Tuesday, March 1, 2011

Epistemicism, vagueness and theism

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:

  1. (Premise) G1 does not fall under "is a heap".
  2. (Premise) G1000000 does fall under "is a heap".
  3. 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)
  4. (Premise) The best explanation of (3) is that human language was created by an agent whose thoughts suffer from no sort of vagueness.
  5. (Premise) Every non-supernatural agent's thoughts suffer from some sort of vagueness.
  6. 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]


Scott said...


This is a really nice proposal.

However, I wonder whether the God-version of Epistemicism might have more trouble with certain Twin Earth type cases than the non-God version.

Suppose that in the beginning, God created the Heavens, the Earth, and the Twin Earth.

Suppose that God's cooperation with English speakers on Earth yields the result that over 30 grains of sand falls under the extension of the English word 'heap' and that 30 or fewer grains of sand does not.

Suppose that God's cooperation with Twin English speakers on Twin Earth yields the result that over 40 grains of sand fall under the extension of the Twin English word 'heap' and that 40 or fewer grains of sand does not.

Suppose that Earth and Twin Earth are as similar as is consistent with the difference just specified.

Now suppose that the inhabitants of Earth and Twin Earth meet. They see 35 grains of sand in a pile. The inhabitants of Earth say 'That is a heap'. The inhabitants of Twin Earth say 'That is not a heap'.

My intuition is that the inhabitants of Earth and Twin Earth are disagreeing. But the theological version of Epistemicism seems to imply that they are not really disagreeing. The inhabitants of the two planets are just talking past each other.

Perhaps the non-theological version of Epistemicism has the same result. I am not sure.

Alexander R Pruss said...


If you're right, a consequence of the view is that it might be that one community uses the term A in a way exactly isomorphic to the other community's use of the term B (whether A and B sound the same is irrelevant), and yet A means one thing and B means another. So, meaning does not supervene on use. I think it's hard for a non-theistic epistemicist to avoid this conclusion, except by saying that there is a dependence of meaning on use that is beyond our ken, and that does not seem preferable.

At the same time, the problem may be lesser in the case of the "natural law" type of proposal on which the meanings are grounded in facts about human nature together with facts about use. For the twin-earthers either have the same nature as we do or not. If they do, then sameness of use does imply sameness of meaning, and the problem disappears. If they do not have the same nature, then it is not clear that they count as using the words in the same way, even if their overt behavior is just like ours. For the context of use is different--they are used by beings with different natures.

Alexander R Pruss said...

I should add that I don't see it as particularly problematic to deny that meaning supervenes on use.

Heath White said...

One odd consequence, and one theological issue.

1. Demonstrations can be vague, and lead to sorites problems.

"He is standing there [points]; if he were standing one angstrom to the left, he would still be standing there ... therefore if he were standing in California he would still be standing there." True premises, false conclusion.

Your solution for this requires God to specify the exact region of "there" which the pointing motion indicates. This can't be handled, I don't think, by appeal to precise divine thoughts. It's downright wierd.

2. Traditional Natural Law holds that human authorities can make specifications in the law; the divine law covers big issues and then there are things like traffic rules and rules of evidence which are human inventions but nevertheless have a moral content. And the law can be vague even then. Your epistemicist theism would remove the equivalent power from human language-authorities.

For both these reasons, I think one ought to resist epistemicism in theistic or other variants.

Alexander R Pruss said...

I think both of the worries could be handled by means of the general rule version of the story.

In regard to indexicals, maybe the divine laws (perhaps implanted in our nature) specify that pointing via a finger points out a region of space determined by such-and-such precise function of the context. (Here's not the right answer for pointing, but gives the idea of what sort of a form the function could take. When you point to an object, you point out the first object whose mass exceeds exactly 0.1kg and which intersects the ray defined by the center of mass of the knuckle and the center of mass of the outermost finger-bone.)

In regard to delegation, it makes sense for God to delegate that which the human authorities can properly handle. But human authorities cannot properly handle the setting of details because of the finitude of our minds. So it could make sense for there to be rules of the form: When human authorities engage in such-and-such a word-introducing act, the meaning of the word is such-and-such.

All that said, I do not like this sort of epistemicism that much. But if the price of avoiding it is losing classical logic, then that's too high a price to pay, I think. (I think the price does not have to be paid. I am inclined to think you can have classical logic at the level of propositions, even if not at the level of language.)