Wednesday, April 20, 2011

'In virtue of' and propositions

Like many metaphysicians, I think the world is structured. Some truths hold true in virtue of others; some things exist in virtue of other things; some truths are made true by things. I think that there’s only one relation here, and it is the in virtue of relation, that holds between true propositions. For A to exist in virtue of B (i.e. for A to be ontologically dependent on B) is for the proposition [A exists] to be true in virtue of the proposition [B exists]; for the proposition P to be made true by A is for P to be true in virtue of the proposition [A exists].

Sometimes I hear the objection that this assumes that propositions are themselves fundamental constituents of reality. This objection is misplaced, for the view does not assume that. I can’t really see why one would think it did, but I’ve heard it enough times that I think it’s worth spelling out why I don’t think it does. If I’m just confused, I’d like to hear why!

Suppose you have an in virtue of chain that terminates in the proposition P. All that is entailed by this is that what P says to be the case is fundamentally the case; but that P exists may well be true in virtue of something else, and so P may itself be a derivative entity, despite its content being a fundamental truth.

Here is a toy example, just to illustrate the consistency. Suppose for every proposition, p, that p exists is true in virtue of the fact that it is possible for someone to entertain the content of p. So P might be true in virtue of Q, which is itself fundamental. But the proposition [Q exists] needn’t be fundamental. On the toy proposal, [Q exists] is true in virtue of [Possibly, someone entertains the content of Q]. Of course, now I’ve invoked another proposition, call it R; so if it is to be a derivative entity I need to invoke a new instance of the in virtue of relation. [R exists] in virtue of [Possibly, someone entertains the content of R]. And now we have another new proposition, so need a new instance of the relation; and so on, and so on. We generate an infinite sequence of in virtue of relations. But this is not, I think, a vicious regress. The success of an instance of the in virtue of relation never depends on the success of the instance of the relation it ‘generates’. P obtains in virtue of Q, and that generates a new instance: [Q exists] in virtue of R. But the success of ‘P obtains in virtue of Q’ doesn’t depend on the success of ‘[Q exists] in virtue of R’, for it doesn’t matter to P’s being grounded in Q whether or not Q is fundamental. That Q is not a fundamental existent is nice, but it’s irrelevant to Q’s ability to be the relata of the in virtue of relation. So the fact that there is an infinite sequence of in virtue of instances is, I think, unworrying.

Now, I don’t particularly recommend that account of what grounds the facts concerning the existence of propositions, but it’s clearly just a placeholder for a better account. So I think taking propositions to be the relata of the in virtue of relation simply has no consequences for whether or not propositions are fundamental constituents of the world.


Anonymous said...

It sounds like your 'in virtue of' relation is the relation of entailment, or something close enough. (Entailment restricted to true propositions...but then we'd need entailment and 'in virtue of', which is unlovely: hence, you should just think that the 'in virtue of' relation is the entailment relation.)

In a sense, I'm pretty sympathetic with this view. But I would never present it the way you do: it seems to me that "in virtue of" talk is often abused, and tends to obfuscate debates and theorizing in general, because it is ambiguous and unclear--different people use it to mean different things. So why even use the phrase if we have a perfectly (well, ok, relatively) clear concept of entailment? No one, outside of philosophy of logic, freaks out/doesn't know what it means when we talk about p entailing q.

Do you think there's some important difference between entailment and 'in virtue of'? If not, do you think there's some important reason to salvage 'in virtue of' talk instead of jettisoning it in favor of talk about entailment?


Jason said...

"2+2=4" entails "it's raining or it's not raining," but I would have thought the latter doesn't hold in virtue of 2+2 being 4. Or am I missing something?

Jonathan D. Jacobs said...

A nice explanation. So it's consistent with your theory that "in virtue of" never has as a relata a fundamental entity. (Since it holds between propositions and propositions need not be fundamental.) But then is "in virtue of" fundamental, on your view?

Ross Cameron said...

JK: What Jason said! The *only* similarity I can see between *in virtue of* as I understand it and entailment is that it is a relation between propositions. But, as Jason says, *which* propositions it relates are entirely different!

Jon: Yeah, it's consistent with my theory that IVO never has fundamental entities as relata. And for similar reasons, the IVO relation itself need not be fundamental, nor need the fact that any particular instance of IVO holds be fundamental. My theory is just neutral on all of this.

