Suppose we want to explain why one tortoise doesn't fall down, and we explain this by saying that it's standing on two tortoises. And then we explain why the two lower tortoises doesn't fall down, we suppose that each stands on two tortoises. And so on. That's terrible: we're constantly explaining one puzzling thing by two that are just as puzzling.
Now suppose we try to explain the puzzle of the transition from bald to non-bald in a Sorites sequences of heads of hair (no hair, one hair, two hairs, etc.). We do this by saying that there are going to be vague cases of baldness. But this is just as the case of tortoises. For while previously we had one puzzling transition, from bald to non-bald, now we have two puzzling transitions, from definitely bald to vaguely bald and from vaguely bald to definitely bald. So, we repeat with higher levels of vagueness. The transition from definitely bald to vaguely bald yields a transition from definitely bald to vaguely vaguely bald and a transition from vaguely vaguely bald to definitely vaguely bald, and similarly for the transition from vaguely bald to definitely bald. At each stage, each transition is replaced with two. We're constantly explaining one puzzling thing by two that are just as puzzling.
That said, it is possible with care to stand a tortoise on two tortoises, and we could have evidence that a particular tortoise is doing that. In that case, the two tortoises aren't posited to solve a puzzle, but simply because we have evidence that they are there. A similar thing could be the case with baldness. We might just have direct evidence that there is vagueness in the sequence. But as we go a level deeper, I suspect the evidence peters out. After all, in ordinary discourse we don't talk of vague vagueness and the like. So perhaps we might have a view on which there is one level of vagueness--and then epistemicism, i.e., there is a sharp transition from definitely non-bald to vaguely bald, and another from vaguely bald to definitely bald. But the more levels we posit, the more we offend against parsimony.
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There are other theories of vagueness besides (a) higher-order vagueness and (b) epistemicism. So maybe title of the post should be "Positing higher-order vagueness doesn't solve a problem"? That I think is quite right.
As soon as we say that there are cases of definite baldness, vague baldness and definite non-baldness, then we have the problem of where the cut-offs between them are. If they are sharp, then we have epistemicism, though at the second-order level. If they aren't sharp, then the problem has returned. I don't think this point depends on which non-epistemicist theory one opts for.
Vagueness is in words, not in things. "That man is bald" is vague because it is a sentence made of words.
But in the same way, and for the same reason, "That sentence is vague" is vague.
If we admit that claims are vague precisely because they are made of words, then the evidence for the series of vague claims does not peter out, because all claims are made of words, including ones about vagueness. So this also does not imply any non-epistemic vagueness.
Words are part of the world, so if there is vagueness in words, there is vagueness in the world.
That doesn't follow in any way that is relevant. Suppose I define the word "katzapa" in this way:
"Things less than three feet tall are not katzapa, and things more than ten feet tall are katzapa."
This leaves the word vague relative to things five feet tall. Sure, the word is in the world, and in that sense the vagueness is in the world. But this is not what anyone means by saying that the world is vague. Each thing is what it is, and a quite definite thing, including the word in question.
Note that all words are vague in pretty much the same way katzapa is vague, including the word "vague."
I think you could posit “vagueness all the way down” if you don’t do it as a way of explaining away vagueness. For comparison, consider the status of classical logic. You can do proofs of its soundness and validity, but the metalogic is classical. It’s classical logic all the way down, and you just accept it as fundamental.
Now suppose one said about vagueness that the fundamental relation of representation (adequation) between language/mind and world was vague; that any representation of that representation would be vague; and so on. Definiteness would be one end of a spectrum of vagueness, but where exactly “the end” is, is vague, and so on. It’s vagueness all the way down because vagueness is fundamental. The map is not the territory.
I actually find this picture attractive. I don’t think it is incoherent, it just doesn’t cohere well with the preferred logical tools of analytic philosophy.
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