Wednesday, March 14, 2007

Vagueness and contradiction in derivative reality

While we disagree on some of the details, both Robbie and I agree one can admit that there are complex objects without, in some sense, being ontologically committed to complex objects: there need be no complex objects in fundamental ontology.

What complex objects exist derivatively then? Well, if they’re not really extra elements of our ontology we might think we should just go ahead and say that the claims of universalism come out true: that for any collection of objects, there is (derivatively) a sum of those objects. That, I think, is Armstrong’s view: complex objects are an ontological free lunch, so we might as well be universalists.

But we’re certainly not forced into saying that. Just as we are concerned with reconciling a nihilistic ontology with the truth of everyday judgements concerning the existence of tables and persons, etc, we might also be concerned with not going too far – that is, preserving the everyday judgements concerning the non­-existence of the sum of Hitler’s left ear, an atom in the sun, and the number 2. So we might tell a story whereby our fundamental, atomistic, ontology accounts for the truth of some theory of restricted composition.

Indeed, it seems that we can avoid one of the main objections to restricted composition: namely, the Sider-Lewis objection from vagueness. If composition is restricted, they say, it must be either brute or vague. If it’s brute, that’s metaphysically arbitrary in an objectionable way. But if it’s vague then this must be ontic vagueness, since there’s no vagueness in the language of quantificational theory, and that’s no good because ontic vagueness is A Bad Thing.

There’s plenty to say about that argument as applied against run-of-the-mill restricted composition theorists, of course, (Is brutality really all that bad?[1] Is ontic vagueness?[2]), but even if you think the argument is good there, it seems to have no weight at all against the kind of restricted composition you would get on the Robbie/Ross route.

Suppose we go organicist. A complex object only (derivatively) exists if the simples that account for its existence jointly and exhaustively participate in some life. There will be cases where it is vague whether we have a complex object. Is this objectionable? It seems not – even on the assumption that there cannot be ontic vagueness. Because what there really is is (we may suppose) perfectly precise. It’s just vague whether some collections of the fundamental existents account for the existence of a complex object. In my terminology, it will be vague whether they make true any existence claims concerning complex objects. Ontic vagueness only looks worrying, if it ever does, if it infects fundamental ontology: the derivative can be as indeterminate as you like. (C.f. Elizabeth’s ‘Ontic vagueness without supervenience’.)

(Maybe this gives us an argument for priority monism: the view (defended by Jonathan Schaffer) that the one big whole is what's fundamental, and the parts derivative on it. Quantum mechanics tells us (my esteemed colleagues tell me!) that the very smallest things are indeterminate. Maybe that gives us reason to deny that they're fundamental and instead accept that the quantum particles are derivative on the fundamental whole.)

If that’s right, it seems to apply to other cases as well. I’m thinking in particular of dialetheism. Many people find objectionable the idea that both a proposition and its negation can be true. I share the suspicion if the proposition concerns how fundamental ontology is; but it doesn’t seem objectionable to me if fundamental reality is consistent, but the consistent way fundamental reality is results in an inconsistent derivative reality.

Think of the particular cases of true contradictions dialetheists are fond of. The Liar sentence – L – springs to mind. L is both true and false! But who cares? Sentences are not, we might think, part of fundamental ontology. What’s fundamental is, on my view, just the truthmakers. So what would be objectionable is if, say, the truthmaker for L both existed and didn’t exist, for then fundamental reality would be inconsistent. But the dialetheist is not committed to anything like this. We could easily tell a story whereby fundamental reality (for me, the truthmakers) is consistent and makes true both L and its negation. And this just doesn’t seem objectionable to me. Why should I care about some sentence being both true and false? Why should I care, even, if some thing both does and doesn’t exist – provided the sense in which it exists is mere derivative existence? All that seems bad to me is if there is inconsistency at the fundamental level; if our best theory tells us that this consistent fundamental reality accounts for true inconsistencies, so be it.

[1] See Ned Markosian’s ‘Brutal Composition’, Daniel Nolan’s ‘Vagueness, Multiplicity and Parts’ and my ‘The Contingency of Composition’.


Robbie said...

Hi Ross,

This seems right to me, and I think it fits in nicely with the kind of "postulationist/interpretationist" story about what fixes the ontological commitments of our language that I offer in the paper "Fundamental and derivative truths" linked to a couple of posts back.

The reason it'd work so nicely is that "mere" metaphysical-vagueness (vagueness at the non-fundamental level) on this analysis has pretty much exactly the same source as semantic/epistemic vagueness: semantic indecision, or epistemic blocks, over the question of what the *right* semantic clauses for our language are.

I'd like to hear more about the truthmaker theorist's story. What we need is for claims like: "proposition p has truthmaker M" and so "proposition p has ontological commitments C" to be vague. I've said why that's ok and non-scary by my lights (it's just another example of semantic/epistemic vagueness). I'm not so clear that you can make that case, since (I gather from conversation) for you these sort of statements express necessary, non-negotiable truths.

