Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

In this ingenious and powerfully argued book Tim Maudlin sets out a novel account of logic and semantics which allows him to deal with certain notorious paradoxes which have bedevilled philosophical theories of truth. All philosophers interested in logic and language will find this a stimulating read.

An attractive approach to the semantic paradoxes holds that cases of semantic pathology give rise to indeterminacy. What attitude should a rational agent have toward a proposition that it takes to be indeterminate in this sense? Orthodoxy holds that rationality requires that an agent disbelieve such a proposition. I argue that a rational agent should be such that it is indeterminate whether it believes the proposition in question. For rational agents, indeterminacy in the objects of their attitudes will filter up (...) to the attitudes themselves. (shrink)

This volume collects some influential essays in which Simon Blackburn, one of our leading philosophers, explores one of the most profound and fertile of philosophical problems: the way in which our judgments relate to the world. This debate has centered on realism, or the view that what we say is validated by the way things stand in the world, and a variety of oppositions to it. Prominent among the latter are expressive and projective theories, but also a relaxed pluralism that (...) discourages the view that there are substantial issues at stake. The figure of the "quasi-realist" dramatizes the difficulty of conducting these debates. Typically philosophers thinking of themselves as realists will believe that they alone can give a proper or literal account of some of our attachments--to truth, to facts, to the independent world, to knowledge and certainty. The quasi-realist challenge, developed by Blackburn in this volume, is that we can have those attachments without any metaphysic that deserves to be called realism, so that the metaphysical picture that goes with our practices is quite idle. The cases treated here include the theories of value and knowledge, modality, probability, causation, intentionality and rule-following, and explanation. A substantial new introduction has been added, drawing together some of the central themes. The essays articulate a fresh alternative to a primitive realist/anti-realist opposition, and their cumulative effect is to yield a new appreciation of the delicacy of the debate in these central areas. (shrink)

Two opposing tendencies in the philosophy of language go by the names of ‘referentialism’ and ‘inferentialism’ respectively. In the crudest version of the contrast, the referentialist account of meaning gives centre stage to the referential semantics for a language, which is then used to explain the inference rules for the language, perhaps as those which preserve truth on that semantics (since a referential semantics for a language determines the truth-conditions of its sentences). By contrast, the inferentialist account of meaning gives (...) centre stage to the inference rules for the language, which are then used to explain its referential semantics, perhaps as the semantics on which the rules preserve truth. On pain of circularity, we cannot combine both directions of explanation. (shrink)

In addition to thin concepts like the good, the bad and the ugly, our evaluative thought and talk appeals to thick concepts like the lewd and the rude, the selfish and the cruel, the courageous and the kind -- concepts that somehow combine evaluation and non-evaluative description. Thick concepts are almost universally assumed to be inherently evaluative in content, and many philosophers claimed them to have deep and distinctive significance in ethics and metaethics. In this first book-length treatment of thick (...) concepts, Pekka Väyrynen argues that all this is mistaken. Through detailed attention to the language of thick concepts, he defends a novel theory on which the relationship between thick words and evaluation is best explained by general conversational and pragmatic norms. Drawing on general principles in philosophy of language, he argues that many prominent features of thick words and concepts can be explained by general factors that have nothing in particular to do with being evaluative. If evaluation is not essential to the sort of thinking we do with thick concepts, claims for the deep and distinctive significance of the thick are undermined. The Lewd, the Rude and the Nasty is a fresh and innovative treatment of an important topic in moral philosophy and sets a new agenda for future work. It will be essential reading to anyone interested in the analysis and the broader philosophical significance of evaluative and normative language. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

Saul Kripke pointed out that whether or not an utterance gives rise to a liar-like paradox cannot always be determined by checking just its form or content.1 Whether or not Jones’s utterance of ‘Everything Nixon said is true’ is paradoxical depends in part on what Nixon said. Something similar may be said about the sorites paradox. For example, whether or not the predicate ‘are enough grains of coffee for Smith’s purposes’ gives rise to a sorites paradox depends at least in (...) part on what Smith’s purposes are. If Smith’s purpose is to make some coffee to drink, so that he can wake up and start his day, then we would be inclined to accept, and would find it strange to deny the following sorites sentence. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

