Here are one way of believing in a totally sharp world:
- Epistemicism: All meaningful sentences have a definite truth value, but sometimes it’s not accessible to us.
This has the implausible consequence that there is a fact of the matter whether, say, four rocks can make a heap, or about exactly how much money one needs to have to be filthy rich.
A way of escaping such consequences is:
- Second-level epistemicism: For any meaningful sentence s, it is definitely true that s is definitely true, or s is definitely false, or s is definitely vague.
While this allows us to save the common-sense idea that there are people who are vaguely filthy rich, it still has the somewhat implausible consequence that it is always definite whether someone is definitely filthy rich, vaguely filthy rich, or definitely not filthy rich. I think it is easier to bite the bullet here. For while we can expect our intuitions about the meaning of first-order claims like “Sally is filthy rich” to be pretty reliable, our intuitions about the meaning of claims like “It’s vague that Sally is filthy rich” are less likely to be reliable.
Still, we can do justice to the second-level vagueness intuition by going for one of these:
- nth level epistemicism: For any meaningful sentence s, and any sequence of D1, ..., Dn − 1 of vagueness operators (from among "vaguely", "definitely" and "definitely not"), the sentence D1...Dn − 1s is definitely true or definitely false.
(Say, with n = 3.)
Bounded-level epistemicism: for some finite n we have nth level epistemicism.
Finite-level epistemicism: For any meaningful sentence s, there is a finite n such that for any sequence of D1, ..., Dn − 1 of vagueness operators, the sentence D1...Dn − 1s is definitely true or definitely false.
The difference between finite-level and bounded-level epistemicism is that the finite-level option allows the level at which vagueness disapppears to vary from sentence to sentence, while on the bounded-level option, there is some level at which it always disappears.
I suspect that if we have finite-level epistemicism, then we have bounded-level epistemicism. For my feeling is that the level of vagueness of a sentence is definitely by something like the maximum level of vagueness of its basic predicates and names. Since there are only finitely many basic predicates and names in our languages, if each predicate and name has a finite level of vagueness, there will be a maximal finite level of vagueness for all our basic predicates and names, and hence for all our sentences. But I am not completely confident about this hand-wavy argument.
In any case, I find pretty plausible that we have bounded-level epistemicism for our languages, but we can extend the level if we so wish by careful stipulation of new predicates. And bounded-level epistemicism is, I think, enough to do justice to the idea that our world is really sharp.
2 comments:
I’m not following this. The higher the level of epistemicism, the further from intuition. Best not to step onto the ladder to start with. Either insist on and defend ‘first level’ epistemicism or reject epistemicism.
An obvious response to epistemicism is a version of the ‘incredulous stare’. It just seems bizarre (and contrary to intuition and natural language use) that there could be a sharp threshold (maybe known to God but not to us) such that, for example, having 299 hairs on your head makes you bald and having 300 makes you not bald. Second level epistemicism requires two such thresholds, which is even worse from this point of view. The higher the level, the worse it gets. If you want to persuade someone who has this sort of response, you have to address this issue at some level. Isn’t it better to do to do so right at the start?
As different issue: Is it the world that’s sharp (or not), or is it our language and concepts? God presumably knows precisely how many hairs each of us has. So he has no need for a concept of baldness, vague or otherwise. But we have sensory and cognitive limits. We can’t count hairs. So we have to resort to vague but useful concepts like baldness. Even if the world is sharp and epistemicism is true (maybe there really are sharp thresholds known only to God), this throws no light on how we devise and use vague concepts so successfully.
Ian:
I think second-level epistemicism reduces the evidential force of the incredulous stare. People's intuitions about ordinary first-order English vocabulary like "bald" can be expected to be correct. Thus it is incredible if there is a sharp transition between not bald and bald. But people's intuitions about phrases like "definitely bald" or "vaguely bald" are much more philosophically fraught. That's technical philosophical vocabulary. (The ordinary language "definitely" and "vaguely" do not have the same meaning as the philosophical terms.) So I think it is less problematic to bite the bullet and say that there is a sharp transition between definitely bald and vaguely bald, but not one between bald and non-bald. Similarly, a view on which cats can be in two places at once is more problematic than a view on which photons can, because we rightly trust ordinary folk more about cats, and the language of "place" with respect to them, than about photons.
I've come to be convinced that saying that our language and concepts are vague but the world is not doesn't work. For, as I heard Merricks say, our language (and presumably our concepts) are a part of the world.
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