Tuesday, December 13, 2016

Vague propositions

Suppose Jim says, in English, “2+2=4”. Then:

  1. What Jim said is such that it is contigent that it is true, because it is contingent that “4” means four rather than five


  1. What Jim said is a necessary truth, because it cannot but be true that 2+2=4.

Here the apparent contradiction is resolved by disambiguating “what Jim said” between the uttered sounds and the expressed meaning.

But when talking about vagueness, this straightfoward point can be a bit less clear. Suppose that it’s vaguely true that “4” in Jim’s dialect means four, rather than five, and Jim says “2+2=4” (and suppose that all the other relevant stuff is definite). Then:

  1. What Jim said is vaguely true, because it’s vaguely true that “4” is four.

  2. What Jim said is not vaguely true, because what Jim said is definitely true or definitely false, depending on what “4” means.

Again, make the same move as in (1)-(2): in (3), “what Jim says” is the uttered sounds or words and in (4) it’s the proposition.

This line of thought suggests one of two possibilities. Either, propositions are never vague, or there are two interestingly different kinds of vagueness. If propositions are never vague, then in the proposition sense of “what was said” it is never correct to say that what was said is vague. That’s a bit counterintuitive, but some counterintuitive things are true.

But if some propositions are vague, then it seems that we have two interestingly different kinds of vagueness an utterance could suffer from. It could be vague which non-vague proposition an utterance expresses or it could be definite which vague proposition an utterance expresses—or one could have combinations, as when it’s vague which vague proposition is expressed. In the case above, I claimed that it was vaguely the case that Jim expressed the non-vague proposition that 2+2=4. But presumably if there are vague propositions, there will be one that has the kind of vagueness that makes the non-vague propositions that 2+2=4 and that 2+2=5 be its admissible precifications.

So now we would have this interesting question: What determines whether Jim’s case was a case of vaguely expressing a non-vague proposition or non-vaguely expressing a vague proposition or some combination? Maybe there is a good answer to this question, but I have some doubts. In light of these doubts, I think that the proponent of vague and non-vague propositions should say is something like this. There are at least three senses of “what was said”: the sounds or words (and that makes for two, but I won’t be interested in this distinction in this post), the non-vague proposition and the vague proposition. What Jim said is vaguely true in the first and third sense, but not in the second. This is sufficiently complicated that one might prefer to go back to the less intuitive option, that in the proposition sense “what was said” is never vague.

I am dreadfully confused.


Arcane Spork said...

I would call propositional vagueness "vagueness." I'm not sure about the existence of the other kind. It could be called "semantic vagueness," I suppose. But I'm not sure that it is really a kind of vagueness at all, except in the sense that it is vagueness of semantic relations. Semantic vagueness, unlike vagueness, does not exclude the possibility of knowledge. If it is vague whether "2+2=4" means that 2+2=4, then it is still possible for someone to know that 2+2=4 (although I think they would have to know it by some means other than internalizing "2+2=4")

Alexander R Pruss said...

I know that it's commonly thought in the vagueness literature that vagueness excludes knowledge, but that seems likely to be false.

If vagueness does not exclude truth and there is such a thing as vagueness, then vagueness does not exclude the possibility of knowledge. After all, God knows all truths, including any vague ones, and he could then testify to vague truths to us, and thereby give us knowledge of them.

Arcane Spork said...

Okay, sure. I don't think I really buy that, but I'm not a Christian so I don't have to. But anyway, even if vagueness doesn't exclude knowledge, it surely excludes something (aprioricity?) that 2+2=4 possesses. We can't seriously hold that all truths are vague, but it seems that for all propositions it is possible that it is vaguely true that an utterance means it. And that doesn't mean that propositions are all vague. So there must be a difference between vagueness and vagueness of meaning.

Alexander R Pruss said...

Maybe vagueness just doesn't apply to propositions, but only to sentences?

Arcane Spork said...

Yes, that'll do. I think it's pretty counterintuitive, though. Wouldn't that have the consequence that it's never vague whether someone is bald, it's just vague whether the word "bald" applies to them?

Michael Gonzalez said...

What about what Jim INTENDED to say? Isn't that really the issue. "Vagueness in sounds/words" only matters to listeners. Jim knows what he intended to express, and there is no vagueness there.

Alexander R Pruss said...

What one intends to express can be vague, too.

Michael Gonzalez said...

Sure, but that's where the distinction needs to be made. If Jim intended the concept of 2 being added to 2 and yielding 4, then there is nothing vague about that, even if his use of language is somehow hampered (or if someone fails to apprehend his meaning).