InFavourofVaguePropositions

Note that this connection between vagueness and ignorance sheds light on the view, discussed in chapter 4, that the notions of propositional vagueness and precision are trivial, or even meaningless.

However, if you think that there are some propositions (such as the proposition that Harry is bald) which in certain circumstances enjoy a kind of incurable ignorance, and other propositions (such as the proposition that Harry has less than 1,000 hairs) which do not, and you can reliably distinguish between the cases where the incurable ignorance is due to vagueness, then you have done everything except verbally accept the distinction between propositions that is being claimed to exist. You might think that the distinction is a product of a more basic phenomenon associated with vague language, but you must at least accept that the distinction between propositions exists and is non-trivial. To go beyond a verbal rejection of the distinction you must rather maintain that the propositions being grouped together as ‘vague, such as the proposition that Harry is bald, do not really exhibit these epistemic features, or argue that the propositions being classified as ‘precise, such as the proposition that Harry has less than 1,000 hairs, do.

I should mention straight away that while the connection between vagueness and ignorance is certainly widely accepted, some philosophers have recently attempted to resist it.

In our preliminary characterization of the phenomenon, we said that there are certain heights such that it is impossible to know that a person is tall when they are that height, a certain number of hairs such that it is impossible to know that a person is bald when they have that number of hairs, and so on. One issue that needs to be addressed is how to characterize these heights, hair numbers, and so on. A partisan way of doing this would be to talk about the heights of people who are borderline tall, or the number of hairs that people who are borderline bald have, and so on. This way of characterizing the cases, of course, uses the adverbial way of talking about vagueness and carves out a distinction between people. Some linguistic theorists would want only to draw a distinction between sentences, leaving the distinction between people derivative at best, and so will say something different in its place. As we discussed in section 4.4 on quantifying in, there are several different ways to do this and perhaps other ways I haven't considered. In what follows I shall leave it to the reader to fill in those details, in whichever way they see fit.

My argument against linguistic theories will revolve around the following example (adapted from Dorr [34]):

Before us is a glass of water that is filled so that it is exactly 70% full.

It should be obvious to everyone that an unqualified positive or negative answer to this question would be inappropriate, even among those who happened to have measured all the relevant precise facts about the exact volume and shape of the glass, the exact volume of water in it, and so on. Modulo a small number of dissenters, mentioned earlier, most philosophers think that the explanation for this fact is that they simply do not know that the glass is pretty full, despite the fact that they know numerous precise facts, such as the proportion of the glass that is filled with water.

Once we have conceded that, for example, the English speakers do not know whether the glass is pretty full, it becomes pretty hard to imagine that speakers of other languages are in a better position to know than the English. Indeed, it becomes hard to imagine that anybody is better placed to discover whether the glass is pretty full—even the people who do not speak any languages at all. Thus I think we have good reason to accept the following:

IGNORANCE: Nobody knows whether the glass is pretty full.

We can also make it explicit that this is not because they are ignorant about how full the glass is:

Knowledge: For each 0 ≤ n ≤ 100, somebody knows whether the glass is at least n% full.

This should also be obvious assuming, as I have been, that among the people meas­uring the glass are people who have measured the exact percentage of the glass that is filled.

Ignorance, I take it, is somehow or other a result of vagueness, and a very puzzling result at that. Each person in our team of measuring experts measures the glass but without fail, each comes away ignorant about whether the glass is pretty full. This isn't just an accident, it is a general fact that calls out for an explanation, and a theory of vagueness ought to surely provide one, or ought at least be capable of providing one within the resources it invokes.

We must be careful to distinguish Ignorance from Linguistic Ignorance, which is surely also true:

Linguistic Ignorance: Nobody knows whether the sentence ‘the glass is 70% full and pretty full' is true in English in 2014, at context c, world w (and...)

Without a doubt, not one of the measurers knows this fact either. However, it is important to bear in mind the difference. Among our international team, we may suppose, are monolingual Chinese speakers who are ignorant of the second fact for reasons that have nothing to do with vagueness. In general, if you do not know what the sentence ‘the glass is 70% full' means in English (at context c and...) then you may not know whether it is true. Conversely, you might know that ‘the glass is 70% full' is true in English (at c and...) without knowing whether the glass in question is 70% full. A competent English speaker knowledgeable about the glass might have told the monolingual Chinese speaker that the sentence in question is true, without telling her that the glass is 70% full.

There are therefore two distinct things we are ignorant about. In fact, there are more than two things: there are countless other languages with sentences like the English one mentioned above whose truth statuses we do not know.

