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- Crispin Wright, On the Characterisation of Borderline Cases.It is a great pleasure to have the opportunity to contribute to this volume dedicated to the critical celebration of Stephen Schiffer’s very considerable philosophical achievements. My focus will be on his recent work on vagueness.1 The broad direction of Schiffer’s researches in this area has been to give priority to what we may call the characterisation problem: the problem of saying what the vagueness of expressions of natural language consists in or, more specifically – since Schiffer takes it as a given that the vagueness he is targeting consist in a propensity of vague expressions to give rise to borderline cases —the problem of saying what being a borderline case of the concept expressed by a vague expression consists in. This has not been a main preoccupation of most of the work in the field since the vagueness “boom” started in the mid 1970s. There has been a tendency to jump straight into devising semantic theories for vague languages, usually aimed at twin desiderata of saving classical logic and dissolving the various paradoxes of vagueness, with a principal focus on the standard sorites, and occasional glances at the Forced March, and others.2 Of course, such work has inevitably implicated commitment to broad conceptions of vagueness, and of borderline cases, of various kinds. The classical epistemicist approach, for example, conceives of borderline cases as instances whose correct classification in terms of the relevant concept is, for reasons it attempts to explain, unknowable. Semantic indeterminist approaches, by contrast, tend (often implicitly) to conceive of borderline cases as items to which the concept in question neither applies nor fails to apply and as coming about because our practice with the concept leaves it, in effect, merely partially defined and so ‘gappy’. A variation on this, still semantic indeterminist, regards vagueness as consisting in a phenomenon akin to divided reference, whereby a predicate, for example, may be associated with a range of extensionally distinct best candidates to be the property it refers to; borderline cases are then items which exemplify some but not all of these properties..
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Vagueness: an expression is vague if and only if it is possible that it give rise to a “borderline case.” A borderline case is a situation in which the application of a particular expression to a (name of) a particular object does not generate an expression with a definite TRUTH-VALUE. That is, the piece of language in question neither applies to the object nor fails to apply.
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| | Scholar | More options ... The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as ‘borderline’ and ‘definitely’) introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio , it does not fare substantially better with respect to immunity to any form of sorites paradox.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, informed speakers (‘CRISPs’) whose competence, etc., is indexed to the scope of the unclarity operator. The unclarity is radical since it eliminates clear cases of unclarity and, that is, clear borderline cases. This radical unclarity leads to a (bivalence-compatible, non-intuitionist) absolute agnosticism about the semantic status of all borderline cases. The corresponding modal system would be a non-normal variation on S4M.
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| | Other links: quod.lib.umich.edu | Scholar | At my library | More options ... Vagueness is given a philosophically neutral definition in terms of an epistemic notion of tolerance. Such a notion is intended to capture the thesis that vague terms draw no known boundary across their range of signification and contrasts sharply with the semantic notion of tolerance given by Wright (1975, 1976). This allows us to distinguish vagueness from superficially similar but distinct phenomena such as semantic incompleteness. Two proofs are given which show that vagueness qua epistemic tolerance and vagueness qua borderline cases (when properly construed to exclude terms which are stipulated to give rise to borderline cases) are in fact conceptually equivalent dimensions of vagueness, contrary to what might initially be expected. It is also argued that the common confusion of tolerance and epistemic tolerance has skewed the vagueness debate in favour of indeterminist over epistemic conceptions of vagueness. Clearing up that confusion provides an indirect argument in favour of epistemicism. Finally, given the equation of vagueness with epistemic tolerance, it is shown that there must be radical higher-order vagueness, contrary to what many authors have argued.
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| | Other links: mind.oxfordjournals.org mind.oupjournals.org jstor.org dx.doi.org | Scholar | At my library | More options ... Standardly, one says that vagueness arises whenever a concept or linguistic expression admits of borderline cases of application. A predicate such as ‘bald’, for example, is vague because there can be situations in which it is indeterminate whether or not it applies to (a name of) a certain object. Some people are clearly bald (Picasso), some are clearly not bald (the count of Montecristo), and some are borderline cases—our concept of baldness and our linguistic practices do not specify any exact number of hairs that marks the boundary between the bald and the non-bald. Similarly, a singular term such as ‘Mount Everest’ is vague because there is no determinate way of tracing the geographical limits of its referent. Some rocks are clearly part of Everest and some are clearly not, but some rocks enjoy a borderline status.
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| | Scholar | More options ... It is generally agreed that vague predicates like ‘red’, ‘rich’, ‘tall’, and ‘bald’, have borderline cases of application. For instance, a cloth patch whose color lies midway between a definite red and a definite orange is a borderline case for ‘red’, and an American man five feet eleven inches in height is (arguably) a borderline case for ‘tall’. The proper analysis of borderline cases is a matter of dispute, but most theorists of vagueness agree at least in the thought that borderline cases for vague predicate ‘ ’ are items whose satisfaction of ‘ ’ is in some sense unclear or problematic: it is unclear whether or not the patch is red, unclear whether or not the man is tall.1 For example, Lynda Burns cites a widespread view as holding that borderline cases “are not definitely within the positive or negative extension of the predicate. … Border- line cases are seen as falling within a gap between the cases of definite application of the predicate and cases of definite application of its negation” (1995, 30). Michael Tye writes that the “concept of a border- line case is the concept of a case that is neither definitely in nor defi- nitely out” (1994b, 18).
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| | Other links: philreview.dukejournals.org philosophy.utoronto.ca jstor.org dx.doi.org | Scholar | At my library | More options ... Some philosophers seem to think that borderline cases provide further cases of apparent faultless disagreement. My aim here is to argue against such a suggestion. I claim that with respect to borderline cases, people typically do not respond by taking a view—unlike what is the case in genuine cases of apparent faultless disagreement. I argue that my claim is indeed respected and actually accounted for by paradigm cases of semantic and epistemic views on the nature of vagueness. And I also argue that my claim turns out to be, initial appearances notwithstanding, compatible with other claims in the literature—to the effect that, in appropriate circumstances, there are indeed, or there might well be, “macho,” admissible, forced, and hesitant responses to borderline cases.
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| | Scholar | At my library | More options ... We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition.
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| | Other links: onlinelibrary.wiley.com dx.doi.org doi.wiley.com | Scholar | At my library | More options ... 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 the predicates’ proper application. For example, the predicates ‘mandates application of “old”’ and ‘can competently be called “old”’ are prescriptively higher-order vague. Higher-order vagueness appears in other guises as well,1 but these two have been of particular interest to philosophers and will be my target here. I want to expose some misconceptions about them. If I am right, higher-order vagueness is less prevalent, and less important theoretically, than is usually supposed.2 In what follows I am going to assume that vagueness is a semantic feature of natural language. For the most part I won’t discuss epistemic or pragmatic views, and I will say nothing about so-called metaphysical vagueness.
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| | Other links: philosophy.utoronto.ca | Scholar | At my library | More options ... The Pyrrhonian sceptic Favorinus of Arelata personified indeterminacy, cultivating his (or her) borderline status to undermine dogmatism. Inspired by the techniques of Favorinus, I show, by example, that ‘vague’ has borderline cases. These concrete steps lead to a more abstract argument that ‘vague’ has borderline borderline cases and borderline borderline borderline cases. My specimens are intended supplement earlier non-constructive proofs of the vagueness of ‘vague’.
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| | Other links: mind.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... Discussion of Crispin Wright, On the characterisation of borderline cases
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