Thursday, March 11, 2004

Vagueness and Two-Place Predicates

Allan and I were talking last night about what kinds of things can be vague. "Big" is definitely vague. So are "is a heap" and "is not bald." We know they're vague because we can construct sorites arguments, using them as soritical predicates. Interestingly, these, and all other examples that quickly come to mind, are all one-place predicates. The discussion started when I asked about the two-place predicate "is better than". My instinct says that there's no way that could be vague, but I'm not able to produce an argument about it. (I'm also not able to produce a sorites about it, which counts in favor of my instinct.) I'm fairly certain that "is larger than" is not vague -- the corresponding sorites has an obviously false generating step ("if A is larger than B, then A is larger than something that is only a tiny bit larger than B.") Early in the discussion, we briefly considered the possibility that there are no vague two-place predicates. But then we realized that there are -- quite a lot of them. For instance, "is a lot bigger than" is vague. But this morning I realized that this looks like a less basic kind of vagueness -- "is a lot bigger than" seems to inherit the vagueness of the myriad one-place vague predicates "is a lot bigger than x". Working hypothesis: vagueness fundamentally belongs to one-place predicates. Crazy? Interesting? Offensive? Speak!

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