It is this latter fact, the ignorance about whether the glass is pretty full, that I think is hard for the linguistic theorist to explain and it is this fact that I shall concentrate on in what follows. If the linguistic theorist is right about the nature of vagueness it would be fairly easy to come up with explanations for Linguistic Ignorance. However, doing so does not exempt her from the burden of addressing one of the central issues in the philosophy of vagueness: explaining Ignorance.

It's worth mentioning that other facts about propositional attitudes need explain­ing, and would have served equally well as the basis of my criticism in the following. For example, I will argue later in the book that both of the following are true:

Bouletic: If you know exactly how much water there is in the glass (and any other precise things that you care about), you should not further care whether it is pretty full or not.

Doxastic: If you are rationally certain that it's borderline whether the glass is pretty full you cannot be rationally certain that it's pretty full.

Similar questions arise for the linguistic theorist concerning how to explain these truths. For now I will focus on the more familiar principle Ignorance. Like Ignor­ance, there are linguistic versions of these principles that we should take care to distinguish.

What follows from the conjunction of Ignorance and Knowledge? An important consequence of these two assumptions is that, given a natural supervenience thesis, propositions are more fine-grained than sets of worlds.

To see why Ignorance and Knowledge require this level of fine-grainedness, take any set of worlds that is putatively identical to the proposition that the glass is pretty full—let's say, the set of worlds where the glass is at least n% full. (This choice is natural once we've make the simplifying assumption that whether the glass is pretty full supervenes on the percentage of the glass that is full.) According to Knowledge somebody knows whether the glass is at least n% full, yet by Ignorance nobody knows whether the glass is pretty full. Thus, applying the proposition role specified in chapter 4 and Leibniz's law, the proposition that the glass is at least n% full (i.e. the set of worlds at which the glass is at least n% full) is not identical to the proposition that the glass is pretty full. Here is the argument explicitly (assume, without loss of generality, that the glass is in fact at least n% full):

1.       Somebody knows that the glass is at least n% full. (By Knowledge.)

2.       Nobody knows that the glass is pretty full. (By Ignorance.)

3.        Thus nobody knows the proposition that the glass is pretty full, and some­body knows the proposition that the glass in at least n% full. (Applying the proposition role.)

4.        Therefore the proposition that the glass is pretty full is not the same as the proposition that the glass is at least n% full. (Leibniz's law.)

Let me clear up two possible misunderstandings about this argument. The first concerns philosophers who reserve the word ‘proposition' for sets of worlds, states of affairs, or for some other coarse-grained entity. Such philosophers can verbally reject any conclusions one might draw from this argument involving the word ‘proposition' by divorcing proposition talk from that-clause talk (for example, they might reject the locution ‘that snow is white' as a term for denoting the proposition the sentence ‘snow is white' expresses—they will end up talking in convoluted ways, but there is nothing that in principle stops them from making this move).

Such philosophers are therefore denying that propositions play what I called the ‘proposition role'. But of course, something has to play the proposition role— at least the way we use that-clauses in English suggests that something does—and so this is just a disagreement about which entities we should grant the honorific title ‘proposition' to. No conclusion that matters to us here can only be stated using the word ‘proposition'—the important upshot of the above argument concerns the objects of thought, the denotations of that-clauses—i.e. the things I have been calling ‘propositions'.

The second misunderstanding concerns a certain approach to the semantics of attitude reports. A common response to Frege puzzles involving Leibniz's law, such as the one above, is to maintain that knowledge and belief, despite their surface form, are fundamentally three place relations between a person, a proposition, and a ‘mode of presentation' which represents the way in which you come to believe that proposition (see Crimmins and Perry [30] and Richard [120]). According to this view no one ever simply stands in this relation to a proposition—they stand in this relation to a proposition relative to a way of entertaining that proposition—a mode of presentation. One might object that in making this argument I have begged the question against these theorists by not being explicit about the mode of presentation.