Anonymous said...

You don't think there will be a large overlap between the ordered pairs of propositions {x, y} where x entails y, and the ordered paris of propositions {p, q} where q holds "in virtue of" p? Isn't Socrates mortal in virtue of the fact that he's a man, and all men are mortal? Aren't all the theorems of a theory true in virtue of the axioms?

As to the example...well, I don't know. What do you think "it's raining or it's not raining" holds in virtue of? If I had robust intuitions about that, I would be able to evaluate this purported counterexample. But offhand, I'm inclined to say that logical truths hold in virtue of anything whatsoever.


Ross Cameron said...

No, I don't think there will be large overlap. I don't think Socrates is moral in virtue of [Socrates is a man & all men are mortal]. What grounds Socrates' mortality, I think, are biological facts about Socrates, and nothing to do with general facts concerning all men.

*Perhaps* theorems are true IVO the axioms of the system in which they are theorems, but it's far from uncontroversial. But even so: theorems are entailed by *anything*, and to single out the axioms as what they are true in virtue of is itself to admit that IVO isn't entailment.

I think [It's raining or it's not raining] is true in virtue of the fact that it's raining, when it is, and the fact that it's not raining, when it's not. But not in virtue of the fact that there are no singing monkeys.

Anonymous said...

An important part of our disagreement is a disagreement about the nature of entailment: I don't think the theorems of theories in general--but including mathematical theories--are entailed by anything whatsoever. Perhaps I should have said "logically entailed", if we're taking those to be different relations. Clearly mathematical theorems aren't logically entailed by anything whatsoever, else we wouldn't need axioms.

I guess for the above reason, I was thinking of 'it's raining or it's not raining' as an example of a logical truth (something logically entailed by the null set), something such that it is impossible for it to be false. It seems sort of peculiar for this necessary eternal proposition to be true "right now" in virtue of contingent facts about the weather, unless we're taking necessary, eternal propositions to be true in virtue of anything whatsoever (as I was initially suggesting). But as I've already admitted, I struggle to understand "in virtue of" talk.

Do you agree that logical entailment is a kind of dependence? If so, do you agree that it seems unlovely to postulate two (fundamental) dependence relations holding between propositions? Or do you think logical entailment can be analyzed in terms of the "in virtue of" relation?

Ross Cameron said...

I don't agree that logical entailment is a kind of dependence, no. Nor do I agree that it's clear that mathematical theorems aren't logically entailed by anything whatsoever; in fact, I think it's false. I don't think that speaks to the usefulness of axiom systems: the purpose of an axiomatisation being, to my mind, an epistemic thing. But I agree there are substantial assumptions lying behind every move here!

Rich Woodward said...

Hey Ross,

I'm just wondering whether you'd be okay the kind of picture you sketch in a setting whereby the IVO relation was fundamental?

So, e.g., you'd then have a picture whereby a ontologically basic relation could relate derivative things. And various people (Ted in particular) have thought that *that*'s off-limits (see, e.g., his "Naturalness and Arbitariness" for one version of this worry.). Maybe you don't buy that, but I can imagine that some of the worries about you being committed to propositions being fundamental came because there tends to be a presupposition that IVO is a fundamental relation.

Of course, there is a package here that makes this worry go away: it takes the picture you sketch and adds it to a view on which IVO is derivative. But that's a package that explicitly want to remain neutral about, right?

Ross Cameron said...

Yeah, I want to remain neutral about that. But I don't have a problem with a fundamental relation relating derivative things.

What can I say . . . I'm an impure kind of guy!

Rich Woodward said...

Can we just call the opposite of Purity "Dirtyness", please?

In any case, the thought was just that one reason why people might have thought you were committed to fundamental propositions is that they were assuming something like Purity and the fundamentality of IVO.

Anonymous said...

So what are you saying about the nature of reality? Can you summarize it in one or two sentences. It's okay to sit in an intellectual ivory tower, expounding this theory and that theory, but in my opinion if all these intellectual abstractions contribute nothing of value to our understanding of reality, what is the point. Even quantum mechanics and general relativity can be explained in terms that a lay person can understand and get meaning from. Surely your 'in virtue of' discussion is not more complicated than quantum mechanics and relativity?