I can say that a building is tall and you can understand me, even if neither of us has any clear idea exactly how tall a building must be in order to count as tall. This mundane fact poses a problem for the view that successful communication consists in the hearer’s recognition of the proposition a speaker intends to assert. The problem cannot be solved by the epistemicist’s usual appeal to anti-individualism, because the extensions of vague words like ‘tall’ are (...) contextually fluid and can be constrained significantly by speakers’ intentions. The problem can be seen as a special case of a more general problem concerning what King has called “felicitous underspecification.” Traditional theories of vagueness offer nothing that can help with this problem. Appeals to diagonalization do not help either. A more radical solution is needed. (shrink)

This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued (...) that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories. (shrink)

Paraconsistent responses to vagueness are often thought to represent a revision of logical theory that is too radical to be defensible. The paracomplete logic of supervaluationism, SpV, is not only taken to be more conservative but is also commonly said to 'preserve classical logic'. This chapter argues that this is wrong on both counts. The paraconsistent logic SbV, or subvaluationism, is no less conservative than SpV nor more so. In the end both logics offer equally compelling theoretical approaches to (...) vagueness. Each approach is also equally objectionable, with neither providing an adequate account of vagueness, but this criticism arises from a feature shared by each approach that is independent of their paracompleteness or paraconsistency per se. For all that has been said, a paraconsistent approach, and the associated recourse to truth-value gluts, remains a contender in accounting for vagueness. (shrink)

Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of (...) vagueness and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)

This paper consists of two parts. The first concerns the logic of vagueness. The second concerns a prominent debate in metaphysics. One of the most widely accepted principles governing the ‘definitely’ operator is the principle of Distribution: if ‘p’ and ‘if p then q’ are both definite, then so is ‘q’. I argue however, that epistemicists about vagueness should reject this principle. The discussion also helps to shed light on the elusive question of what, on this framework, it (...) takes for a sentence to be borderline or definite. In the second part of the paper, I apply this result to a prominent debate in metaphysics. One of the most influential arguments in favour of Universalism about composition is the Lewis-Sider argument from vagueness. An interesting question, however, is whether epistemicists have any particular reasons to resist the argument. I show that there is no obvious reason why epistemicists should resist the argument but there is a non-obvious one: the rejection of Distribution argued for in the first part of the paper provides epistemicists with a unique way of resisting the argument from vagueness. (shrink)

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. (shrink)

This paper addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalised, contributes towards the solution of the other two. The key to this response is a generalised conception of indeterminacy as a specific kind of intellectual bafflement-Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as (...) liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, e.g., matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight. (shrink)

Rampant non-factualism is the view that all non-fundamental matters are non-factual, in a sense inspired by Kit Fine (2001). The first half of this paper argues that if we take non-factualism seriously for any matters, such as morality, then we should take rampant non-factualism seriously. The second half of the paper argues that rampant non-factualism makes possible an attractive theory of vagueness. We can give non-factualist accounts of non-fundamental matters that nicely characterize the vagueness they manifest (if any). (...) I suggest that such non-factualist theories dissolve philosophical puzzlement about vagueness. In particular, the approach implies that philosophers should not try to say which of the sorites-paradox-forming claims are true; we should not try to solve the sorites paradox in that sense. (shrink)

I aim to develop a tool for comparing theories of vagueness, using Structured Query Language. Relevant SQL snippets will be used throughout.

One of the most influential arguments in favour of perdurantism is the Argument from Vagueness. The argument proceeds in three stages: The first aims to establish atemporal universalism. The second presents a parallel argument in favour of universalism in the context of temporalized parthood. The third argues that diachronic universalism entails perdurantism. I offer a novel objection to the argument. I show that on the correct way of formulating diachronic universalism the principle does not entail perdurantism. On the other (...) hand, if diachronic universalism is formulated as Sider proposes, the argument fails to establish his principle, and thus perdurantism. (shrink)

We are grateful to Paul S. Appelbaum and Wayne Martin for their thoughtful remarks on our paper. Among the various aspects that we might address and refute in return, we have decided to focus on just two issues that we believe have potential to advance the debate. According to Appelbaum, the “assessment of an intuitive process is being predicated on a patient having the ability to reflect on determinants of which he may be completely unaware.” In this passage, he points (...) to an apparently “self-evident paradox.” Also, Martin is skeptical about the assessment of intuitive reasoning ability. We agree that relying entirely on unarticulated gut feelings is problematic in terms of... (shrink)

There are several different forms of comparability involving prudential values. Comparisons of values in the abstract, of realizations of some value, and of options which realize values, are distinct, and related, though not mutually exclusive. Furthermore, if rough equality is thought of as an evaluative relation in terms of which comparisons can be made, it does not imply incomparability. If it involves epistemic vagueness, this does not imply incomparability, since our not knowing which relation holds does not imply that (...) no relation holds. Finally, if it is true to some degree that some relation holds, there may be some fuzzy ordering. Given that we may not be able coherently to talk about degrees of truth, I propose an open-ended comparability condition, which takes account of rough equality, epistemic vagueness and fuzziness. (shrink)

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. (shrink)

Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms -- such as 'tall', 'red', 'bald', and 'tadpole' -- have borderline cases ; and they lack well-defined extensions. The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate.This anthology collects for the first time the most important papers in the field. After a substantial introduction (...) that surveys the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent the best recent work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity. (shrink)

Think of the color spectrum, spread out before you. You can identify the different colors with ease. But if you are asked to indicate the point at which one color ends and the next begins, you are at a loss. "There is no such point", is a natural thought: one color just shades gradually into the next.

Derek Parfit’s mere addition paradox has generated a large literature. This paper articulates one response to this paradox - which Parfit hirnself suggested - in terms of a formal account of the relation of parity. I term this response the ‘parity view’. It is consistent with transitivity of ‘at least as good as’, but implies incompleteness of this relation. The parity view is compatible with critical-band utilitarianism if this is adjusted to allow for vagueness. John Broome argues against accounts (...) which involve incompleteness. He thinks they are based on an intuition of ‘neutrality’, which is most naturally understood in terms of equality. There is no rationale, on Broome’s view, for seeing it as ‘incommensurateness’ which leads to incompleteness. Parity provides one. Broome’s worries that ‘incommensurateness’ makes neutrality implausibly ‘greedy’, and that ‘incommensurateness’ and vagueness are incompatible do not constitute a knock-down case against the parity view. Similar worries arise for his preferred vagueness view. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We (...) will show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)