Tuesday, August 26, 2008

Vagueness and Naturalness

I've posted a draft of a new short paper on vagueness. I want a view of vagueness that upholds both classical logic and bivalence. I commit, then, to saying that there is a sharp cut-off between the things that satisfy any vague predicate and the things that don't. Williamson secures that by accepting the claim that our usage is fine grained enough for our predicates to latch onto a particular meaning, and that we'd have meant something different had we used the term ever so slightly differently. Like many, I don't find that plausible. Instead, I want to let the other factor that determines meaning do the work: naturalness. The claim I defend is that for any vague predicate there are a bunch of meanings that fit equally well with use, but that one is always the most natural. This is the one we mean, and this determines where the cut-off is: we can't know where the cut-off is because we have no naturalness detector. I explore extending this to arbitrary reference. The idea is that when we say 'Let 'n' be an arbitrary number', 'n' refers to the most natural number. And so on: so I secure bivalence at the cost of some heavy duty metaphysical claims concerning naturalness. It then becomes weighing up the costs and benefits.

But my real view is that the naturalness facts are themselves ontically indeterminate. There is a most natural meaning for 'is bald', but the world hasn't settled which of the candidate meanings is the most natural. In that case, while it is settled that there is a sharp cut-off between the bald and the non-bald things, it is ontically indeterminate where the sharp cut-off is. There is a most natural number that 'n' refers to; but it is ontically indeterminate which one it is.

Comments welcome!


Duncan Watson said...

Hi Ross,

Would someone who wanted to combine your real view about naturalness facts with Elizabeth and Robbie's way of modeling ontic vagueness be committed to impossible worlds?

Suppose you had 'has less than 1000 hairs' and 'has less than 1001 hairs' as the candidate meanings for 'is bald'. On Elizabeth's account you'd want it to be indeterminate which world was selected, the one that represented 'has less than 1000 hairs' as the most natural meaning for 'is bald' or the one that represented 'has less than 1001 hairs' as the most natural meaning for 'is bald', on Robbie's account you'd want both worlds to be selected.

But supposing that what is natural is necessarily so then at least one of the worlds would be impossible.

Ross Cameron said...

I'd be happy to admit possible worlds; but really, why do you think the naturalness facts are necessary? I was supposing them to be contingent.

Duncan Watson said...

Oh, OK. Probably should have guessed that that would be what you thought.

The Lewisian might think that his theory was more elegant and had less primitives if which properties were natural was a necessary truth. I see that he could probably do most of the work he wants natural properties to do with just the actually natural properties or world-indexed natural properties, although I struggle a bit to see what the analysis of being a perfect duplicate would be, but that looks like a cost in terms of simplicity. If the Lewisian thought that natualness was a primitive of his system then if which properties are natural is necessary rather than varying from world to world it looks like he has less primitives too.

But one needn't be a Lewisian about these things.

Do you have a particular account of what it is for something to be natural?

Mike Almeida said...

Hi Ross,

I'm not sure how bad the problem is. Suppose you're supervaluationist and you want a sharp cutoff between bald and non-bald. Well, take any finite increment i in hair-width you'd like. It is undeniable that, for some such increment i, some person with Ni hairs will be non-bald and the person with (N + 1)i will be bald. Of course, among the nonbald people are some borderline bald people. But that is not such a worry, given sufficient high borderlines. I guess what I'm getting at is that superV's can get something close to bivalence, since for all x and F, x is on some borderline or other (low or high) of F or x is not on any borderline of F. That's true for any increment in F-ness you like. Maybe your intuition in favor of bivalence is just the intuition that x is either borderline or not.

Mike Almeida said...

That is, it is undeniable that, for any such increment i you like, a person with Ni hairs will be non-bald and a person with (N + 1)i will be bald.