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.