In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox. (shrink)

What the Sorites has to tell us is a simple truth regarding our categories. It appears to saddle us with something other than a simple truth—something worse, a contradiction or a problem or a paradox—only when we insist on viewing it through a discrete logic of categories. Discrete categories and discrete logic are for robots. We aren’t robots, and the simple truth is that we don’t handle categories in the way any discrete logic would demand. For us non-robots, what the (...) Sorites has to offer is a straightforward truth regarding how incapable robots and their logic are of handling categories like ours. (shrink)

If there are fundamental laws of nature, can they fail to be exact? In this paper, I consider the possibility that some fundamental laws are vague. I call this phenomenon 'fundamental nomic vagueness.' I characterize fundamental nomic vagueness as the existence of borderline lawful worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as (...) 'vagueness in the world.' For a case study, we turn to the Past Hypothesis, a postulate that (partially) explains the direction of time in our world. We have reasons to take it seriously as a candidate fundamental law of nature. Yet it is vague: it admits borderline (nomologically) possible worlds. An exact version would lead to an untraceable arbitrariness absent in any other fundamental laws. However, the dilemma between fundamental nomic vagueness and untraceable arbitrariness is dissolved in a new quantum theory of time's arrow. (shrink)

‘Puzzles’, ‘word games’, ‘logical anomalies’, whatever we call them, they perplex us and challenge our familiar patterns of reasoning. One of these puzzles, among many others, originated from the mind of an ancient Megarian logician, Eubulides of Miletus, and endures to the modern day.1 Its name, ‘sorites’, can be traced to the Greek word soros, meaning ‘heap.’ The answer to whether one grain of sand ‘is a heap’ or ‘is not a heap’ seems quite simple: it is not a heap. (...) However, as we add grains to the one, at what future point does the non-heap become a heap? Our decision is fraught with uncertainty. Are the objects or the language we are using to describe them vague? In academic philosophy, the ancient Greek puzzle has gained the status of a paradox, as philosophers apply stoic and modern logic to these propositions considered to have vague predicates. The current debate has developed quite serious and wide-ranging implications, such as whether sorites issues provide adequate grounds for abandoning our standard ontology (or our understanding of what really exists), 2 and (germinating into another discipline) whether vagueness in the language of legal rules can generate disagreement as to whether there are right answers to questions of law. 3 Several unique solutions to the paradox have been proposed, yet all suffer from specific inadequacies that might, upon further reflection, disappear in the event that we endeavour to produce a synthesis. When we say that we are attempting to derive a synthesis, we seek to combine elements of two solutions for the sake of creating a new (and hopefully, though not necessarily, a better) one. The paradox of the sorites, or ‘the heap’, appeals to us because it challenges our assumption that we may categorically describe clear cases and their negations, yet fail to distinguish the borderline ones. I will demonstrate that some combinations of solutions are easy fits while others are extremely weak and awkward as attempts at resolving the paradox. Nonetheless, the process of synthesis produces three noteworthy combinations. (shrink)

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, as is (...) then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements. (shrink)

Epistemic two-dimensional semantics, advocated by Chalmers and Jackson, among others, aims to restore the link between necessity and a priority seemingly broken by Kripke, by showing how armchair access to semantic intensions provides a basis for knowledge of necessary a posteriori truths. The most compelling objections to E2D are that, for one or other reason, the requisite intensions are not accessible from the armchair. As we substantiate here, existing versions of E2D are indeed subject to such access-based objections. But, we (...) moreover argue, the difficulty lies not with E2D but with the typically presupposed conceiving-based epistemology of intensions. Freed from that epistemology, and given the right alternative—one where inference to the best explanation provides the operative guide to intensions—E2D can meet access-based objections, and fulfill its promise of restoring the desirable link between necessity and a priority. This result serves as a central application of Biggs and Wilson, according to which abduction is an a priori mode of inference. (shrink)

This paper explores the relationships between Davidson's indeterminacy of interpretation thesis and two semantic properties of sentences that have come to be recognized recently, namely semantic incompleteness and semantic indecision. More specifically, I will examine what the indeterminacy thesis entails for sentences of the form ‘By sentence S, agent A means that m’ and ‘Agent A believes that p.’ My primary goal is to shed light on the indeterminacy thesis and its consequences. I will distinguish two kinds of indeterminacy that (...) have very different sources and very different consequences. But this does not purport to be an exhaustive study: there may well be other forms of indeterminacy that this paper does not address.I will first explain the phenomena of semantic incompleteness and semantic indecision, and then explore their relationships with the indeterminacy thesis. (shrink)

