My previous speculation about the Midwest, that it determinately excluded all of New York, seems to have been conclusively mistaken. The speculation I reported (due to Andy Egan) that the Ohio-Penn border may be a sharp boundary between the determinately Midwestern and the not determinately Midwestern, has received more support. Let me try one other speculation.

I suspect that everywhere in Missouri is determinately part of the Midwest. And I suspect that everywhere in Tennessee is determinately not part of the Midwest. But those states share a (relatively short) border constituted by the Mississippi river. And I think (or at least I think I think) that it’s a sharp boundary around the Midwest at that point.

Note that this doesn’t prove that some vague terms can have sharp boundaries. (I owe the following suggestion to David Sosa. Unless I’m getting what he thought all confused, in which case I owe it I guess to the Fates.) We might take it to be constitutive of vagueness that it always percolate all the way up. More plausibly, we might think that vagueness is really a property of boundaries, rather than of terms. The Midwest has some vague boundaries (though just where they are is a matter of some dispute) and some sharp boundaries. The Mississippi river is, for a while, a sharp boundary. We could, derivatively, talk about terms being vague when some of their boundaries are vague, or when all of their boundaries are vague, but primarily vagueness is a property of boundaries. And what the Midwest shows is that once we think this way, whether we require that vague terms have all vague boundaries or merely some makes a difference.