What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

According to contextualism about vagueness, the content of a vague predicate is context sensitive. On this view, when item a is in the penumbra of the vague predicate ‘F’, speakers may utter ‘Fa’, or they may utter ‘not-Fa’, without contravening the literal meaning of ‘F’. Unlike its more popular variants, the version of contextualism I defend rejects the principle of tolerance, a principle according to which small differences should not affect the applicability of a vague predicate. My goal is to (...) show how such a rejection allows for a plausible treatment of higher-order vagueness, and for a dissolution of paradoxes of higher-order vagueness. (shrink)

This piece gives an overview of the supervaluationist theory of vagueness. According to that theory, a sentence is true if and only if it is true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The article presents the view and some of its merits and briefly compares it with other theories of vagueness. It raises issues about higher-order vagueness and the definitely operator (...) and about the supervaluationist's accounts of truth and validity. (shrink)

In this paper I offer a critique of the recent popular strategy of giving a contextualist account of vagueness. Such accounts maintain that truth-values of vague sentences can change with changes of context induced by confronting different entities (e.g. different pairs through a sorites series). I claim that appealing to context does not help in solving the sorites paradox, nor does it give us new insights into vagueness per se. Furthermore, the contextual variation to which the contextualist is committed is (...) problematic in various ways. For example, it yields the consequence that much of our everyday (non-soritical) reasoning is fallacious, and it renders us ignorant of what we and others have said. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal).

ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It corresponds (...) to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

Contextualism about vagueness (hereafter ‘Contextualism’) is the view that vagueness consists in a particular species of context-sensitivity and that properly accommodating this fact into our semantic theory will yield a plausible solution to the sorites paradox.[1],[2] But Contextualism, as many commentators have noted, faces the following immediate objection: if we hold the context fixed, vagueness still remains, therefore vagueness is not a species of context-sensitivity. Call this ‘the simple objection’.[3] Absent a convincing reply to the simple objection, Contextualism is in (...) very bad shape. Oddly enough, defenders of Contextualism have said very little in reply. Proponents of the objection have tended to assume that this is because no reply is in the offing—the simple objection is taken to be unassailable. In this short paper, we sketch two replies to the simple objection which result in two very different kinds of Contextualism: Epistemicist Contextualism and Radical Contextualism. With these two theories in hand, the simple objection loses its force. (shrink)