Identity and the Facts of the Matter

Graeme Forbes

There are a number of Sorites-type puzzles in the literature concerning identity through time and across possible worlds. I suggest that these are at bottom the same puzzle, and therefore should have, at bottom, the same solution. This "uniformity" constraint rules out certain solutions to particular puzzles, including, regrettably, one due to myself. In this paper I present a unified solution to the puzzles, based on the idea of indeterminate identity as recently elaborated and defended by Terence Parsons.

Is perceptual indiscriminability transitive ?

Leon Horsten

The received view, which goes back at least to Nelson Goodman, has it that perceptual indiscriminability is an intransitive relation. But in recent years, arguments have been put forward that seek to cast doubt on the standard view. In my presentation, at least two views opposing the standard view will be discussed in some detail: the view of Delia Graff and that of Diana Raffman. One of the aims of the presentation will be to defend the standard view against the objections that they mount against it. On the hypothesis that perceptual indiscriminability is indeed intransitive, I shall then go on to discuss attempts to formulate a satisfactory theory of perceptual notions (such as colors). Here I shall concentrate on Timothy Williamson's theory of indiscriminability and variants on it.

In Defence of Degrees

John MacFarlane

One of the most powerful considerations in favor of epistemic approaches to vagueness is that alternative theories, such as degree theories and supervaluationism, are committed to semantic boundaries no less inscrutable or arbitrary than those posited by classical bivalent semantics. Nonclassical theorists will need a story about how these inscrutable lines are drawn, why they can't be known, and why sorites arguments that attempt to exploit them seem plausible. Since any story they tell could also be used in defense of classical semantics, is unclear why the alternatives are worth the trouble.

The point of this talk is to answer that question. My starting point is Stephen Schiffer's acute observation that the attitude of increasing ambivalence we feel as we go down a sorites series is not well understood as increasing uncertainty, as it ought to be if the epistemicist is right. When we are uncertain about the truth of several independent propositions, our degree of belief in their conjunction ought rationally to be the product of our degrees of belief in each of them singly. It seems, however, that when Joe is borderline tall, borderline fat, and borderline bald, it is not irrational to endorse the conjunctive proposition that Joe is tall and fat and bald to about the same degree that we endorse the conjuncts singly. Schiffer proposes that we understand the ambivalence characteristic of borderline cases as a special kind of "vagueness-related partial belief" that is subject to different norms than standard partial belief. However, as I have shown elsewhere1, his approach faces substantial technical obstacles.

Instead of understanding vagueness-related ambivalence as a nonstandard kind of partial belief in the truth of a content, I argue, we should understand it as standard belief in its partial truth, or, more accurately, as a distribution of standard (uncertainty-related) degrees of belief over a range of candidate degrees of truth. This proposal makes better sense of the patterns of partial endorsement we deem rational with borderline propositions than the epistemic theory can. Unlike standard motivations for degree theories, this one is not undermined by its commitment to hidden boundaries. Indeed, it embraces the idea that part of what is distinctive about vagueness is our ignorance of where boundaries lie, while rejecting the epistemicist's claim that this is the whole story.

1 "The Things We Kinda Sorta Believe", Philosophy and Phenomenological Research 73 (2006), 218–224.

Vagaries about Vagueness

Nathan Salmon

Two approaches to vagueness are distinguished. The vagueness-in-language approach sees the world as exact, and all vagueness as inherent in our means of representing the world. By contrast, the vagueness-in-the-world approach sees the world itself as fuzzy, in the sense that for some things and some attributes of things, allegedly there is no fact of the matter whether those things possess or lack those attributes. The former approach is criticized on several grounds. The vagueness-in-language approach is either incoherent or collapses into vagueness-in-the-world. A recent objection to direct-reference theory, based upon the criticized approach, is shown to be fundamentally mistaken.

Degrees of Truth, Degrees of Belief, and Pragmatics

Nicholas Smith

Vagueness is the home ground of degrees of truth, and degree theorists have been kept busy defending their view against objections based specifically on considerations having to do with vagueness. However a broader worry also looms for degree theories. The semantic notions (most notably truth) of which, for reasons having to do with vagueness, the degree theorist gives a non-classical account, play a crucial role right across philosophy. Can the idea that truth comes in degrees be made to mesh with important developments in other areas of philosophy, where bivalence has hitherto been taken for granted? If not, that would be a serious mark against degree theories.

In this paper I take up the challenge, with respect to Stalnakerian theories of pragmatics. Standard versions of such theories presuppose bivalence. I show how such theories can be extended in a natural way to accommodate degrees of truth. Part of what is involved here is the idea that, once we countenance intermediate degrees of truth for propositions, we need to countenance intermediate degrees of (confidence of) assertion of propositions, and intermediate degrees of belief in propositions.

This brings us to the key issue of the relationship between degrees of truth and degrees of belief. A number of authors have noted that if we have degrees of truth, then we should have corresponding degrees of belief---but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief? I argue that we cannot coherently do so, and present instead a formal framework in which there is a single notion of degree of belief, which in certain circumstances behaves like a subjective probability assignment, and in other circumstances does not. The framework is surprisingly neat and uncomplicated, and affords a clear picture of the relationship between subjective probabilities, degrees of truth and degrees of belief.

The Possibility of Partial Definition

Scott Soames

The paper defends the coherence of partially-defined predicates against the Glanzberg-Dummett argument that the connection between truth-values and the intrinsic norm of assertion makes such predicates, and the kinds of "gaps" to which they give rise, impossible. Williamson's conception of the relation between knowledge and assertion is endorsed, and the error inherent in asserting undefined propositions is attributed to their unknowability—which is explained without characterizing them as untrue. Supervaluationist attempts to embrace both undefined propositions and excluded middle are criticized, and an argument is given for rejecting some instances of excluded middle (as undefined). Finally, the epistemicist explanation of borderline cases involving ordinary vague predicates is contrasted with the explanation provided by a theory invoking partial definition, contextual variability, and expressive indeterminacy. Although it is argued that the latter theory has an advantage that the former doesn't, it is further suggested that, in the end, the proponent of such a theory must either admit that something central to vagueness has been left out, or acknowledge certain sorts of apparently unknowable Williamsonian facts.

Examples of the Vagueness of ‘Vague’

Roy Sorensen

I shall show, by example, that ‘vague’ has borderline cases. These concrete steps lead up to a more abstract argument that ‘vague’ has borderline borderline cases and borderline borderline borderline cases. My specimens are intended to defend and extend an earlier (Sorensen 1985) non-constructive proof of the vagueness of ‘vague’.