Tuesday, November 14, 2006

The Necessity of Composition I

I’ve been revisiting Ross Cameron’s paper arguing that principles of composition need not be necessary. (He is not the only one. I hope to post on Josh Parsons’ paper somewhen—hence the ‘I’ in the title.) I think I still have the worry I tried to express at the Arché Modality Seminar and Workshop. Let me try it again here.

Suppose that one thinks, as I am inclined to, that principles of composition—of the sort of: whenever there are some things, there is something that is a sum of them—are necessary if true as the result of being ‘analytical,’ at least in a certain sense (which I won’t pause to explicitly state ;-)).

Ross objects:

“Existence claims are, seemingly, never analytic; so it seems that a conditional whose consequent was an existence claim could be analytic only if the antecedent asserted the existence of the thing in question. But if the sentence ‘If some objects are in conditions C, then there exists something that is composed of those objects’ is informative then the antecedent does not assert the existence of the thing in question (namely, the sum of the objects in conditions C). The sentence is synthetic, then; there is nothing in the concept of certain things meeting certain conditions that there is a fusion of those objects.”

This seems puzzling to me. Consider the following:

Whenever something is a proper part of another, there is something that is part of the latter but not of the former.

I take it that this has a good claim to be necessary if true as a result of analyticity. And it has the relevant considered form: a conditional whose consequent is an existence claim. In a certain sense, such existence is not “asserted” in the antecedent—hence the “informativeness”—; in another sense, it is (“implicitly”) so asserted—hence the analiticity—.

Mutatis mutandis, Ross’ opponent contends, for the envisaged principles of composition.


Ross Cameron said...

One man's modus ponens is another man's modus tolens, I guess!

I don't think the remainder principle is analytic either, for the same reasons I don't think the answer to SCQ is analytic.

Is the remainder principle necessary (assuming it's true)? It may be - but then I think it is a case of a synthetic necessity.

But I'm not convinced it's necessary either. I'm not convinced you couldn't have a world where both universalism and anti-gunk are true - and in such a world it's plausible that the Dan sentence is false.

But I'm not particularly concerned to defend the contingency here - I merely state for the record here that I don't think the sentence is analytic. Of course, we *could* stipulate to use 'part' so that Dan's sentence came out true, in which case it would be analytic of 'part' that it was true: but then the question would be whether anything had parts (in this sense of 'part'), and *that* wouldn't be analytic.

Dan López de Sa said...

Hi Ross, thanks for commenting here!

I am still a bit puzzled, though. I guess you don't want to say the same thing for the following:

'Whenever two things overlap, there is something that is part of both.'

(Or maybe you do.) But which would be the relevant difference?

Besides, I didn't quite see why my sentence would be false in a world where both universalism and anti-gunk were true. Could you please give me a hint of what you are thinking?

Ross Cameron said...

No: that sentence, I'm happy to grant, is analytic. The term 'overlap' is introduced in such a way that that term must express a truth. What term is introduced in such a way that either the answer to the SCQ or your first sentence (not quite the remainder principle - sorry for the mistake) must express a truth? Is it 'thing'? No - we all know how to apply 'thing', it applies to everything. Is it 'part'? Well, you *could* use 'part' that way, but then it's not analytic whether there are any parts.

Universalism and anti-gunk seem, on first glance, incompatible. For universalism tells us that there's a sum of everything - call it U. Anti-gunk tells us that everything is a proper part of something. So U is a proper part of something, call it U*, which means there is something bigger than U. But then how can U have been the sum of *everything*?

One way to resist the conclusion is to deny that there is something that is a part of U* but not U. That requires denying your sentence.

Dan López de Sa said...

Yeah, I guess ‘thing,’ ‘sum,’ ‘part,’ and ‘proper part.’

Of course, it might be synthetic whether there are any (proper) parts (or perhaps parts at all), in as much as it might be synthetic whether there are any circles. But this does not preclude the principles of geometry being non-analytic, does it? (Perhaps not the best example, given what some people say, but you know what I mean.)

Thanks for the anti-gunk explanation! I guess there might be other possible paths available. In any case, I take the apparent unconceivability of my sentence failing to be firmer than the apparent conceivability of anti-gunk ;-)!

Dan López de Sa said...

I meant, of course: that this does not preclude the principles of geometry being analytic, sorry ;-)!

Ross Cameron said...

No. But while I think we can discover that there are no perfect circles I don't think we can discover that there are no proper parts - at least, not by finding out that there're no things that obey the axioms of classical mereology.

I don't learn what the parthood relation is by learning what axioms it obeys. I learn it by being pointed to the relation that holds between me and my hand, a house and a wall, etc. We then set about discovering what axioms that relation obeys.

If you introduced 'part' into your language so that it would conform to the axioms of classical mereology that's fine - you can do that. But you can't at the same time stipulate that your sense of 'part' is the same as the same as that that applies to the relation we're introduced to by ostension. (This is the problem with hanging around with neo-Fregeans too much :-) It's the ontological argument all over again!)

Dan López de Sa said...

Mmm interesting!

So, recapitulating a bit, it seems to me that your objection against the “analyticity” claim in the original composition case (and also wrt my sentence) is not, then, that much that "existential" statements cannot be analytic, for you grant that some, with the relevant form, are indeed analytic after all (like the one on overlapping). Rather the objection is that, in the problematic cases, the supposition that the considered ones are analytic is in tension with certain facts about the way we have acquired mastery of the relevant terms. Is this right, concerning the form of your objection?

As to its matter, I would be curious to learn which facts about use make it the case that unrestricted mereological composition principle does not hold for ordinary ‘part.’