It had rained for days and everyone was getting irritable so someone suggested a game and I said, “Why don’t we play defining vagueness?” which was a splendid suggestion since we’re in St Andrews and the gold standard of papers on vagueness is Patrick Greenough’s “_Vagueness: A Minimal Theory_”:http://www3.oup.co.uk/mind/hdb/Volume_112/Issue_446/. I have my disagreements with Patrick’s paper, some of them set out “here”:http://brian.weatherson.org/cpg.pdf but it’s clearly the standard setter in this area. (I didn’t like the original gold standard either, so perhaps I’m just hard to please. And my reply paper looks insufferably _impolite_ from my current distance. Someone must have said something rude about the blog or something the week I wrote it. I will try and do better in the future.)
One of my objections to Patrick’s paper was that it only gave a definition of what it was for a predicate to be vague. And, as I’ve said once or twice before, all sorts of things can be vague. Determiners, predicate modifiers, connectives, and of course names, can all be vague. So we want a theory that handles all that. If I knew how to do that I’d be writing a paper not a blog entry, so obviously I don’t know how to solve the puzzle. But I have an idea for how to start it, and a road map as to how to end it.
Here’s the start. Assume that Montague was basically correct so we can regard all terms in the language as referential. Some terms refer to objects, some terms refer to truth values, most terms refer to functions of various kinds. And assume supervaluationism is correct. Then _t_ is vague iff _t_ refers to different things on different acceptable precisifications. That was easy!
At this point Uncle started making his usual comparisons between my philosophy and theiving and hard work, and Allan decided to “run the metaphor into a nuclear bomb crater”:http://www.brown.edu/Departments/Philosophy/Blog/Archives/004534.html and everyone complained that they hadn’t heard of this Montague fellow and besides no one who was anyone was a supervaluationist any more, so I thought I should make a list of what’s wrong with the definition.
1. It assumes Montague is right.
Well, this isn’t necessarily a mistake, because I’m perfectly happy to assume a basically Montagovian semantics if that’s what it takes. In any case, I’m not going to try and overturn Montague for the sake of a vagueness paper. Not this summer anyway.
2. It assumes supervaluationism is right.
Ah, this is the biggy. Let’s come back to it below.
3. It doesn’t distinguish between vagueness and indeterminacy.
Lots of people (e.g. Greenough, Eklund, everyone except me, etc.) think that there’s an important distinction here. Even if Hartry Field is right and “mass” is indeterminate in meaning, or if an epistemicised version of Field is right and it’s meaning is unknowable, it isn’t _vague_. Vagueness requires some kind of continuous variation between the possible referents. “Spoils to the victor!” I might say, but Uncle would point out that no one thinks I’m winning so I better not.
The main reason I disagree with everyone here is that I think there’s much more continuity between Fieldian cases and unproblematically vague terms than is usually acknowledged. The orthodox view, following Sainsbury, is that vague terms have blurry boundaries. (The blur might be metaphysical or semantic or contextual or epistemic, so this is kinda theory neitral.) And this, it is thought, distinguishes them from terms like “mass” that are at least second-order precise. I think a lot of vague terms are much lumpier, even on their vague boundaries. (What follows is _not_ meant to be a point about predicates like _early thirties_ with a vague boundary and a sharp boundary – I’m talking just about vague boundaries here.) To rehash an old example of mine, consider an appointment that was set for a vague time, like _shortly after midday_. And consider what it takes to satisfy _late for that appointment_. Many folk would think (I think) that the clock ticking from 14{3/4} past midday to 15 past midday makes a bigger difference to whether you satisfy that predicate, or determinately satisfy it, or don’t determinately not satisfy it, etc than the clock ticking from 12{1/2} to 12{3/4} past midday. In cases like this, not all steps in a Sorites are alike. It’s possible, indeed, that one of the higher-level boundaries is perfectly precise, and is precisely at 15 past midday. So I think _late for that appointment_ has a lumpy boundary, and I think it’s vague at just that boundary, so lumpy boundaries are sufficient for vagueness. And I think (though this bit is controversial) that “mass” is just an extreme case of lumpiness.
This isn’t meant to be definitive – I might tinker with the definition on this point.
4. The definition isn’t sufficiently informative.
Quick, if my definition is right, is “very” vague? I don’t know, and I’m not sure how I’d come to know. It’s not clear a definition of vagueness should let us answer these questions directly, but it isn’t clear that it shouldn’t either.
5. Defining vagueness for predicates is definition enough
The point here isn’t that things other than paradigm vague predicates are not vague. Rather, the point is that if we can generalise Delia Graff’s arguments in “Descriptions as Predicates”:http://instruct1.cit.cornell.edu/research/graff/papers/descriptions.pdf perhaps we can find enough ways to analyse ‘other-looking’ kinds of vagueness as predicate vagueness. But only perhaps. Delia’s arguments are very sensitive to the particular properties of descriptions, and it isn’t clear they could be, or should be, generalised. Ultimately I suspect an account of what it is for ‘if’ to be vague (if it is) or ‘and’ not to be vague (if it is not) will have to be given directly in terms of properties of connectives not properties of predicates.
Back to problem 2. There’s a hard technical problem here, and though Grannie says that technical problems always have technical solutions, I’m not at all sure where to find it. The supervaluationist, you see, provides an account of what goes on term-by-term in a vague language. Other theorists tend to operate at the level of sentences. Epistemicists talk about what sentences can and can’t be known. Many-valued theorists (including this one) talk about the truth-values of various sentences, and so on. And, as Quine pointed out, it is not trivial to extricate the meanings of words from merely the meanings (let alone from the truth values) of sentences. So even if we have an account of what sentences are vague, working out which terms are vague is hard. As I said, it’s a hard question whether “very” is vague. If I knew how to solve this problem I’d probably have written my vagueness book by now, so this is not a good omen for the success of the project sketched in this post.
It has by the way rained for days at Brian’s location, wherever in the world that happens to be. For a while I thought the theme song for this trip would be “Weather With You”. But it really has been fun and no one is getting too irritable, so perhaps Franz Ferdinand’s “Jacqueline” would be more suitable, and more Scottish.