Consider an object or property a and the predicate F. Then a is vague if there are questions of the form: Is a F? that have no yes-or-no answers. In brief, vague properties and kinds have borderline instances and composite objects have borderline constituents. I'll use the expression "borderline cases" as a covering term for both. ;Having borderline cases is compatible with precision so long as every case is either borderline F, determinately F or determinately not F. Thus, in addition (...) to borderline cases, vagueness requires "fuzzy borders". A has fuzzy borders if there is no sharp line between a's borderline cases, a's determinate cases and a's determinate non-cases. To illustrate, loudness is vague because in a continuum of gradually increasing volume, there is no fact about where the last definite loud noise is and where the first borderline noise is. ;Actual borderline cases are not required for vagueness. Suppose actual noises are either ear-shatteringly loud or silent. Even so, loudness is vague since it could have borderline instances. Just so for objects. Suppose a table is cleanly bounded such that there is a sharp break between the table and its surroundings. Still, that table is vague since there are worlds at which it is indeterminate whether some wood molecule a is, or is not, part of that table. ;There are three views about which things can be vague. On the linguistic view, vagueness is solely a feature of expressions. On the nihilistic view, nothing is vague because vagueness is incoherent. Pitted against these views is the ontological conception of vagueness according to which borderline instances and constituents arise due to genuine indeterminacy in nature. ;My dissertation defends the ontological conception. I argue against the adequacy of the theory's rivals, disarm a damaging objection and demonstrate the causal superiority of vague events. Anyone familiar with the literature on vagueness will notice that only a subset of issues are discussed. What I offer is preliminary--I hope only to make the theory of ontological vagueness attractive enough to merit future work. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from law (...) to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

Sally Haslanger’s ‘What Good Are Our Intuitions? Philosophical Analysis and Social Kinds’ is, among other things, a part of the theoretical underpinning for analyses of race and gender concepts that she discusses far more fully elsewhere. My reply focuses on these analyses of race and gender concepts, exploring the ways in which the theoretical work done in this paper and others can or cannot be used to defend these analyses against certain objections. I argue that the problems faced by Haslanger’s (...) analyses are in some ways less serious, and in some ways more serious, than they may at first appear. Along the way, I suggest that ordinary speakers may not in fact have race and gender concepts and I explore the ramifications of this claim. (shrink)

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

This paper motivates and explores an expressivist theory of vagueness, modelled on Allan Gibbard’s normative expressivism. It shows how Chris Kennedy’s semantics for gradable adjectives can be adjusted to fit into a theory on Gibbardian lines, where assertions constrain not just possible worlds but plans for action. Vagueness, on this account, is literally indecision about where to draw lines. It is argued that the distinctive phenomena of vagueness, such as the intuition of tolerance, can be explained in terms of practical (...) constraints on plans, and that the expressivist view captures what is right about several contending theories of vagueness. (shrink)

This paper investigates the way that linguistic expressions influence vagueness, focusing on the interpretation of the positive (unmarked) form of gradable adjectives. I begin by developing a semantic analysis of the positive form of ‘relative’ gradable adjectives, expanding on previous proposals by further motivating a semantic basis for vagueness and by precisely identifying and characterizing the division of labor between the compositional and contextual aspects of its interpretation. I then introduce a challenge to the analysis from the class of ‘absolute’ (...) gradable adjectives: adjectives that are demonstrably gradable, but which have positive forms that relate objects to maximal or minimal degrees, and do not give rise to vagueness. I argue that the truth conditional difference between relative and absolute adjectives in the positive form stems from the interaction of lexical semantic properties of gradable adjectives—the structure of the scales they use—and a general constraint on interpretive economy that requires truth conditions to be computed on the basis of conventional meaning to the extent possible, allowing for context dependent truth conditions only as a last resort. (shrink)

Theorists analyzing the concepts of race and gender disagree over whether the terms refer to natural kinds, social kinds, or nothing at all. The question arises: what do we mean by the terms? It is usually assumed that ordinary intuitions of native speakers are definitive. However, I argue that contemporary semantic externalism can usefully combine with insights from Foucauldian genealogy to challenge mainstream methods of analysis and lend credibility to social constructionist projects.

