Epistemicism and Supervaluationism

Perhaps the most famous classical accounts of vagueness are epistemicism and super- valuationism.3 As we shall see later, both of these terms are fairly slippery: different theorists emphasize different things, and the clearest indication as to when one of these labels can be applied is when the theorist herself identifies one way or the other.

The epistemicist, it is said, takes the argument for sharp cutoffs from classical logic at face value. However initially compelling the thought that a nanosecond cannot make the difference between being young and not young, the epistemicist reasons, it is false: logic sometimes teaches us surprising things. The epistemicist therefore embraces sharp cutoff points. The other distinctive feature of epistemicism is that it tries to explain vagueness in terms of our ignorance about the location of these cutoff points. Since there is a last nanosecond at which I ceased to be young, and it is unknown which nanosecond that was, and since similar ignorance about the locations of cutoff points is common to all sorites sequences, some epistemicists have suggested that vagueness just is a kind of ignorance. No doubt this ignorance is unusual: while it is easy to find out at what age one is eligible to vote, it is hard or impossible to find out at what age one stops being young. However, the epistemicist maintains, ignorance about vague cutoff points is fundamentally the same sort of thing as ignorance about other ordinary matters such as eligibility to vote.

Just as the sorites paradox teaches us something surprising about youngness, similar conclusions about language are also often emphasized by the epistemicist.

Supervaluationists, by contrast, are not directly motivated by the sorites paradox and, to the extent that they acknowledge the existence of sharp cutoff points, do not usually engage in the proj ect of explaining them. Rather, they are frequently motivated by general considerations concerning language use. In contrast to epistemicism, supervaluationism maintains that there are lots of ways of assigning precise (classical, bivalent) interpretations to predicates like ‘young’ that accord with the linguistic practices of English speakers. Our practices are determinate enough to exclude some interpretations—for example, interpretations in which ‘small’ applies to the sun, and other similarly uncontroversial cases are ruled out—but not determinate enough to narrow the possible interpretations down to a unique one. Rather, a vague language gets associated with a collection of interpretations: what are called the admissible precisifications, or admissible interpretations of that language. An admissible precisifi- cation is roughly a classical interpretation that fits with the practices of the language users in the right sort of way.

Unlike the epistemicist, the supervaluationist appears to reject classical semantics.

Unlike the epistemicist, then, the orthodox Supervaluationist rejects the law of bivalence. For given the identification of truth with supertruth, the law of bivalence becomes:

Bivalence: For every meaningful sentence P, either P is true in every admissible interpretation or P is false in every admissible interpretation,

and we have just seen that this has counterexamples. Note, however, that we must draw a sharp distinction between bivalence and the truth of the law of excluded middle. The claim that the law of excluded middle is true, given this account of truth, becomes:

Truth of LEM: The sentence ‘P or not P^, is true according to every admissible interpretation.

Since admissible interpretations are just special kinds of classical interpretation, it follows that the law of excluded middle is true according to all admissible inter­pretations. More generally, every classical tautology will be true in all admissible interpretations for exactly the same reason.

What I have described above is the orthodox version of supervaluationism.⁶ Not all supervaluationists accept the identification of truth with the notion of supertruth defined above—there are other reasonable candidates out there.

Note that it is always possible to introduce a predicate of sentences that behaves disquotationally and which, assuming classical logic, is bivalent. Let us introduce the artificial term ‘dtrue’, and stipulate that it applies to the sentence ‘Harry is bald’ if Harry is bald, and doesn’t apply if he isn’t. Since we’ve acknowledged that Harry is either one or the other this definition is perfectly well-defined on this sentence. By making lots of similar stipulations we can ensure that dtruth behaves disquotationally for every sentence of our original language. (Of course, in making these stipulations I can’t use the word I’m trying to introduce within those stipulations: thus I can’t make stipulations that use the word ‘dtrue’, but this will matter little for our purposes since we are not primarily interested in disquotational sentences involving the word ‘dtrue’.)

To see that dtruth is a bivalent concept, let us adopt the usual convention of identifying falsity with having a true negation: say that a sentence is dfalse if its negation is dtrue. Without loss of generality, we can show that the sentence ‘Harry is bald’ is either dtrue or dfalse. By excluded middle either Harry is bald or he isn’t, by the disquotational nature of dtruth it follows that either ‘Harry is bald’ is dtrue or ‘it’s not the case that Harry is bald’ is dtrue, and so ‘Harry is bald’ is either dtrue or dfalse.

Note, however, that the claim that ‘Harry is bald’ is dtrue is just as borderline as the claim that Harry is bald (after, our stipulations were designed so as to make these two claims materially equivalent).

Some proponents of supervaluationism have suggested that dtruth is a better candidate than supertruth for doing the philosophical work of truth (see McGee and McLaughlin [104]). For this brand of supervaluationism borderline sentences do not lack truth values, but they lack what you might call a ‘determinate truth value’: while borderline sentences can be true, we shall say that a sentence is determinately true only if it is true without being borderline.

If we were to reduce both views to a one line slogan, they might go something like the following:

Epistemicist Slogan: Vagueness is ignorance.

Supervaluationist Slogan: Vagueness is lack of truth value (or, determinate truth value).

Note that epistemicists do not identify vagueness with just any kind of ignorance, but with the special kind of ignorance associated with borderline cases—the details of which will depend on the specific version of epistemicism in question.

There are several theories of vagueness on the market that accept the existence of cutoff points, but epistemicism and supervaluationism in particular have enjoyed pride of place in the literature. Indeed, if one is in the business of cataloguing the important questions in the philosophy of vagueness one might expect one or more of these disputes to be at stake between the epistemicist and the supervaluationist since, in the minds of many, supervaluationism and epistemicism are the two main com­peting classical theories. In this section I shall use the supervaluationist/epistemicist debate as a springboard for my discussion of some of the traditional questions in the philosophy of vagueness.

Although the dispute between supervaluationism and epistemicism has dom­inated much of the debate on classical theories of vagueness, a few philosophers have begun to question how substantive the dispute actually is.^[23] Indeed, despite the seemingly straightforward differences between the views outlined above, I’m inclined to think the accepted classification of classical views into ‘epistemicism’ and ‘supervaluationism’ to be thoroughly unhelpful: the issues that are sometimes thought to characterize the epistemicist and supervaluationist positions either turn out to be issues on which both sides agree, or issues that have few repercussions for the central problems in the philosophy vagueness.

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