldn't be able to do human-like stuff seems to be a counter-example). As I said before, it's just an intuition pump.

Dan said...

Homework: restate Ben's assumption

let P be the predicate expressed by "x is absent from world w*"

(B) Px being true at some possible world at which x is present does not restrict x from having properties at w*

Now I think... hmmm... if Px is true at some possible world then it must be true at every world at which x can have properties. That means the following would be logically equivalent to (B):

(B') If Px holds at some possible world then Px holds at every possible world.

I believe both B and B' can be coherently denied.

Chris Tillman said...

(B') is equivalent to:

If there is a w such that the proposition that x is absent from w* is true at w, then every world w** is such that the proposition that x is absent from w* is true at w**.

So if we deny that, we accept both of the following:

(a) There is a w such that the proposition that x is absent from w* is true at w, and

(b) It's not the case that for every w**, the proposition that x is absent from w* is true at w**.

So suppose (a) holds. Now consider an arbitrary world, w'. The proposition that x is absent from w* is true at w' iff at w', it is true at w*, that x is absent. By (a), it is true at w* that x is absent. But all it takes for a proposition P about another world to be true at a world is for the proposition that P is true at that other world to be true. So (b) is false, since by our assumption, it is true at our arbitrary world w'.

Another way to put it:

Suppose the proposition that x is absent is true at w.

Then it follows that, possibly, x is absent.

But then by S5 (if possibly P, then necessarily possibly P), it follows that necessarily, it's possible that x is absent.

But since it's true that it's possible that x is absent because it's true that x is absent at w, it follows that, necessarily, x is absent at w.

But this amounts to an argument for (B'). So if (B') is false, this argument (and the preceeding argument) is unsound.

Dan said...

>The proposition that x is absent >from w* is true at w' iff at w', >it is true at w*, that x is >absent.

This is treating "being absent at w*" as having a property at w*, which is what I was trying to avoid (and yet I defined a property in those terms, silly me). But, since it seems like being absent from somewhere actually is a property, something else must be done! Some logical apparatus must capture the concept of presence or absence at a world.

So suppose you divide the domain up according to what exists at each world (like Kripke does). Suppose you can still quantify over the entire domain, but you don't have to. So consider a world w' at which everything is red.

w'(for all)xRx would be true but simply
(for all)xRx would be false.
The former saying "for all x at w', x is red" and the latter saying "for all x, x is red". Sticking the world at the beggining of a sentence restricts the immediate quanitifier to those things existing at that world. I've made no such restrictions on proper names though. This seems like a legit move (I hope). I've tried not to take anything away from SQML.

So, being absent at a world can be expressed:
(suppose a does not exist at w')
~w'(there exists)x(x=a)

So, Ben's assumption...
for some object a and world w', ~w'(there exists)x(x=a) AND for some property P, Pa is true at w'.

Man I wish there were quantifiers as standard keyboard keys.
I'm not sure what I think about this yet, so... just throwing it out there.

Chris Tillman said...

Well it seems that there's no way to capture the assumption without taking something away from SQML since it seems you have to take something away from regular old predicate logic. In particular, if the proposal is correct, then the following inference will not be valid with respect to a world:

Fa .: ExFx

Note that the inference could be preserved if the quantifier in the conclusion is read as absolutely unrestricted, however.

Dan said...

But it seems like the denial of that assumption is akin to the denial of that inference. I.E. it would be saying that something can have a property at a world without existing at that world. But as you say, the inference is still valid with the unrestricted quantifier.

As I see it, I don't see that we're taking away anything we didn't mean to.

Dan said...

P.S. if you get a chance, read the Dilbert in last saturday's free press. The colour comic.

Chris Tillman said...

Yes, I agree. I was just pointing out that we can't keep everything in SQML if we go along with Ben's assumption.

Chris Tillman said...

Are you equipped with a Dilbert link?

Dan said...

here's the dilbert link:

anyway, the inference is still valid with the unrestricted quantifier. So

Fa .: ExFx
is valid, but

Fa .: w'ExFx
is not

So do we really lose out on anything?

Chris Tillman said...

Yeah, that seems to be the inference that Ben wants to reject. (Though recall that he defends it here: http://people.cohums.ohio-state.edu/caplan16/a_new_defence_of_the_modal_existence_requirement.pdf)