Tuesday, August 08, 2006

Semantics for nihilists

Microphysical mereological nihilists believe that only simples exist---things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it's not so much fun.

If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.

I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.

Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).

Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.

Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.

I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.

The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.

The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.

So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.

(cross posted on theories 'n things)

4 comments:

Andrew said...

What about the Sider-sentence itself? Does it have parts?

In the case of possibilia, the SS is normally taken to be an abstract, actual existent. So it doesn't itself fall into the problematic kind (non-actually existent possibilia). So it's fair game for the Sider-style constructivist to appeal to such an entity in giving their explanation of the problematic cases.

But in the case of mereology, it looks as if things might be a bit more problematic. It seems halfway plausible that the Sider-sentence is mereologically complex, and so falls into precisely the problematic kind. So it has to be made clear how the MMN-theorist can appeal to it in good faith to explain away the existence of actually existent complex objects.

Here's one issue. If the sentence has no parts, then how does it stand in entailment relations standardly defined in terms of free reinterpretation of non-logical parts?

Robbie said...

Hmmmm. Will have to think about that one. An initial thought: one might say that it hasn't got mereological structure, but rather (non-mereological) set-theoretical structure. Perhaps in the (Lagadonian) language which includes the pluriverse sentence, strictly "Billy" won't be a part of "Billy runs"; rather, it will be in the transitive closure of the set that is identified with "Billy runs".

(I'm not intending by this to take a stand on the metaphysics of ordinary sentences; I'm willing to let the "pluriverse sentence" be any construction that can play the theoretical role.)

It is a bit embarressing to have to lean heavily on some *other* structuring relation, which you might think to be in worse standing than part-hood. That does seem a sense in which Sider's use of the pluriverse sentence might be stabler than mine.

Of course, granted the use of set theory here, the nihilist might just try to put sets of particles arranged rabbit-wise into the extension of "rabbit", and do pw-semantics that way. So maybe you can get a dilemma going against me that way.

Andrew said...

The set-theoretic structure does seem in better standing in some respects. You might say that giving up talk of set-theoretic structure just entails giving up (literal) talk of sets. But if the Van Inwagen approach can be made defensible, giving up mereological structure doesn't entail giving up literal talk of e.g. chairs.

Moreover, we understand the set-theoretic structure pretty well, as compared with the mereology of actual concreta, you might say.

Just to check I'm understanding your positive suggestion right - is it that e.g. if we have exactly 2 possible particles A and B, and two worlds w1 and w2, and a predicate G, then we could assign e.g. the following kinds sets to the relevant syntactic entities (using standard brackets for ordered triples - HTML trouble!):

(i) the name 'A' = {A},
(ii) the predicate 'G' = e.g. {(A, True, w1), (A, False, w2), (B, False, w1) (B, True, w2)}
(iii) the sentence 'GA' = e.g. {(A, True, w1), (A, False, w2)}

so that the name 'A' wouldn't be literally a part of the sentence GA, but would be (in this case) e.g. a member of a member of that sentence?

Robbie said...

(A previous version of this comment was eaten by some internet monster... maybe it'll turn up sometime!)

The idea I had in mind was the following:

(i) A name N will be identified with some object o.
(ii) A predicate P will be identified with some object o'.
(iii) The sentence N^P will be identified with the ordered pair (N,P) , i.e. (o,o').

(So concatenation of expressions is identified with being first/second members of an ordered pair).

Then (following Sider's example) you do the Lagadonian thing: e.g. you let Billy himself be the name of Billy; the property of running be the name of the property of running, etc. So you end up identifying atomic sentences with an ordered pair containing an object and a property. (That's the simplest version: it might need to be tweaked, e.g. by adding markers for syntactic category to the things identified as names/predicates.)

There's some interesting issues going on with exactly what the "property" should be here. One natural thought is for it to be a function from worlds to extensions (sets of possibilia). But you'd have to check through to see that this doesn't induce circularity in the account. I guess when we talk of the "possiblia" in the transitive closure of the Lagadonian name for a property, what we're doing is talking about whatever actual-worldly-objects play the role of possibilia in the "realistic modal model" that Sider builds the pluriverse sentence from. But this is exactly the area in which you have to keep track carefully of the construction: I'll have to check back to see what Sider says at this point.