This thesis explores the possibility of composite consciousness: phenomenally conscious states belonging to a composite being in virtue of the consciousness of, and relations among, its parts. We have no trouble accepting that a composite being has physical properties entirely in virtue of the physical properties of, and relations among, its parts. But a long­standing intuition holds that consciousness is different: my consciousness cannot be understood as a complex of interacting component consciousnesses belonging to parts of me. I ask why: (...) what is it about consciousness that makes us think it so different from matter? And should we accept this apparent difference? (shrink)

Neutralism is the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit Fine calls penumbral (...) connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature (...) of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

Does vagueness exclude knowledge? After arguing for an affirmative answer to this question, I consider a fascinating objection. Barnett offers purported counterexamples to the following: Vagueness as to whether p entails that nobody knows whether p. These putative counterexamples, were they successful, would establish that standard accounts of vagueness are mistaken. I defend three central theses: First, whenever it is vague whether p competent speakers would be ambivalent about whether p when considering whether p, and such ambivalence would exclude knowledge (...) of whether p. Second, it is impossible for there to be vagueness regarding which of two polar opposite mental states obtains when only one of such states obtains. Finally, this type of impossibility constitutes evidence for dualism; i.e., the thesis that mental states are neither identical to physical states nor obtain in virtue of the obtaining of physical states. (shrink)

Most words in natural language are vague, that is to say, they lack sharp boundaries and, hence, they have (actual or potential) borderline cases, where the word in question neither definitely applies nor definitely fails to apply. Vagueness gives rise to paradoxes, the best known of which is the sorites (concerned with how many grains of sand are needed to make a heap). Besides offering a solution to such paradoxes, a theory of vagueness should systematically describe how the truth conditions (...) of sentences with vague terms are determined; and it should also define the right logical principles for reasoning with such sentences. This article offers an introduction to the main theories of vagueness and to the problems they have to face. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (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)

As far as ‘modern’ logical theories of vagueness are concerned, a main distinction can be drawn between ‘semantical’ ones and ‘pragmatical’ ones. The latter are defended here, because they tend to retake into account important contextual dimensions of the problem abandoned by the former. Their inchoate condition seems not alarming, since they are of surprisingly recent date. This, however, could very well be an accidental explanation. That is, the true reason for it might sooner or later turn out to be (...) bearing exactly on the fundamental human limitations, when it comes to theorizing, that these approaches are urging us to appreciate. (shrink)

Just about every theorist holds that vague terms are context-sensitive to some extent. What counts as ?tall?, ?rich?, and ?bald? depends on the ambient comparison class, paradigm cases, and/or the like. To take a stock example, a given person might be tall with respect to European entrepreneurs and downright short with respect to professional basketball players. It is also generally agreed that vagueness remains even after comparison class, paradigm cases, etc. are fixed, and so this context sensitivity does not solve (...) the problems with vague terms. In this paper, I briefly sketch the main features of my broadly contextualist account of vagueness, that of the late Ruth Manor, and that of Agustín Rayo, showing how the three accounts relate to, and reinforce, each other, noting a seeming difference. A key item used to articulate my own view is David Lewis's notion of conversational score. This is used to track which borderline cases have been called in the course of a conversation. Manor alludes to Lewis's notion of accommodation, a key aspect of the kinematics of conversation, and Rayo invokes Stalnaker's notion of common ground. I'll show how the conversational score could be employed to develop and extend their views, showing how vague terms, as they construe them, are (or can be) deployed in conversation, consistent with both the underlying indeterminacy of the terms and normal communicative goals. To help develop all three views further, I invoke Craige Roberts's notion of Retrievability, a tool developed to show how definites, such as definite descriptions, singular pronouns, and proper names, are deployed in conversation, in a Lewis-style scorekeeping framework. This, I think, is exactly the right way to understand conversations in what Manor calls non-sorities situations and, to invoke my own view, in sorites situations as well. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