Now, it's not clear I can pin (non-mere) metaphysical-vagueness on you, in virtue of you endorsing metaphysical vagueness in the "is an ontological commitments of" or "is the truthmaker for" relation. I could if you thought that propositions and truth-making relations were part of the fundamental level: but I expect you to deny this.

Still, you haven't got the clean *vindication* of where the vagueness comes from, if not heavy-duty metaphysical vagueness, that I've got.

Does that strike you as right at all?

(By the way, it doesn't seem to me there's any parallel worry on the dialethist point. It doesn't look like there need to be contradictions about what truth-makes what, in order for reality to truth-make both a proposition and its negation.)

Ross Cameron said...

Hey Robbie,

(There’s something really weird about corresponding like this when I could just knock on your door!)

I agree, the case is more clear cut (on the truthmaker story) for dialetheism than for vagueness. There’s no need at all to say that A both does and does not make L true, only that A makes L true and that it, or indeed something else, also makes not-L true.

On the vagueness case, I guess there’s a couple of ways the TM theorist could go. The way I was thinking of it was definitely that it is indeterminate whether or not A makes p true. Now certainly for me statements concerning what makes what true, as you put it, “express necessary, non-negotiable truths.” What does that mean? Well, I take it to mean that if it is true that A makes p true then it is necessary that if you’ve got A you’ve got p being true, and that this doesn’t depend on the context of utterance or anything (the latter to rule out Lewis’ things-qua-truthmakers story). I don’t see immediate trouble with indeterminacy, then. I commit myself to thinking that if these simples make it true that there’s a complex object then you can’t have those simples without it being true that there’s a complex object – but since it’s indeterminate whether the simples do make that true it’s simply indeterminate whether that claim is necessarily true or not.

The big question is how to treat the indeterminacy of ‘A makes p true’. If you really want to purge ontic vagueness I guess we might say: look, there’s loads of relations out there, and we’ve not settled which one is picked out by the locution ‘makes true’. Personally, I prefer something of a middle ground. I like the view that there is a unique truthmaking relation but sometimes it’s just indeterminate whether or not it holds between some things and some proposition. (And, incidentally, I’m happy to take this relation to be part of fundamental reality.) I’m happy to treat this as ontic indeterminacy. But I still think the position is advantageous, because we don’t have a commitment to ontically indeterminate existence. Vague existence seems to me more worrying than ontic vagueness per se. So if I can have vague existence only at the derivative level, in virtue of having ontic vagueness (but no vague existence) at the fundamental level, that seems quite attractive to me.

Robbie said...

That sounds right. I guess the "many candidate truth-making relations" would be to drop the sense in which truth-making is a single non-negotiable, and make it a bit more like my position (In so far as I can reconstruct a notion of truthmaking in my picture---which isn't very far---then what it'll say is exactly that there's a multiplicity of candidate relations, and how we select among them is a semantic matter).

The other line: where there's ontic vagueness, but not of any worrying kind, in the truthmaking relation, seems interesting. That'll make our views very different. I can avoid ontic vagueness for longer than you can. (But given that I'm sympathetic to there being ontic vagueness, at the fundamental level, I'm not going to press this one too hard).

One difference between our two views, which leads to this difference, is that for you the proposition-to-reality relation (Truthmaking) is part of the fundamental level. For me that relation is at the derivative level (I guess that's why my view looks a lot more like fictionalism than yours does).

I want to ask some questions about truthmaking at the fundamental level. If we're operating with something like a Finean framework, then that means we have: REALLY(a makes p true), at least in some cases. So at least some propositions will also be around at the fundamental level, no?

Now, I'm wondering what these propositions are like to be around. Do we think of them as Russellian? If so, then if the proposition that Robbie exists, is at the fundamental level, you'd have thought it's consituents would be too. And that's a way of me getting back in there, which you didn't want.

So maybe you've got a non-Russellian conception: but what? Fregean thoughts? Sets of possible worlds? Strikes me that all these kinds of things would be nice to explain away as merely derivative. But then I'm not sure how a relation between them and really existing stuff can itself be fundamental.

Ross Cameron said...

I want to have the truthmaking relation be fundamental, and it be really true that A makes p true, but resist that the proposition [p] is fundamental. I don't see why I can't have a fundamental relation link a fundamental entity to a derivative entity.

On the multiple candidates view. Call that abandoning non-negotiability if you like; but I was thinking of non-negotiability as just that what things bear the truthmaker relation to what propositions doesn't vary from context to context. I can still hold that. *Whatever* the TM relation is, it holds or doesn't hold independently of context. But it's just not clear which realtion *is* the TM realtion.

Robbie said...

Ok. I was thinking of things with a Finean setup, where we express what's fundamental via an operator "it is fundamentally the case that". And it's *really* hard to see how to articulate the view that there are fundamental relations whose relata (at least at one end) are always derivative.