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- Crispin Wright (forthcoming). The Illusion of Higher-Order Vagueness. In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press.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 my reading list | Discuss this article | Edit | Categorize |My bibliography
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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. (...)
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| | Other links: mind.oxfordjournals.org jstor.org | Scholar | More.. Higher-order vagueness is widely thought to be a feature of vague predicates that any adequate theory of vagueness must accommodate. It takes a variety of forms. Perhaps the most familiar is the supposed existence, or at least possibility, of higher-order borderline cases—borderline borderline cases, borderline borderline borderline cases, and so forth. A second form of higherorder vagueness, what I will call ‘prescriptive’ higher-order vagueness, is thought to characterize complex predicates constructed from vague predicates by attaching operators having to do with (...)
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 (...)
It is generally supposed that borderline cases account for the tolerance of vague terms, yet cannot themselves be sharply bounded, leading to infinite levels of higher order vagueness. This higher order vagueness subverts any formal effort to make language precise. However, it is possible to show that tolerance must diminish at higher orders. The attempt to derive it from indiscriminability founders on a simple empirical test, and we learn instead that there is no limit to how small higher order tolerance (...)
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 (...)
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| | Other links: interscience.wiley.com | Scholar | More.. Difficulties in arriving at an adequate conception of vagueness have led many writers to describe a phenomenon that has come to be known as "higher-order vagueness". Almost as many have found it to be a problem that needs to be addressed. In what follows I shall argue that, whilst we must acknowledge its presence, it is a pseudo-problem. The crucial point is the vagueness of "vague", which shows the phenomenon to be unproblematic though real enough.
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| | Other links: mind.oxfordjournals.org jstor.org | Scholar | More.. Is higher-order vagueness a real phenomenon? Dominic Hyde (1994) claims that it is, and that it is part and parcel of vagueness itself. According to Hyde, any genuinely vague predicate must also be higher-order vague. His argument for this view is unsound, however. The purpose of this note is to expose the fallacy, and to make some related observations on the vague, the higher-order vague, and the vaguely vague.
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| | Other links: mind.oxfordjournals.org jstor.org | Scholar | More.. In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...)
After a brief account of the problem of higher-order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like ‘borderline red’ and ‘determinately red’ are, or at least can be, vague, but they are different in kind from ‘red’. In particular, ‘borderline red’ and ‘determinately red’ are not colours. These predicates have linguistic components, and invoke notions like ‘competent user of the language’. On my (...)
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| | Other links: interscience.wiley.com | Scholar | More.. A short follow-up to Anna Mahtani’s paper ‘Can Vagueness Cut Out at Any Order?’. I describe a model implementing Mahtani's idea of “variable accessibility ranges” in which, for every n, there is a sentence that is nth-order vague but n+1th-order precise, in the sense of Williamson’s paper ‘On the Structure of Higher-Order Vagueness’.