Using a vague predicate can make commitments about the appropriate use of that predicate in the remaining part of the discourse. For instance, if I assert that some particular pig is fat, I am committed to judging any fatter pig to be fat as well. We can model this update effect by recognizing that truth depends both on the state of the world and on the state of the discourse: the truth conditions of ‘This pig is fat’ rule out evaluation (...) points for which the pig in question in world w is thinner than the cutoff for fatness in the discourse d. Then disagreements about taste are disagreements about the discourse. Unlike disagreements about the world, disagreements about the discourse can be faultless, given that none of the discourse participants has privileged authority to make pronouncements about conventions for appropriate use of a predicate. Thus on the dynamic view developed here, whether or not a dispute about taste turns out to be faultless depends in part on predictable features of the previous discourse. On this account, faultless disagreement involving predicates of personal taste does not force relativizing truth to a judge or assessor. (shrink)

During the last couple of decades, several attempts have been made to come up with a theory that can handle the various semantic, logical and philosophical problems raised by the vagueness of natural languages. One of the most influential ideas that have come into fashion in recent years is the idea that vagueness should be analysed as a form of context sensitivity. Such contextualist theories of vagueness have gained some popularity, but many philosophers have remained sceptical of the prospects of (...) finding a tenable contextualist solution to the problems of vagueness. This paper provides an introduction to the most popular contextualist accounts, and a discussion of some of the most important arguments for and against them. (shrink)

Several psychological experiments have suggested that concepts can influence perceived color (e.g., Delk and Fillenbaum in Am J Psychol 78(2):290–293, 1965, Hansen et al. in Nat Neurosci 9(11):1367–1368, 2006, Olkkonen et al. in J Vis 8(5):1–16, 2008). Observers tend to assign typical colors to objects even when the objects do not have those colors. Recently, these findings were used to argue that perceptual experience is cognitively penetrable (Macpherson 2012). This interpretation of the experiments has far-reaching consequences: it implies that the (...) way we think of objects determines how we see them, thus threatening the role of perception in justifying beliefs. In this paper, I show that the psychological findings can be accounted for without admitting cognitive penetrability. An underestimated but key feature of the experiments is that observers had to judge colors in borderline cases, in conditions of reduced acuity, or on the basis of color-concepts instead of matching. Such judgments are sensitive to the form of bias that Tversky and Kahneman (Science 185:1124–1131, 1974) have termed ‘anchoring’. Adopting a suggestion from Raffman (Philos Rev 103(1):41–74, 1994), I argue that the way subjects in the experiments think of the objects could affect their color judgments without altering their color experiences. (shrink)

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 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. (shrink)

Taking a series of colour patches, starting with one that clearly looks red, and making each so similar in colour to the previous one that it looks the same as it, we appear to be able to show that a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they do not need such a solution, nor (...) do they succumb to one. In particular, I reject the claim made by Fara and Raffman that looks the same is a transitive relation, which would allow us to solve phenomenal sorites paradoxes by denying the possibility of the required kind of sorites series. (shrink)

An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ 'only microscopically'. We formulate the classificatory sorites on arguably the (...) highest possible level of generality and show that the 'paradox' is dissolved on grounds unrelated to vague predicates or other linguistic issues traditionally associated with it. If stimulus effects are properly defined (i.e., they are uniquely determined by stimuli), and if the space of the stimuli is endowed with appropriate (not necessarily metric) closeness and connectedness properties, then this space must contain points in every vicinity of which, 'however small', the stimulus effect is not constant. The effects can only be 'tolerant' to very small differences between stimuli if the closeness structure that is used to define very close stimuli does not render the space of stimuli appropriately connected: in this case the 'paradox' cannot be formulated. Nor can it be formulated if the response properties considered are not true effects, i.e., if they do not supervene on stimuli. (shrink)

