Thursday, October 11, 2007

Truthmakers, propositions as sets of worlds, and triviality

In a couple of papers on truthmaker theory I’ve appealed – more for convenience than anything else – to the Lewisian identification of propositions with sets of possible worlds. This has, on a couple of occasions, elicited comments to the effect that if such an identification is made truthmaker theory is trivial and uninteresting. The argument for this is never made explicit but appears to be something like this.

1) Every proposition p is a set of possible worlds.

2) What it is for a proposition to be true at a world is for that world to be a member of that proposition.

3) From 2, what it is for a proposition to be true is for the actual world to be a member of it.

4) From 3, a proposition p is true in virtue of whatever makes it true that the actual world is a member of p.

5) When p is necessary, locating a truthmaker for p is (in some sense) trivial.

6) When a is a member of S, it is necessary that a is a member of S.

7) From 3, 5 and 6, the task of finding truthmakers for true propositions of the form ‘the actual world is a member of the proposition p’ is trivial.

8) From 4 and 7, all truthmaking is trivial.

I think there’s got to be something wrong with this argument; the task of explaining why a proposition is true can’t be so easy just because we identity propositions with sets of worlds. So what’s wrong with the argument? I deny premise 5 in general, and it’s certainly open to deny 6, especially if you’re a counterpart theorist. But even granting these, I think something’s got to be wrong.

Here’s what I think is wrong. Why is it true that there is something red? The proposition ‘there is something red’ is true because it has the actual world as a member. But why is that proposition the proposition ‘there is something red’? I’m not asking here why something is identical to itself – that is also (allegedly) necessary and therefore (allegedly) trivial. I’m asking why that proposition deserves the name ‘the proposition that there is something red’. The truthmaker explanation is: because at every member of that proposition a truthmaker for ‘there is something red’ (the redness universal, or a redness trope) exists, and at no world that is not a member of that proposition does such a truthmaker exist. This is itself no necessary truth, because even though sets have their members essentially, it’s (at least arguably) not the case that worlds have their constituents essentially. (I might not have existed; and had I not existed, the world would not have had me as a constituent.)

My suggestion then is that if propositions are sets of worlds the demand for explanation should be characterised as follows. If you want to hold that it is true that there are cats, say, then you need to explain why one of the many sets of worlds that the actual world is a member of deserves the name ‘the proposition that there are cats’. There are deflationist explanations available (“because it is the proposition that there are cats”), but the truthmaker theorist insists that the explanation will be the contingent truth that at every member of one of those propositions is a thing that couldn’t exist and it not be the case that there are cats, and at no world that is not a member of that proposition is there such a thing. Since the actual world is a member this means there must be some such thing at the actual world. And so the truthmaker demand places constraints on actual ontology and hence is in no way trivial.

Does this sound right to people? And if not, what (if anything) is wrong with the triviality argument?


Mike said...


I might be missing something; I'm not sure how you get to the triviality conclusion. You want to say (given 2) that a proposition P is true just in case the actual world @ is a member of P. By (6) I think you want to say that the actual world is a member of P only if it is necessary that the actual world is a member of P. But that's false, isn't it? The actual world is not necessarily a member of P unless 'the actual world' is rigid. But I take it that we want to say that @ might not have been the actual world. But then we should reject (6). But as I said, I might be missing something.

Ross Cameron said...

Hmmmm . . . yeah, that might be right Mike. Thanks. I'll think about it, but offhand I think that sounds right.

As long as the triviality argument fails, I'm happy!