Epistemicists say that our vague natural language is, in fact, fully sharp. If I place grains of sand onto a sheet of paper, there will eventually be a grain of sand such that prior to placing it, there was no heap, and after placing it, there was a heap. We don't know which grain it is, but we know there is one on the basis of the following argument. Let Gn be the sand after the nth grain has been placed. Then, G1000000 is a heap, and G1 is not a heap. It is a logical consequence of this that there is a number n, between 1 and 1000000, such that Gn is not a heap and Gn+1 is. And it's obvious that there is no number n which we know to be as above. So, epistemicism is true--there is a boundary, and plainly we don't know where it lies.
The above is a very plausible argument. But it runs into two kinds of problems. First, the incredulous stare: it just doesn't seem like there should be such an n. This has some force, but only if the alternative to epistemicism is something other than revising logic. Plus the epistemicist can give a good explanation of why we are mistaken here. We have a tendency, often exploited by anti-realists, especially in ethics and aesthetics, of confusing what we cannot know with what there is no fact about. Still, the incredulous stare does indeed have a pull on me here.
Second, there is this argument: Language is defined by our practices. Our practices underdetermine which number n is such that Gn fails to fall under the predicate "is a heap" but Gn+1 does fall under it. But something falls under the predicate "is a heap" if and only if it is a heap. Hence, there is no fact about which number n is such that Gn is not a heap but Gn+1 is. One might try to deny that language is defined by our practices or that our practices underdetermine the number n, but unless there is a theory of how language is defined in such a way as to determine the nmber n, this is intellectually unsatisfying.
Theism seems to make it possible to be an intellectually fulfilled epistemicist. For the theist can accept the following theory. God thinks perfectly precise thoughts with no vagueness of any sort. Our language comes to us from God. Just as my use of the words "Beijing" and "quark" get their meanings from other people's earlier use of it, so too our language ultimately gets its meaning from God's decision as to what should mean what. God thinks perfectly sharply, and then set perfectly sharp boundaries for human language's predicates. He didn't, in general, inform us as to the perfectly precise independent specifications of the boundaries. But our language is, nonetheless, perfectly precise.
There are two paths to further development. One path has it that each time our practices have seemingly created a new predicate, God was behind the creation. Jones hears an idea and says it is "cool". No one has used the word earlier in this sense, and the usage takes off. But, in fact, Jones didn't introduce the word by herself in to the language. God cooperated with Jones and filled out the vagueness in Jones' concept of the "cool".
The second path is that God defined precise rules by which bits of language gain meaning. These rules are every bit as precise and deterministic as the laws of Newtonian physics. These rules specify what exactly falls under the predicate "is cool" when the predicate is introduced by Jones in such-and-such a way under such-and-such circumstances.
Both paths further divide into two variants: a constitutive and a causal variant. On the constitutive variant, God's intentions as to what should mean what (specifically in each case, on the first path, and under more general descriptions, on the second) at least partly constitute what meaning-facts there are—that would be akin to divine command theory (in its divine-will variant). On the causal versions, God causes meaning-facts. These meaning-facts may be embedded in the natures of speakers—that would be a Natural Law version—or they may be "out there" (wherever "there" is). (I like the Natural Law version most.)
This gives us a cool argument:
- (Premise) G1 does not fall under "is a heap".
- (Premise) G1000000 does fall under "is a heap".
- There is a number n such that Gn+1 falls under the predicate "is a heap" and Gn does not. (Follows by classical logic from 1 and 2)
- (Premise) The best explanation of (3) is that human language was created by an agent whose thoughts suffer from no sort of vagueness.
- (Premise) Every non-supernatural agent's thoughts suffer from some sort of vagueness.
- Probably, there is a supernatural agent whose thoughts suffer from no sort of vagueness and who created human language. (Inductively from 3-5)
I am not endorsing epistemicism. I am still pulled to thinking the sentence-proposition relation is many-many and that classical logic governs propositions rather than sentences. But the above line of thought, and the comparison with Natural Law, makes epistemicism very attractive to me. If God, in creating human beings, can create them with a nature that grounds normative facts about them, he can create them with a nature that defines meanings as well. (Moreover, there may be a reduction of meaning to normativity. One might say that a type A of action is an asserting that p if and only if A ought not be done if not p. There are difficulties in this—it makes the notion of assertion very expansive—but it has its attractions.)
And I can't, off-hand, think of a credible Euthyphro problem here.
[Some minor refinements made from the initial post. -ARP]