For almost twenty years, Penelope Maddy has been one of the most consistent expositors and advocates of naturalism in philosophy, with a special focus on the philosophy of mathematics, set theory in particular. Over that period, however, the term ‘naturalism’ has come to mean many things. Although some take it to be a rejection of the possibility of a priori knowledge, there are philosophers calling themselves ‘naturalists’ who willingly embrace and practice an a priori methodology, not a whole lot different (...) from traditional conceptual analysis. Along a different line, some take naturalism to involve the rejection of abstract objects—a sort of physicalism—while other naturalists not only allow the existence of abstracta; they take this existence to be all but obvious.For present purposes, we can begin with W.V.O. Quine, who once characterized naturalism as ‘the abandonment of the goal of first philosophy’ and ‘the recognition that it is within science itself …that reality is to be identified and described’. For Quine, the ‘naturalistic philosopher begins his reasoning within the inherited world theory as a going concern …[The] inherited world theory is primarily a scientific one, the current product of the scientific enterprise’ [Quine, 1981, p. 72]. This characterizes at least the bulk of contemporary philosophers who call themselves ‘naturalists’, and it characterizes the targets of many who oppose what they call ‘naturalism’. But as Maddy notes at the start, ‘the term has come to mark little more than a vague science-friendliness’.An attempt to define naturalism more fully would surely require a characterization of science—at least so that the reader can see when someone sins against that naturalism by being unscientific. But, as Maddy notes, one ‘lesson won through decades of study in the philosophy of science [is that] there is no …. (shrink)

Contextualism about vagueness (hereafter ‘Contextualism’) is the view that vagueness consists in a particular species of context-sensitivity and that properly accommodating this fact into our semantic theory will yield a plausible solution to the sorites paradox.[1],[2] But Contextualism, as many commentators have noted, faces the following immediate objection: if we hold the context fixed, vagueness still remains, therefore vagueness is not a species of context-sensitivity. Call this ‘the simple objection’.[3] Absent a convincing reply to the simple objection, Contextualism is in (...) very bad shape. Oddly enough, defenders of Contextualism have said very little in reply. Proponents of the objection have tended to assume that this is because no reply is in the offing—the simple objection is taken to be unassailable. In this short paper, we sketch two replies to the simple objection which result in two very different kinds of Contextualism: Epistemicist Contextualism and Radical Contextualism. With these two theories in hand, the simple objection loses its force. (shrink)

I examine the radical contextualists’ two main arguments for the semantic underdeterminacy thesis, according to which all, or almost all, English sentences lack context-independent truth conditions. I show that both arguments are fallacious. The first argument, which I call the fallacy of the many understandings , mistakenly infers that a sentence S is semantically incomplete from the fact that S can be used to mean different things in different contexts. The second argument, which I call the open texture fallacy , (...) wrongly concludes that a sentence S lacks context-independent truth conditions from the fact that there are circumstances in which the truth value of S would be indeterminate. I do however defend the claim that a certain class of sentences not containing any indexicals do lack context-independent truth conditions, and put forward an argument to that effect. But this argument, as I show, does not generalize to all sentences, and thus fails to support the semantic underdeterminacy thesis. (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

This is an encyclopedia entry on vagueness, focusing mainly on the opposition between re re and de dicta (linguistic or cognitive) accounts.

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 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)

Precautionary principles are frequently appealed to both in public policy and in discussions of individual decision-making. They prescribe omission or reduction of an activity, or taking precautionary measures whenever potential harmful effects of the activity surpass some threshold of likelihood and severity. One crucial appeal of precautionary principles has been that they seem to help guard against procrastinating on confronting certain kinds of risk. I raise a challenge for precautionary principles serving as effective action-guiding tools to guard against (policy) inaction, (...) procrastination, or recklessness. Since risks that are sufficiently harmful and sufficiently likely to fulfil the antecedent of a precautionary principle typically accumulate over time, precautionary principles are only effective if they constrain an agent’s decision-making over time. On the basis of this observation, I argue for two claims. First, to yield the verdicts proponents of precautionary principles would like to make, precautionary principles must be understood to be diachronic principles, which requires some added structure to how they are commonly formulated. Second, such diachronic precautionary principles invite policy procrastination and inaction in their own right, due to both the vagueness of thresholds, and because agents will often fail to abide by the principles if they ignore bygone risks. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

In Replacing Truth, Scharp takes the concept of truth to be fundamentally incoherent. As such, Scharp reckons it to be unsuited for systematic philosophical theorising and in need of replacement – at least for regions of thought and talk which permit liar sentences and their ilk to be formulated. This replacement methodology is radical because it not only recommends that the concept of truth be replaced, but that the word ‘true’ be replaced too. Only Tarski has attempted anything like it (...) before. I dub such a view Conceptual Marxism. In assessing this view, my goals are fourfold: to summarise the many components of Scharp’s theory of truth; to highlight what I take to be some of the excess baggage carried by the view; to assess whether, and to what extent, the extreme methodology on offer is at all called for; finally, to briefly propose a less radical replacement strategy for resolving the liar paradox. (shrink)

