Monday, June 30, 2014

The argument from vagueness

Here's an argument inspired by Plantinga's argument from counterfactuals:

  1. The meaning of a word is wholly determined by the decisions of language users.
  2. The meaning of "bald" is not wholly determined by the decisions earthly language users.
  3. Therefore, there is a non-earthly language user whose decisions at least partly determine the meaning of "bald".
The argument for (2) is this:
  1. In any hypothetical sequence to whose last member "bald" does not apply and to whose first it does, there is a transition point in the sequence, i.e., a member to whom "bald" applies but to whose successor it does not.
  2. The points in a hypothetical sequence at which "bald" does or does not apply are wholly determined by the meaning of "bald".
  3. There are hypothetical sequences where the decisions of earthly language users do not determine the transition point.
  4. So, (2) is true.
The argument for (6) is simply to exhibit a series of people, with someone completely bereft of hair on one end, and someone with a full head of hair on the other, with very slight transitions. Clearly our decisions and those of our ancestors do not determine where the transition point is. Claim (5) seems very plausible.

That leaves (4). But that's a matter of logic for any fixed sequence, as a standard argument for epistemicism points out. For suppose there is no transition point. Then:

  • not ("bald" applies to xn and "bald" does not apply to xn+1)
is true for n=1,...,N where N is the number of items in the series. Given the fact that "bald" applies to x1, we can then conclude by classical logic that "bald" applies to x2, and to x3, and so on up to xN, contrary to assumption.

And the best candidate for the non-earthly language user is God. For any finite language user, say an alien who gave us language, would be in the same boat: its decisions would be insufficient to determine all meaning.


Michael Gonzalez said...

From the title, I take it that you are more generally saying that all (or some large set of) cases of vagueness require this non-Earthly arbiter. Someone who grounds the proper usage of what seems to us to be a vague term. Interesting idea.... Your argument would essentially be an argument against there being any vague terms in the first place; concluding instead that the terms are not vague in God's mind, but specific and delineated. Is that right?

Alexander R Pruss said...

Yes, that's the suggestion.

Michael Gonzalez said...

What if baldness is a sort of subjective aesthetic judgment which has no exact meaning? In other words, what if even God has no opinion on an exact line on the one side of which a person is bald, and on the other side of which the person is not bald?

Michael Gonzalez said...

I guess I'm questioning whether P1 is true with regard to vague terms (indeed it seems that contradicting P1 is something like the very meaning of the term "vague"). Compromising P1 makes P4 and P5 meaningless. So do you have justification for P1?

Alexander R Pruss said...

Then you have to have some way out of the argument that there is a transition point.

One way is to deny that "John is bald" expresses a proposition. Then logic doesn't apply. That's pretty radical, though I am friendly to it.

Alexander R Pruss said...

I don't think you're questioning premise 1. You're not saying that there is something other than language users that is determining the meaning of "bald". What meaning it has is, on your view, still wholly determined by the decisions of language users.

Michael Gonzalez said...

Well, if we deny that there is an objectively true delineating point for baldness then we seem to have a couple of options. If "meaning" entails "specifically delineated and objectively true", then P1 holds, but "baldness" simply doesn't have a meaning. If "meaning" can be vague, then P1 is problematic, since a vague meaning can't really be "wholly determined by decisions of language-users". That's what makes it vague.

I don't know that we should deny that "John is bald" expresses a proposition, or rather just accept that propositions can be vague. For example, "intelligent" seems to have meaning and "John is intelligent" does seem to express a proposition which can be either true or false, but the term is still vague and subjective. In a group of geniuses, John might not seem all that intelligent. In a group of idiots, he might seem like the next Kurt Godel.

I guess I'm not sure what to think. Do we deny that vague terms have meaning at all, or do we just deny that "meaning" has to include specific delineations that are objectively (situation-independently) true?

Michael Gonzalez said...

Or, third option, do we accept that vague terms have meaning, and that "meaning" entails an objectively true specified delineation, and thus embrace that God (or some unlimited mind) must be making that decision? I guess that's the point of your argument, isn't it? Options 1 and 2 seem problematic, so why not just accept 3, and think that God has an opinion on the exact number of hairs (or the exact ration of covered to uncovered areas on the head, or whatever) which defines "baldness"?

Heath White said...

I would deny (4). But (4) is a matter of logic! Well, it is a matter of classical logic, and classical logic has no room for vagueness. So the appeal to classical logic, against vagueness, appears to the friends of vagueness to be circular.

Something similar goes for “proposition.” If expressing a proposition entails having a classical truth value, then “John is bald” does not express a proposition. But if expressing a proposition entails only having a meaning, and meanings can be vague, then there’s no objection to the sentence expressing a proposition.

(How long before someone comes up with an argument for atheism from the existence of vague terms? :-) )

Heath White said...

Incidentally, if you believe in libertarian free will, wouldn’t the meaning of terms in human languages be exactly the kind of thing God would let humans determine on their own? (“I know exactly how many hairs everybody has. For baldness, I’ll go along with whatever you guys come up with.”)

Michael Gonzalez said...
This comment has been removed by the author.
Michael Gonzalez said...


I think the fact that what one person considers "baldness" isn't the same as what someone else does shows that there is only a fuzzy definition of the concept (having something to do with coverage of the scalp). As such, I don't think (4) applies in a strict sense. But what if there is a range, within which one might be considered bald, but no exact spot at which to delineate. It would definitely be true that having more coverage (or more hairs) than the highest value in the hazy area would constitute one "not bald". But there would be variance among cultures, personal opinions, and other circumstances that would be involved within the hazy area. God would know under exactly which conditions a given person at a particular time would consider another person to be bald. And He would know the range of those values and even a probability distribution among them, etc. But there wouldn't be an exact value associated with "baldness".

As for libertarian free will, I have to say I don't quite agree. Free will doesn't entitle us to decide objective truths. We can decide whether to speak in line with those objective truths, but we couldn't decide whether they were true or not. Thus, in morality, God grounds the good and the bad, and we don't get to decide them; though we do get to decide whether to abide by them.

William said...

Perhaps there is a way we could do a poll of some sort of all such human language users with some kind of series of pictures of progressive balding and get an empiric poll distribution of the cut-off for the meaning of bald from it.

Presumably such an ideal polling process with parallel presentation of multiple images in a series would give a definition that would agree with what God would say, within error limits.

Alexander R Pruss said...


If I thought that this argument is sound, I would say this: God doesn't directly decide meanings, but instead decides the precise semantic rules that map human practices to meanings. Thus, both divine decisions and our practices go into defining the meanings.

Thus, maybe God defines some precise function from practices to meanings such that when you apply that function to our practice of "bald" attribution, it yields a meaning of "has at most 20.53 milligrams of opaque head hair".

If our practice were different, the meaning of the analogous word would have been different.

I would dispute the claim: "So the appeal to classical logic, against vagueness, appears to the friends of vagueness to be circular."

Supervaluationists are friends of vagueness and yet they think that the definitely true is closed under all the classical inferences. Thus, the supervaluationist who agrees that the premises in the argument are definitely true will have to accept the conclusion. This is, of course, a standard problem for supervaluationism. :-)