Does Vagueness Involve Truth Value Gaps?
Let us turn to another question that has occupied the attention of many philosophers of vagueness:
Truth Gaps: Do borderline sentences have truth values?
This is, of course, the central point of contention between the ordinary supervalu- ationist on the one hand and the epistemicist and disquotational supervaluationist on the other.
But is it a substantive question? Hartry Field thinks that it is not:[... ] let us set aside a verbal issue. Proponents of [determinately operators] differ as to their preferred use of ‘it is true that p’: some take it as equivalent to ‘p’ (call this the weak reading), others take it as equivalent to ‘it is a determinate fact that p’ (the strong reading). Obviously nothing can hang on whether we use the term ‘true’ in its weak or its strong sense. Perhaps the safest policy is to introduce two distinct words, ‘truew’ and ‘true/, for these notions.
(Field [53]) What is clear from Field’s presentation is that the point of contention is not over the coherence of either of these two notions of truth. As noted above, one can always introduce a disquotational notion of truth stipulatively. Similarly, I can always introduce a stronger notion of determinate truth by defining it as a (weak) truth that’s not borderline. Since everyone theorizing about vagueness ought to have the notion of borderlineness at their disposal, the notion of determinate truth, so defined, will always be available.
One question we might ask is: Which of these two notions best fits our use of the word ‘true’ in English (parallel questions could be asked about the word ‘vrai’ in French, ‘wahr’ in German, and so on).
One way to settle this question would be to look at a body of data concerning the way that ‘true’ is used in English and see which fits best. I strongly suspect that the answer to this question is neither: most uses of‘true’ in English apply not to sentences but to propositions (for example ‘everything Alice said is true’), and is thus not the kind of property of sentences that a supervaluationist is attempting to capture. Of course we can talk about true sentences in English, even though it is less common, but it is well known that context sensitive sentences are neither true nor false on their own but only relative to a context and the typical speaker is not particularly careful about these subtleties. Thus the question becomes about which of the two notions of truth best fits our use of the somewhat technical notion of‘truth in English relative to a context c. This is no longer a question about ordinary language but about philosophers’ technical vocabulary.A better way to approach these questions is to outline a wider theoretical role that our philosophical notion of truth is supposed to play, and to see whether disquotational truth or determinate truth plays it. This wider role presumably relates the concept of truth to assertion, reasoning, the possibility of knowledge, necessity, belief, evidence, disquotational principles, compositionality, and so on. It is unlikely, however, that either concept satisfies all of these connections: disquotational truth is compositional, disquotational, and is presumably more useful for semantic theorizing, whereas determinate truth presumably is more closely connected to the possibility of knowledge, being a prerequisite for proper assertion, and so on. The question of which role to associate with the word ‘true’ is no more substantive than the question we began with.
Perhaps one can disagree about whether determinate truth or disquotational truth plays a specific part of this role (for example, one might maintain that a good argument only needs to preserve determinate truth, or one might insist that this is not enough and that good arguments must also preserve disquotational truth). Once this move is made the debate is no longer isolated to sentences involving the word ‘true’.
Depending on the wider role, we may find ourselves disagreeing about what kinds of inferences are permissible, about the kinds of doxastic attitudes we should have about the borderline, what rational credences in vague propositions should be like, and so on.The thing to note here, however, is that these further questions do not need to be formulated in terms of truth at all, and can be formulated directly as questions about the relation between borderlineness and these other concepts such as good reasoning, and rational belief. Indeed, I will argue shortly that some of these debates are in fact substantive, non-verbal disputes: disputes that aren’t purely about which notion to call ‘truth’.
Relating our discussion back to supervaluationism and epistemicism, note also that while the question about truth has the appearance of being central to that dispute, these further questions about rational credences and reasoning are not obviously part of that debate. No consensus exists among supervaluationists about how these further questions should be answered: there is, for example, no consensus among supervaluationists about what kind of doxastic and credential attitudes we ought to have towards the borderline (contrast, for example, Field [53], Williams [152]).
I am thus inclined to agree with Field: the dispute about whether borderline sentences have ‘truth values’ is not substantive if it is a debate isolated purely to questions involving the word ‘true’. If one attempts to widen the dispute to questions about belief, reasoning, and so on, it might be better to just ask questions directly about the relation between borderlineness and belief, reasoning, and so on, instead of making the detour through the debate about ‘truth’. After all, presumably there are roles for both disquotational truth and determinate truth, so the question of which role to give the honorific title ‘truth’ does not seem like an important issue.
Before we move on, it is worth noting that a completely parallel dispute can be raised about other semantic vocabulary, such as ‘refers’ and ‘expresses’ The analogue of the view that a borderline sentence doesn’t have a truth value is that a borderline sentence doesn’t express exactly one proposition, and that a vague name doesn’t refer to exactly one thing.
A traditional supervaluationist will usually chalk this up to non-uniqueness rather than non-existence: borderline sentences express many propositions, and borderline names refer to many objects. But as before, we can also introduce notions that behave disquotationally on a limited fragment of the language: we can stipulate that ‘Harry is bald' expresses the proposition that Harry is bald and nothing else, that ‘Harry’ refers to Harry and nothing else, and so on. Thus unless this dispute about the words ‘expresses’ and ‘refers’ is hooked up to further questions it begins to look no more substantive than the question about truth.Since the choice is for the most part terminological, I shall use the words ‘true’, ‘expresses, and ‘refers’ to denote the disquotational notions: I shall adopt this convention throughout this book unless I indicate otherwise. When I discuss orthodox super- valuationism I shall reserve the technical term ‘supertruth’ for the non-disquotational notion of truth.
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