Across the humanities and social sciences it has become commonplace for scholars to argue that categories once assumed to be “natural” are in fact “social” or, in the familiar lingo, “socially constructed”. Two common examples of such categories are race and gender, but there many others. One interpretation of this claim is that although it is typically thought that what unifies the instances of such categories is some set of natural or physical properties, instead their unity rests on social features (...) of the items in question. Social constructionists pursuing this strategy—and it is these social constructionists I will be focusing on in this paper—aim to “debunk” the ordinary assumption that the categories are natural, by revealing the more accurate social basis of the classification.2 To avoid confusion, and to resist some of the associations with the term ‘social construction’, I will sometimes use the term ‘socially founded’ for the categories that this sort of constructionist reveals as social rather than natural. (shrink)

It is always awkward when someone asks me informally what I’m working on and I answer that I’m trying to figure out what gender is. For outside a rather narrow segment of the academic world, the term ‘gender’ has come to function as the polite way to talk about the sexes. And one thing people feel pretty confident about is their knowledge of the difference between males and females. Males are those human beings with a range of familiar primary and (...) secondary sex characteristics, most important being the penis; females are those with a different set, most important being the vagina or, perhaps, the uterus. Enough said. Against this background, it isn’t clear what could be the point of an inquiry, especially a philosophical inquiry, into “what gender is”. (shrink)

An original and elegant work of metaethics, this book brings a new clarity and rigor to the discussion of these tangled issues, and will significantly alter the ...

Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...) we reject excluded middle, with special emphasis on the conditional. There is also discussion of higher order indeterminacy (in several different senses) and of penumbral connections; and there is a suggested definition of determinateness in terms of the conditional and a discussion of the extent to which the notion of determinateness is objective. And there are suggestions about a unified treatment of vagueness and the semantic paradoxes. (shrink)

In this collection of previously published essays, Sally Haslanger draws on insights from feminist and critical race theory and on the resources of contemporary analytic philosophy to develop the idea that gender and race are positions ...

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)

Philosophers of language have tended to focus on examples that are not politically significant in any way. We spend a lot of time analyzing natural kind terms: We think hard about “water” and “pain” and “arthritis.” But we don’t think much about the far more politically significant kind terms (natural or social—it's a matter for dispute) like “race,” “sex,” “gender,” “woman,” “man,” “gay,” and “straight.” In this essay, I will try to show, using the example of “woman,” that it's worth (...) thinking about terms like these, for at least three reasons: (1) There are some interesting puzzles. (2) Politically significant terms matter to people's lives— and it's worth spending at least some of our energy thinking about things that matter in this way. (3) Most importantly, interesting methodological issues emerge at the intersection of philosophy of language and politics. (shrink)

In constructing semantic theories of normative and evaluative terms, philosophers have commonly deployed a certain type of disagreement -based argument. The premise of the argument observes the possibility of genuine disagreement between users of a certain normative or evaluative term, while the conclusion of the argument is that, however differently those speakers employ the term, they must mean the same thing by it. After all, if they did not, then they would not really disagree. We argue that in many of (...) the cases in which this argument is deployed, the conclusion not only fails to follow from the premises, but is very likely false. Disagreements between speakers who do not mean the same things by their words are common, genuine, and not easily distinguished from ordinary disagreements over the truth of literally expressed content. We make this case by developing the notion of a metalinguistic negotiation, an exchange in which speakers tacitly negotiate the proper deployment of some linguistic expression in a context. Metalinguistic negotiations express disagreements over information that is conveyed pragmatically and about what concepts should be deployed in the context at hand. We argue that neither of these features poses any obstacle to metalinguistic negotiations serving to express genuine, substantive disagreements that can be well worth engaging in. Contrary to what has been widely assumed in the literature, many normative and evaluative disputes—among ordinary speakers and even among philosophers themselves—may be of exactly this type, a conclusion with important consequences for both the subject matter and the methodology of metanormative theory. (shrink)

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion of degree (...) of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth. (shrink)