Vagueness and the Objects of Thought

This chapter has provided a quick tour of the primary differences between the linguistic and non-linguistic approaches to vagueness, and a look at some of the outstanding technical issues.

The view I am defending in the present book belongs to the non-linguistic camp: propositional vagueness will take centre stage in our theory. While sentential vagueness is a perfectly good notion—it is just a sentence that expresses a vague proposition—it will play little theoretical role in the theory. It is very natural to associate the view I am going to defend, according to which language-independent entities—propositions—are the primary bearers of vagueness and precision, with the view that the adverbial and operator ways of speaking about vagueness are basic.

I do in fact endorse both these ideas, but it is important to be clear about how they are different. For example, it ought to be obvious that the operator and adverbial ways of speaking about negation are theoretically more basic than the linguistic analogue of negation—the falsity predicate.^[56] We should be non-linguistic theorists about negation. Yet it's clear that a nominalist about propositions can perfectly well accept this view, and freely employ the negation operator, whilst resisting the further claim that propositions can be negated, on the grounds that there are no propositions.^[57] There is a non-trivial step between employing certain operator expressions and accepting the existence of analogous properties belonging to a special class of entities: propositions.

Nominalists could in principle avoid commitment to propositions, but paraphrase many of the things I say in this book by using the language of higher-order logic, in which one can directly quantify into the position that a sentence occupies (as, for example, Prior does in [112]).

I shall therefore generally help myself to these entities and leave it to the nominalists to do whatever they need to in order to make sense of what I say. Once we have helped ourselves to these entities we must get clear on the kinds of things they are supposed to do. In my view there are a number of different roles that philosophers want propositions to play. For some philosophers, these entities are, like ‘facts' or ‘states of affairs', supposed to do heavy-duty metaphysics. For others, propositions are the semantic values of sentences and provide their truth conditions. Yet another important characterization, the one I will adopt, identifies propositions with the denotations of that-clauses and the objects of propositional attitudes. It may turn out that no single kind of entity can play all these roles, in which case a dispute can arise about which entities are the real propositions. These disputes are verbal—if entities filling each of the roles in question exist, then so long as we are careful about which things occupy which roles, no issue of substance will turn on which of these entities we choose to call ‘propositions'. For my purposes, a proposition will be just whatever the denotation of a that-clause is.

This way of talking about propositions suggests that they are abundant. Whenever there is a sentence, for example ‘Harry is bald', there is also a singular term ‘that Harry is bald', or more perspicuously, ‘the proposition that Harry is bald', which denotes a singular entity, a proposition, that is true if and only if Harry is bald.^[58]

It might seem that the theory that merely says that propositions are the denotations of that-clauses tells us very little about their nature. On the contrary, we can deduce quite a lot about them. Indeed, one can assume that they satisfy what I'll call ‘the proposition role' described below. Each of these principles simply falls out of the stipulation that propositions are the things expressed by that-clauses.

The Proposition Role:

One believes (knows, desires, asserted, said, etc.) that P if and only if one believes (knows, desires, asserted said, etc.) the proposition that P.

It's necessary that P if and only if the proposition that P is necessary.

It's true that P if and only if the proposition that P is true.

A sentence means that P if and only if it means the proposition that P.

It's determinate that P if and only if the proposition that P is determinate.

From these facts we can deduce many things, including that propositions can be said and asserted, are the objects of our attitudes, are necessary and contingent, are the meanings of our sentences, and the objects of truth and falsity, and perhaps also determinate truth and falsity.^[59]

In choosing to use the word ‘proposition’ in this way I have made at least one substantive commitment—that the proposition role is consistent, and that there are entities that occupy the role.

Of course, I don’t mean to suggest that this is a complete theory: more concrete theories of propositions tell us whether propositions are structured entities, whether they are set theoretic constructions, whether they have a Boolean structure (see section 3.2), and so on. For all I’ve said the things playing the proposition role are just linguistic entities—sentences of a particular language, or equivalence classes of sentences from different languages. However, these theories must all agree that these entities satisfy the proposition role if they are engaging in the project of describing the denotations of that-clauses, and it is only facts like those described in the proposition role that I shall need in the following chapters; it is unnecessary to be more specific than this.

Note that a consequence of the proposition role, if you accept the claim that it’s borderline whether Harry is bald (and thus the adverbialist way of drawing these distinctions), is that there are vague propositions. For if it’s not determinate that Harry is bald then, by The Proposition Role, that Harry is bald (a proposition by our lights) is not determinate. If it is furthermore not determinate that Harry is not bald, then we may also infer that that Harry is bald is a borderline proposition.

One issue I want to address is whether a non-linguistic view—one that accepts the operator and adverbial ways of speaking about vagueness as basic—has to be a view in which vagueness is, in some sense, ‘in the world’ (or, alternatively, whether I am committed to ‘metaphysical vagueness’). The answer to this question will depend on how the question is posed. On a very deflationary use of the word ‘fact’ there will be vague facts.

This is just one thing that ‘metaphysical vagueness' might mean; it might mean other things, and these too might require clarification. At any rate, I suspect that once it is clear what I mean by ‘fact' in the above argument many philosophers will find the sense in which I am committed to there being ‘vagueness in the world' an uninteresting one.

The real issue at stake, in my view, is whether the entities which serve as the objects of thought are vague in a way that cannot be reduced to the relations they stand in to public (or private) language sentences. The role that vague propositions play in thought will be examined in chapters 6, 8, 9, and 10, where we connect vagueness to evidence, uncertainty, decision, and desire. We begin in chapter 5, however, by looking at the relation between vagueness and knowledge. This is of course one of the most puzzling issues in the philosophy of vagueness; I shall argue that the role that propositional vagueness plays in explaining vagueness-related ignorance is so fundamental that this ignorance cannot be equivalently explained by a relation to a public language.