Online research in philosophy

Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal.

It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum— so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. My main purpose in what follows is to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no basic datum but an illusion, fostered by misunderstandings of the nature of (ordinary, if you will ‘first-order’) vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes.

In a seminal paper of 1923 on vagueness, Bertrand Russell discussed some of the most important problems concerning the nature of vagueness, its extension within the language, and its relation to truth and logic. The present paper inquires into Russell's theory. The following topics will be analysed and discussed in turn in sections 1?5: Russell's definition of vagueness; his claim that all phrases are vague; his theory of the source of the vagueness in our language; his principles for the transmission of vagueness; and his claim that logic is incompatible with vagueness. This paper is an attempt to give a rational reconstruction of Russell's position as expressed in his paper. Compatible passages in other of his works are also studied.

It is often assumed that indeterminacy in mereological relations—in particular, indeterminacy in which collections of objects have fusions—leads immediately to indeterminacy in what objects there are in the world. This assumption is generally taken as a reason for rejecting mereological vagueness. The purpose of this paper is to examine the link between mereological vagueness and existential vagueness. I hope to show that the connection between the two forms of vagueness is not nearly so clear-cut as has been supposed.

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe’s response to combat both paradoxes.

Transvaluationism makes two fundamental claims concerning vagueness. First, vagueness is logically incoherent in a certain way: vague discourse is governed by semantic standards that are mutually unsatisfiable. But second, vagueness is viable and legitimate nonetheless; its logical incoherence is benign.

The two standard theories of vagueness—vagueness-as-ignorance and vagueness-asindeterminacy—agree on the following principle: if you are certain that it is clearly vague whether p, then you clearly should not believe p and you clearly should not believe not-p. I argue against the principle, and thus against the two standard theories. I offer an explanation of the initial appeal of the principle. And I show how a rival principle helps to better explain a recalcitrant trio of widely accepted data.

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is an inconsistency view on vagueness.

According to one account, vagueness is "metaphysical." The friend of metaphysical vagueness believes that, for some object and some property, there can be no determinate fact of the matter whether that object exemplifies that property. A second account maintains that vagueness is due only to ignorance. According to the epistemic account, vagueness is explained completely by and is nothing over and above our not knowing some relevant fact or facts. These are the minority views. The dominant position maintains that there is a third possible variety of vagueness, linguistic vagueness. And, it goes on to insist, all vagueness is of this third variety. I shall argue, however, that linguistic vagueness is not a third variety of vagueness. Either it is a species of metaphysical vagueness or a kind of ignorance. And this, I argue, makes trouble for the claim that all vagueness is linguistic.

The seminar is intended as an introduction to vagueness. We'll survey some prominent accounts of vagueness, so that people get a sense of what `accounting for vagueness' is all about, and why it's hard.