Despite the pervasiveness of vagueness, it is natural to find some version of the following schematic thought extremely compelling:
that there is some definite collection of completely factual propositions upon which all truths supervene which are unaffected by vagueness.
Supposing that one has the notion of a proposition being ‘factual’ in this sense, we can spell out what it means for it to consist of a ‘definite collection of propositions unaffected by vagueness’ a bit more precisely:[F1] Every factual proposition is either determinately true or determinately false.
[F2] If a proposition is factual, then it is determinately factual.
[F3] If a proposition is not factual it is determinately not factual.
Although I am sympathetic with those who are sceptical of this notion (see Dorr [33], Dreier [36], Field [50]), in this chapter I am interested in exploring views that theorize in terms of the notion of being factual and take it to be integral to the explication of vagueness.[174] The distinction employed by such philosophers abides by F1-F3: factual propositions are always determinately true or false and it is not a vague matter which propositions are the factual ones.
class=a7 style='text-indent:18.0pt'>It should be noted that for F2 and F3 to be remotely plausible, one cannot simply take ‘factual’ to be a synonym for ‘precise’. Due to the existence of higher-order vagueness, it is vague which propositions are the precise ones, and the analogues of F2 and F3 for precision are false. Factual propositions are supposed to be rock bottom—perhaps they are just the propositions about the values and properties of fundamental particles and fields at each space-time point (for example). Certainly every factual proposition is precise, but there can be some precise but higher-order vague propositions that are not rock bottom and thus not completely factual. Another candidate synonym is the notion of a fundamental proposition, for I think it is clear that only precise propositions are fundamental, and it is a precise matter which propositions are the fundamental.What might some plausible candidates for these factual or fundamental propositions be? We have already ruled out the precise propositions due to considerations of higher-order vagueness. For similar reasons, the propositions which are precise at all orders will not do either, since, as we saw in chapter 13, it is also a vague matter which propositions are precise at all orders (see section 13.4.1).
What about the propositions of physics: propositions specifying the locations of fundamental particles, their charges, spin, and other fundamental properties? Let us suppose, for the sake of argument, that it is a completely precise matter which propositions are the physical propositions, and let us also assume physicalism. Even under these assumptions, the physical propositions will not serve our purpose once we have accepted the idea, defended in chapter 12, that the propositions of physics are not precise (although they are plausibly necessarily determinately true or deter- minately false).
Although the above considerations indicate that the idea of some collection of basic propositions of this sort is not a forgone conclusion, it is arguably implicit in a certain way of making use of the notion of a possible world. For example, on the face of it, the supervaluationist formalism, in which the truth of a formula is evaluated relative to a possible world and a precisification, appears to employ worlds in this way. The formalism suggests a clean separation between the kind of factors that cause variation in truth value that depend on facts to be found ‘in the world' (things like height and hair number) and variation of truth value that is due to the arbitrary locations of cutoff points—differences in truth value that are merely a result of how we settle the cutoff points for things like tallness and baldness.
In such a formalism, one can identify a vague proposition with a set of world-precisification pairs, and from among those one can distinguish a special class of‘worldly' propositions—sets which contain all ordered pairs involving a given world if they contain any ordered pairs involving that world. The semantics straightforwardly validates the claim that such propositions are precise and that it is a precise matter which propositions are worldly in this sense.Despite the pervasiveness of possible worlds talk in philosophy, one might wonder what the alternative might look like. That is, one might wonder what it would be like for there to be vagueness all the way down: for there to be no definite collections of precise propositions on which all truths supervene or, perhaps, even, no definite collections of precise propositions whatsoever. According to this alternative, one can approximate the ordinary notion of a possible world by talking about propositions that settle all precise matters—that divide up logical space into cells of maximally strong consistent precise propositions—but unlike the usual way of thinking about worlds, it will be vague where these lines in logical space lie, for it is vague which propositions are precise.
In this chapter, I'll look at some reasons, relating especially to the paradoxes of higher-order vagueness, to reject the idea that vagueness bottoms out in this way. In doing so, I'll sketch an alternative to the supervaluationist picture, based on the symmetry analysis of precision, that eschews the usual notion of a possible world altogether.
14.1