Wednesday, August 17, 2005

Vague Existence Gets Murkier

I was talking vague existence over lunch today with Katherine Hawley and Daniel Nolan.

Daniel suggested that in order correctly and exhaustively to represent an ontically vague world, a world (let's say) where it is an ontically vague matter whether an F exists, our best theory BT must be such that it is a vague matter whether or not BT is committed to Fs. It wouldn't be enough for the theory to include a sentence which says that it's a vague matter whether Fs exist.

This would, I think, be a way to respond to my suggestion that ontic vagueness creates tension with the Quinean criterion for ontological commitment. The Nolan line (I use that description without intending to suggest that Daniel endorses the view) would seem to be that although BT is not committed to Fs just by dint of containing a sentence which says that it's vague whether Fs exist, BT is vaguely committed to Fs (or at least, it becomes problematic to say that it is not committed) because it is a vague matter whether or not BT says that Fs exist.

One interesting feature of this proposal is that it seems to imply that ontic vagueness cannot be limited to Fs alone. If it's vague whether there are Fs, it's also vague whether BT includes 'There are Fs'. And to say the latter vagueness is merely linguistic would seem somewhat strange under the circs. How could two different things be responsible for the vagueness of reality and the vagueness of BT, when the latter kind of vagueness exists merely because BT has to be an exhaustive representation a reality which exhibits the former kind?

That aside, though, I'm not sure I can yet see what independent motivation there is for taking this sort of line. It must be that in this situation BT leaves something out (or more cautiously, does not determinately capture everything) if it attempts to say all there is to say on the matter of the existence of Fs just by including the sentence 'It's vague whether there are Fs'. To do its job properly, it must also vaguely include the sentence 'There are Fs'. But why think that? What's been left out exactly?

One motivating thought Daniel mentioned: suppose we take exhaustive representation of the universe to be possible by theories that are not such that it's vague whether they include certain sentences. That skirts close to a bivalence assumption: we might like to think that (best theories are ideally good enough for it to be the case that) the true sentences are the ones in the theory, and it's determinate which ones those are, and all the others are false. Defenders of ontic vagueness who refuse to accept bivalence should therefore be equally unhappy with the idea that correct and exhaustive representation is possible by theories which are not vague in the aforementioned way.

But as far as I can see there is no need to say that the sentences not included in the best theory are false. All we want is for our best theory to include all the sentences that we think are true. So if we think 'It's vague whether there are Fs' is true, that should be in BT. And if we think it's a vague matter which of 'There are Fs' and 'There are no Fs' is true, then we don't think 'There are Fs' is true and we don't think 'There are no Fs' is true. (Which is not to say that we think either of them is untrue. We aren't committed either way.) So BT needn't include either of these sentences. But that's not to say that (either actually, or according to BT) these sentences are false. And if it were we'd have bigger trouble on our hands than a commitment to bivalence ...

BT of course needs to include the information that it's a vague matter which of the two sentences is true, but it does this, not by vaguely including them both, but by including 'It's vague whether there are Fs'.


Mike said...

". . .our best theory BT must be such that it is a vague matter whether or not BT is committed to Fs. It wouldn't be enough for the theory to include a sentence which says that it's a vague matter whether Fs exist."

The question is then the scope of the quantifier, right? Nolan wants to say about our best theory BT that it says (1),

1. (Ex)(it is is vague that Fx).

And the contrasting case is that our BT says (2),

2. It is vague that (Ex)Fx.

These claims seem to say radically different things. (1) says that it is definite that there is an x that is (at some order) indefinitely F. But (2) says that it is (at some order) indefinite that there is any x that is definitely F. I wonder what strong reasons there are that BT is committed to the former?

Carrie Jenkins said...

Hi Mike,

I think the question is about scope, but I would see it as a question about whether the defender of vague existence should think
A: BT says that it's a vague matter whether ExFx
B: It's a vague matter whether BT says that ExFx
(or maybe both).

Mike said...

Hi Carrie:
I think this is right, on second reading. But it would be very interesting if an accurate representation required (B). Assume BT is in English and BT contains a sentence that is syntactically vaguely English. So in English it says "there is something that is an F", but it is not determinately English. Very strange that a BT might have to include sentences like that. But then maybe the source of vagueness would have to be elsewhere.

Carrie Jenkins said...

Hi Mike,
Yes, I think it would be very interesting. Though as I said, I can't yet see the motivation for it. But I was thinking that the most plausible version of this sort of view would take it that the vagueness was not over whether a sentence that was determinately in BT was or was not an English sentence meaning 'There's an F', but rather over whether a sentence which determinately meant 'There's an F' was or was not in BT.

Mike said...

I see, I think. So, for instance, it might be because of the vagueness of 'in' or 'a part of' that it is indeterminate whether 'Def(something's F)' is in or a part of BT. In order then to formulate the best theory our metalanguage would have to include a vague 'in' or 'a part of' relation. And I guess vagueness resolves as (what?) the sentence plays a more and more central role in the theory. Something like this?

Carrie Jenkins said...

I think this would have to be ontic (rather than linguistic) vagueness, as I suggested in the original post, so it might be potentially misleading to describe it as vagueness in 'in' or 'part of' (as opposed to vagueness in the relation of being in or the part-whole relation). But also, perhaps it would be enough to postulate that BT has vague boundaries, rather than that there is any vagueness in the part-whole relation or the relation of being in.

Mike said...

Carrie, you say this,
". . . the most plausible version of this sort of view would take it that the vagueness was . . . over whether a sentence which determinately meant 'There's an F' was or was not in BT."
Let's agree that the vagueness about what's in BT reflects in some way the ontic vagueness you note. Still the ontic vagueness does not explain how a sentence might be vaguely in or a part of BT. Not as far as I can see. Rather vagueness on the linguisitic side has to reflect vagueness ontically, right? How else is BT going to be our best theory? A set of precise sentences is not going to accurately describe what there is.