A fundamental property is a property such that other properties are instantiated in virtue of its instantiation, but it isn’t instantiated in virtue of the instantiation of any other property. In Plurality Lewis [60, ft. 44] claims that if P is a fundamental property (a “perfectly natural” property in his terminology), it's essentially fundamental; i.e., if P is fundamental, then it's necessary that, for any object x, if x has P, then there is no object y and property Q such that x has P in virtue of y having Q. Here the idea is that fundamentality is absolute rather than world-relative.
I’m sympathetic with the idea that fundamental properties are essentially fundamental in this sense. Hence, if priority monism (PM) is true (the thesis that (i) the proper parts of the world exist ultimately in virtue of the world’s existence; and (ii) the properties of the proper parts of the world are instantiated ultimately in virtue of the properties the world itself instantiates), and if a distributional property (in Josh Parson’s sense) D is the one and only fundamental property, then D is essentially fundamental. Hence, there is no world in which D is instantiated in virtue of any other property.
Ben Caplan in conversation suggested something like the following. Following Peter Vallentyne, a contraction of a world is ‘a world “obtainable” from the original one solely by “removing” objects from it’. Consider a world, w, that is a contraction of the actual world, @, that lacks one of @’s proper parts, say my left shoe. (As a contraction of the actual world, W is otherwise as similar to the actual world as possible.) Suppose that PM is true, and if PM is true, then PM is necessarily true. So PM is true in w. Let D* be the global distributional property that’s fundamental in w. Ben suggested that it seems that D* is instantiated in the actual world, and D* is instantiated in virtue of the instantiation of D. But if this is right, then D* is fundamental in one world but not in another, so fundamental properties aren't essentially fundamental.
I’m curious what you all think of this example. Do you think this case undermines the claim that fundamental properties are essentially fundamental?
-Kelly
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9 comments:
How are we supposed to think about distributional properties? I think it will make a difference to whether or not the argument you attribute to Caplan is a good one.
Consider analogs of D and D*, P and P*, instantiated in much simpler worlds. We can represent them as follows:
P: red-here-and-blue-there-and-leftshoe-over-there
P*: red-here-and-blue-there
In this case, it looks like P* is somehow contained in P, or that P* overlaps P, or that P* would be instantiated whenever P is. But if these distributional properties are holistic in some sense (which is what the hyphens are supposed to represent) then this appearance is deceiving. P and P* are just totally different properties. Of course the correct representation could be this:
P: red-here AND blue-there AND leftshoe-over-there
P*: red-here AND blue-there
(notice the lack of hyphens)
On this way of representing things it looks like P* would be instantiated in virtue of P's instantiation. But we'd have to know that distributional properties are like this latter representation rather than the former. (And I thought that this latter case is more like what a structural property is.)
It's an interesting argument, but now I'm not sure if I see the intuitive force behind the claim that fundamental properties are essentially fundamental (I don't have my copy of Plurality on hand).
Forget about contraction worlds and distributional properties and monism and the like -- why would Lewis have wanted to say this? If we're pluralists, then won't there always be some other world where some lower ontological level is instantiated (assuming fundamental properties are something like intrinsic properties of fundamental objects)? If the fundamental properties here turn out to be properties of quarks, can't there be another possible world where quarks are composed of other things? And another world where quarks don't exist?
I agree with Jeff. I take it that an irreducible distributional global property of w will not be the same in another subtraction w* because they will differ in their DISTRIBUTION.
-Einar
This has been helpful. Let’s see… So if distributional properties are nothing over and above structural properties, then it seems that D* is in some sense a component of D. The idea here is perhaps that D is a conjunctive property consisting of various properties, and D* is one of its constituents and is itself conjunctive.
Jeff suggests that if all of this is right then it looks like D* may well be instantiated in the actual world, and it’s instantiated in virtue of the instantiation of D. One might, however, object to this idea thus. Normally we think that conjunctive properties are instantiated in virtue of the instantiation of their conjuncts, not the other way around. But in this case the suggestion is that D*, a conjunct of D, is instantiated in virtue of the instantiation of the conjunctive property it’s constitutive of. (It seems that priority monism at least doesn’t require that we think that conjuncts are instantiated in virtue of the instantiation of their conjunctions. This would be a bad consequence of any thesis.) It is certainly true that the instantiation of conjunctive properties *necessitate* the instantiation of their conjuncts, but one might think that this just supports the idea that there is something more to the in-virtue-of relation than necessitation.