I think that whatever that view says about the fundamental psychological structure of propositional attitudes, it still has to account for ordinary language belief reports which have a binary structure and make no explicit mention of modes of presentation. The most natural way to do this is to suppose that a natural language belief report which on the surface appears to be a binary relation in fact states a ternary connection between a person and a proposition (supplied by the referents of the subject and the that-clause respectively) and a contextually supplied mode of presentation which does not appear grammatically as a third term on the surface.¹

The point to stress here is that my argument was not stated using the fundamental ternary relation; it was stated using the ordinary language binary relation that is expressed in the present context by the verb ‘knows’; which binary relation this verb expresses is context sensitive on this view, but that is not to say that I didn’t express a particular binary relation when I stated Ignorance and Knowledge. The correct response to this argument for a contextualist is not to reject the validity of the argument—it was literally an application of Leibniz’s law, along with a stipulation about what I meant by ‘proposition’—but to reject one of the premises. Suppose that the proposition that the glass is pretty full is, in fact, identical to the proposition that the glass is at least n% full—call this proposition p. If the contextually salient mode of presentation is the vague one then, presumably, nobody stands in the three- place knowing relation to p relative to that mode of presentation. In this context Knowledge expresses a falsehood. On the other hand, if the contextually salient mode of presentation is the precise one then presumably the people who measured the percentage of the glass that is full do stand in the three-place knowing relation to p relative to the precise mode of presentation. In this context Ignorance expresses a falsehood. Either way the argument is valid, and it is one of the premises that fails.^{[60] [61]}

Thus, I contend, anyone who accepts both Ignorance and Knowledge in the same breath, without changing the context, must acknowledge the thesis that there are vague propositions.^[62]

I will treat those who deny the conjunction of Ignorance and Knowledge in section 5.3. The simplest way to deny the conjunction is to deny Ignorance flat out. However, the contextualist variant of the no-ignorance type view, briefly described above, allows certain attitude reports to depend on a contextually salient mode of presentation. There will be some contexts where they behave like the straightforward kind of no-ignorance theorist by denying Ignorance (and asserting Knowledge). However, there will be many other contexts in which they can assert Ignorance (albeit, in these contexts they must deny Knowledge) thus allowing themselves more flexibility than the simplest no-ignorance view. Of course, at no context will both Ignorance and Knowledge express a truth. In section 5.2, however, I shall simply assume that Ignorance and Knowledge are being granted, and that propositions are therefore somewhat fine-grained.

Before we move on, let me stress that the question we are dividing our discussion around concerns how coarse- or fine-grained we take the objects of attitudes to be. However, it is evident that settling this question still leaves a number of different possibilities regarding the relation between sentences and propositions open. The two most salient options to choose between are the views that vague sentences (i) express exactly one proposition and (ii) that they express several.⁴

Both views about the relation between sentences and propositions can be combined with both the coarse- and fine-grained view about propositions. Ifwe were to combine a coarse-grained account of propositions with the view that ‘Harry is bald' expresses a unique proposition, then it presumably has to be a view in which we cannot know which proposition it expresses (presumably because it is vague). For it would be hard to maintain that we can know that ‘Harry is bald' expresses, say, the coarse­grained proposition that Harry has at most 1,023 hairs, whilst also maintaining that we can't know whether ‘Harry is bald' is true or not.⁵ On the other hand, on a more fine-grained view in which there is the proposition that Harry is bald in addition to propositions like the proposition that Harry has at most 1,023 hairs, there is a particularly natural candidate for the proposition that ‘Harry is bald' expresses: the proposition that Harry is bald. In which case we can know what proposition ‘Harry is bald' expresses. We can also combine the coarse- and fine-grained views in various jointly true in the same context and so propositions are fine-grained enough to be the objects of vagueness and precision.

⁴               A variant of (ii) would be that sentences don't express propositions simpliciter, but only relative to a precisification, much like a context-sensitive sentence only expresses a proposition relative to a context. I haven't considered the more radical view that borderline sentences don't express propositions at all, since this view is subject to straightforward problems. For example, the sentence ‘Either Harry is bald and electrons have charge or Harry is not bald and electrons have charge' is a precise sentence equivalent to ‘electrons have charge', and should therefore express a proposition. However, it is hard to see how to compute that proposition compositionally according to this account, given that neither disjunct expresses a proposition.

⁵               Note that although some self-described linguistic theorists adopt the latter idea, it is stated in the adverbialist vocabulary so it is unclear whether the latter theory is open to a linguistic theorist.

7á VAGUENESS AND THOUGHT

ways with option (ii). The most natural view is a coarse-grained view in which a vague sentence expresses a bunch of precise propositions, but one could also maintain that vague sentences express a collection containing both precise and vague propositions, or even exclusively vague propositions. My purpose, in bringing this up, is to stress that the subsequent discussion relies only on the stance we have taken towards the possibility of ignorance in the vague, and on how coarsely or finely we individuate the objects of ignorance; the status of the relation between sentences and propositions will, for the most part, be absent from this discussion, and nothing I say turns on how we ultimately settle that question.

5.2