Inspired by Castañeda, Perry and Lewis argued that, among singular thoughts in general, thoughts about oneself ‘as oneself’ – first-personal thoughts, which Lewis aptly called de se – call for special treatment: we need to abandon one of two traditional assumptions on the contents needed to provide rationalizing explanations, their shareability or their absoluteness. Their arguments have been very influential; one might take them as establishing a new ‘effect’ – new philosophical evidence in need of being accounted for. This is (...) questioned by the skeptical arguments in recent work by Cappelen & Dever and Magidor, along lines that a few discrepant voices had already announced earlier. Skeptics content that the evidence does not really call for revising traditional theories of content. I will discuss their challenges – first and foremost, concerning action explanations – aiming to make the case that the ‘De Se effect’ is no illusion: de se attitudes require us to revise one of the two tenets of traditional views. (shrink)

Causal contextualism holds that sentences of the form ‘c causes e’ have context-sensitive truth-conditions. We consider four arguments invoked by Jonathan Schaffer in favor of this view. First, he argues that his brand of contextualism helps solve puzzles about transitivity. Second, he contends that how one describes the relata of the causal relation sometimes affects the truth of one’s claim. Third, Schaffer invokes the phenomenon of contrastive focus to conclude that causal statements implicitly designate salient alternatives to the cause and (...) effect. Fourth, he claims that the appropriateness of a causal statement depends on what is contextually taken for granted or made salient. We show that causal invariantism can explain these linguistic data at least as well as contextualism. We then argue that pace Schaffer, some causal sentences are always correct and can never be plausibly denied, regardless of the context. (shrink)

A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...) the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision. (shrink)

The aim of this essay is to argue that, if a robust form of moral realism is true, then moral vagueness is ontic vagueness. The argument is by elimination: I show that neither semantic nor epistemic approaches to moral vagueness are satisfactory.

The puzzle of the self-torturer raises intriguing questions concerning rationality, cyclic preferences, and resoluteness. Interestingly, what makes the case puzzling has not been clearly pinpointed. The puzzle, it seems, is that a series of rational choices foreseeably leads the self-torturer to an option that serves his preferences worse than the one with which he started. But this is a very misleading way of casting the puzzle. I pinpoint the real puzzle of the self-torturer and, in the process, reveal a neglected (...) but crucial dimension of instrumental rationality. (shrink)

Vagueness is understood as the problem of associating imprecise application criteria with ordinary predicates such as ‘bald’ or ‘blue’. It is often construed as due to one’s tolerance to a minute difference in forming a verdict on the application of a vague predicate. This paper reports an experiment conducted to test the effect of tolerance, using as paradigm categorisation tasks performed with respect to transitional series, e.g., a series of tomatoes from red to orange. The findings suggest a negative effect (...) of tolerance on categorisation with vague predicates. The implication of the findings for certain commonly-held assumptions about tolerance is discussed. (shrink)

Agent relativists about vagueness (henceforth ‘agent relativists’) hold that whether or not an object x falls in the extension of a vague predicate ‘P’ at a time t depends on the judgemental dispositions of a particular competent agent at t. My aim in this paper is to critically examine arguments that purport to support agent relativism by appealing to data from forced-march Sorites experiments. The most simple and direct versions of such forced-march Sorites arguments rest on the following (implicit) premise: (...) If competent speakers' judgements vary in a certain way, then the extensions of ‘P’ as used by these speakers must vary in the same way. This premise is in need of independent support, since otherwise opponents of agent relativism can simply reject it. In this paper, I focus on the idea that one cannot plausibly reject this premise, as that would commit one to implausible claims about linguistic competence. Against this, I argue that one can accommodate the data from forced-march Sorites experiments in a way that is compatible with a plausible picture of linguistic competence, without going agent relativist. Thus, there is reason to be sceptical of the idea that such data paired with considerations about linguistic competence can be invoked in order to lend any solid support to agent relativism. Forced-march Sorites arguments of this kind can, and should be, resisted. (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)

According to anti-atomism, we represent color properties (e.g., red) in virtue of representing color relations (e.g., redder than). I motivate anti-atomism with a puzzle involving a series of pairwise indistinguishable chips. I then develop two versions of anti-atomism.

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)