But let’s put this issue to the side and agree with Parson’s that distributional properties are something over and above structural properties. I still think that Ben’s objection has some pull. I’ll try to put it in an intuitive fashion.
D and D* certainly are different properties. But again consider w. D* is instantiated in w, and let’s say that w is thereby such-and-such way. Now consider @. @ is also such-and-such way, but it has something extra: my left shoe. So the instantiation of D* in @ ensures that @ is just like w, save for the something extra. This seems to suggest that @ having D *makes* @ be the D*-way. It thus seems that there might be some in-virtue-business here; it seems that in @ D* is instantiated in virtue of the instantiation of D.
-Kelly
I like the Caplan/Trogdon argument. I'm wondering if you can give it the other way: instead of working from @ (the larger world) to w (the smaller world), take a third world, v, where v contains a duplicate of @ as a proper part. Call this "dup(@)".
If intrinsic properties are preserved under duplication, then, since distributional properteis are intrinsic, any distributional property instantiated by @ will be instantiated by dup(@). In particular, the FUNDAMENTAL distributional property instantiated by @ will be instantiated by dup(@). Call this "F".
If PM is true, then F cannot be fundamental at v, since v has only one fundamental property, and this is a distributional property instantiated only by v and not by any of its proper parts. Therefore, the fundamental properties are not essentially fundamental.
-Ed
A request for clarificatoin regarding Kelly's final paragraph above ... Kelly says,
"So the instantiation of D* in @ ensures that @ is just like w, save for the something extra. This seems to suggest that @ having D *makes* @ be the D*-way."
Let's say that it's true that necessarily, if, @ has D, then a proper part of @ has D*. But is it right to say that, in some sense, a proper part of @ has D* in virtue of @'s having D? Consider a sheet of paper. It has two sides, S1 and S2.
S1 is red
S2 is blue
Suppose that the sheet has the color distribution 'being-red-at-S1-and-blue-at-S2'. Necessarily, if the sheet as this distribution, then S1 is red (and S2 is blue). But should we say that S1 is red BECAUSE the sheet has this distribution?
Think of it this way: what matters as far as the color of S1 is concerned is not the distributional property of the whole per se, but whatever color this distributional property assigns to S1. Consider another distribution 'being-red-at-S1-and-green-at-S2'. Consider the class of distributions 'being-red-at-S1 ....' where the blank is filled by any assignment of color to S2 or something else or where the blank is blank (no assignment of color and nothing else because the entire sheet is S1).
If we are going to say that S1 is red because ... , shouldn't we say that S2 is red because the sheet instantiates the distributional property that is the disjunction of all the distirbutional properties in this class?
Ok, I'm running out of steam and I'm not sure exactly where I was going with this. I was going to try and say that there's not really much difference between this property and the property 'being red at S1'. The disjunction is nothing but the list of all the ways that the sheet could be red at S1.
Ed
The next to last paragraph in my last comment should say "S1" where I wrote "S2". Oops.
Re Barak's comment: Suppose that quarks are mereological atoms in the actual world. Lewis can say that there are other possible worlds in which (counterparts of the) atoms instantiate completely different properties. These properties would be "alien" fundamental properties. It's just that the actual fundamental properties can't be instantiated in any possible world in a non-fundamental fashion, and the same goes for alien fundamental properties.
Re Ed's two comments: I agree that the dupication argument you sketched works too. I'm not sure, however, about the second concern. Earlier I remarked that it's weird to say that conjuncts are instantiated in virtue of the conjunctive properties they are constitutive of. I think it may also be strange to say that a non-distributional property is instantiated in virtue of a disjunctive property consisting of various distributional properties, each of which if instantiated ensures the instantiation of the non-distributional property in question.
-Kelly
Kelly, I think you're misreading me, or else I mistyped. I would think that the property instantiated in virtue of the disjunctive property IS distributional (as is the disjunctive property). Does this avoid the wierdness you're talking about?
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