Follow-up on Vagueness

I've been wanting for a while now to follow-up on last week's post on vagueness and two-place predicates. In the comments, John gave a good example of a two-place candidate for a vague predicate in 'is a friend of', and Brian made a nice sorites out of it. Brian also suggested a sorites for 'is better than', but I don't think it was really a sorites, because the generating step is intuitively false. Here is his suggestion:

It's really easy to make a Sorites paradox out of 'is better than', although you have to use fictional objects. Here's how I'd do it. Start with some things that are relatively close in quality, say Joe Montana and Steve Young. (I'm assuming in the context 'better than' means 'better quarterback than over their careers'. And I'll assume Joe is better than Steve. That last assumption can obviously be amended depending on your view of recent history.) Now consider a string of quarterbacks each of them mostly like Joe Montana, but each one a teensy bit worse than the one before. For each n>0, Joen completed one fewer pass in some regular season game, or completed one pass for slightly fewer yards, than did Joen-1. I take for large enough n, Joen is not better than actual Steve. But it's vague where the crossover occurs.

There are two interesting things here. The first, which I already pointed to, is that I don't think this is a sorites argument. The implicit generating step seems to be, 'for any n, if Joe-n is better than Quarterback X, then so is Joe-n-1. But that's not just non-intuitive, it's obviously false -- let Quarterback X equal Joe-n-1. So I don't think this is a sorites, since the generating steps in sorites arguments are intuitively true. But the other noteworthy thing about Brian's argument is that it does tend to convince me of his conclusion, that 'is a better quarterback than' is vague. I talked to Brian briefly about this today. One interesting thing that I learned was that there is not a philosophical consensus as to whether all vague predicates can play the soritical role in sorites arguments. The quarterback story to me counts as evidence that not all of them can. (Although Brian hinted at an additional worry that I don't yet fully understand about the difference between vagueness and indeterminacy -- so I may want to end up saying that 'is a better quarterback than' isn't vague after all.) He recommended a paper which I've added near the top of my reading list and hope to get to in the next couple days:

Patrick Greenough, "Vagueness: A Minimal Theory", Mind, Vol. 112, 446, April 2003, pp. 236-281.

Since I respect Brian's opinion on such matters, I will go ahead and recommend the paper to you, based on his recommendation to me.