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)
This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.
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)
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)
Roy Sorenson offers a unique exploration of an ancient problem: vagueness. Did Buddha become a fat man in one second? Is there a tallest short giraffe? According to Sorenson's epistemicist approach, the answers are yes! Although vagueness abounds in the way the world is divided, Sorenson argues that the divisions are sharp; yet we often do not know where they are. Written in Sorenson'e usual inventive and amusing style, this book offers original insight on language and logic, the (...) way world is, and our understanding of it. (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)
Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive 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 according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of vague (...) terms also vary in the course of conversations and that, in some cases, a competent speaker can go either way without sinning against the meaning of the words or the non-linguistic facts. 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. (shrink)
The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.
Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.
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.
We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the (...) sorites paradox, with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)
The goal of this paper is a comprehensive analysis of basic reasoning patterns that are characteristic of vague predicates. The analysis leads to rigorous reconstructions of the phenomena within formal systems. Two basic features are dealt with. One is tolerance: the insensitivity of predicates to small changes in the objects of predication (a one-increment of a walking distance is a walking distance). The other is the existence of borderline cases. The paper shows why these should be treated as different, though (...) related phenomena. Tolerance is formally reconstructed within a proposed framework of contextual logic, leading to a solution of the Sorites paradox. Borderline-vagueness is reconstructed using certain modality operators; the set-up provides an analysis of higher order vagueness and a derivation of scales of degrees for the property in question. (shrink)
Vague existence can seem like the worst kind of vagueness in the world, or seem to be an entirely unintelligible notion. This bad reputation is based upon the rumour that if there is vague existence then there are non-existent objects. But the rumour is false: the modest brand of vague existence entailed by certain metaphysical theories of composition does not deserve its bad reputation.
In this paper I develop a framework for understanding ontic vagueness. The project of the paper is two-fold. I first outline a definitional account of ontic vagueness – one that I think is an improvement on previous attempts because it remains neutral on other, independent metaphysical issues. I then develop one potential manifestation of that basic definitional structure. This is a more robust (and much less neutral) account which gives a fully classical explication of ontic vagueness via (...) modal concepts. The overarching aim is to systematically investigate the puzzling question of what exactly it could be for the world itself to be vague. (shrink)
In this paper I explore the implications of moral vagueness (viz., the vagueness of moral predicates) for non-naturalist metaethical theories like those recently championed by Shafer-Landau, Parfit, and others. I characterise non-naturalism in terms of its commitment to 7 theses: Cognitivism, Correspondence, Atomism, Objectivism, Supervenience, Non-reductivism, and Rationalism. I start by offering a number of reasons for thinking that moral predicates are vague in the same way in which ‘red’, ‘tall’, and ‘heap’ are said to be. I then (...) argue that the moral non-naturalist seeking to countenance moral vagueness faces a dilemma: are moral properties vague, or perfectly sharp? On either horn of the dilemma, serious problems arise for some of the central tenets of non-naturalism: vague properties seem to threaten Objectivism, Supervenience, and Non-reductivism; on the other hand, sharp properties raise problems for Supervenience and Rationalism. The difficulties on each horn of the dilemma are real, and while they may not be insuperable, they do, at the very least, drastically limit the things non-naturalists can consistently say about moral properties, facts, and reasons. (shrink)
You are morally permitted to save your friend at the expense of a few strangers, but not at the expense of very many. However, there seems no number of strangers that marks a precise upper bound here. Consequently, there are borderline cases of groups at the expense of which you are permitted to save your friend. This essay discusses the question of what explains ethical vagueness like this, arguing that there are interesting metaethical consequences of various explanations.
David Lewis (1986) criticizes moderate views of composition on the grounds that a restriction on composition must be vague, and vague composition leads, via a precisificational theory of vagueness, to an absurd vagueness of existence. I show how to resist this argument. Unlike the usual resistance, however, I do not jettison precisificational views of vagueness. Instead, I blur the connection between composition and existence that Lewis assumes. On the resulting view, in troublesome cases of vague composition, there (...) is an object, which definitely exists, about which it is vague whether the relevant borderline parts compose it. (shrink)
It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a natural interpretation arises that (...) suggests a hypothesis concerning how we can improve the accuracy of aggregate credences. I present empirical results in support of this hypothesis. I also discuss how this modeling interpretation of imprecise probabilities bears upon a philosophical objection that has been raised against them, the so-called inductive learning problem. (shrink)
In this paper we advance a new solution to Quinn’s puzzle of the self-torturer. The solution falls directly out of an application of the principle of instrumental reasoning to what we call “vague projects”, i.e., projects whose completion does not occur at any particular or definite point or moment. The resulting treatment of the puzzle extends our understanding of instrumental rationality to projects and ends that cannot be accommodated by orthodox theories of rational choice.
Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper (...) will be short to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper). (shrink)
Ted Sider has famously argued that existence, in the unrestricted sense of ontology, cannot be vague, as long as vagueness is modeled by means of precisifications. The first section of Chapter 9 exposes some controversial assumptions underlying Sider’s alleged reductio of vague existence. The upshot of the discussion is that, although existence cannot be vague, it can be super-vague, i.e. higher-order vague, for all orders. The second section develops and defends a novel framework, dubbed negative supervaluationary semantics, which makes (...) room for the possibility of super-vague existence. (shrink)
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. (shrink)
In his note "can there be vague objects?" ("analysis", 1978), Gareth evans presents a purported proof that there can be no vague identity statements. Some readers think that evans endorses the proof and its false conclusion. Not so. His point is that those who put vagueness in the world, Rather than in language, Will have no way to fault the proof and no way to escape the false conclusion.
The book is about the problem of vagueness. It begins by discussing some of the existing views on vagueness and then explains why they have not been thought to be satisfactory. It then outlines a new account of vagueness, based on the general idea that vagueness is a global rather than a local phenomenon. In other words, the vagueness of an expression or object is not an intrinsic feature of the object or an expression but (...) a matter of how it relates to other objects and expression. The development of this idea leads to a new semantics and logic for vagueness. The semantics and logic are then applied to a number of issues, including the sorites paradox, the transparency or luminosity of mental states, and personal identity. It is shown that the view allows one to hew to a much more intuitive position on these various issues. (shrink)
Some comparisons are hard. How should we think about such comparisons? According to John Broome, we should think about them in terms of vagueness. But the vagueness account has remained unpopular thus far. Here I try to bolster it by clarifying the notion of comparative vagueness that lies at its heart.
Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for (...) postulating this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)
In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.
According to an old and attractive view, vagueness must be eliminated before semantic notions — truth, implication, and so on — may be applied. This view was accepted by Frege, but is rarely defended nowadays.1 This..
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)
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)
John Broome has argued that incomparability and vagueness cannot coexist in a given betterness order. His argument essentially hinges on an assumption he calls the ‘collapsing principle’. In an earlier article I criticized this principle, but Broome has recently expressed doubts about the cogency of my criticism. Moreover, Cristian Constantinescu has defended Broome’s view from my objection. In this paper, I present further arguments against the collapsing principle, and try to show that Constantinescu’s defence of Broome’s position fails.
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)
I motivate and briefly sketch a linguistic theory of vagueness, on which the notion of indeterminacy is understood in terms of the conventions of language: a sentence is indeterminate iff the conventions of language either forbid asserting it and forbid asserting its negation, under the circumstances, or permit asserting either. I then consider an objection that purports to show that if this theory (or, as far as I can see, any other theory of vagueness that deserved the label (...) "linguistic" were true, there would be no such thing as indeterminacy. I respond to this objection by arguing on independent grounds against its main premise, the widely-accepted claim that if it is indeterminate whether P, no human being knows whether P. I defend an alternative view according to which, when it is indeterminate whether P, it is often also indeterminate whether we know that P. (shrink)
Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this book, first published in 2000, Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main (...) theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics. (shrink)
Words, languages, symphonies, fictional characters, games, and recipes are plausibly abstract artifacts— entities that have no spatial location and that are deliberately brought into existence as a result of creative acts. Many accept that composition is unrestricted: for every plurality of material objects, there is a material object that is the sum of those objects. These two views may seem entirely unrelated. I will argue that the most influential argument against restricted composition—the vagueness argument—doubles as an argument that there (...) can be no abstract artifacts. There is no way to resist the vagueness argument against abstract artifacts that does not also undermine the vagueness argument against restricted composition. (shrink)
Book synopsis: 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. Another striking problem to which vagueness gives rise is the sorites paradox. If you remove one grain from (...) a heap of sand, surely you must be left with a heap. Yet apply this principle repeatedly as you remove grains one by one, and you end up, absurdly, with a solitary grain that counts as a heap. This anthology collects papers in the field. After an 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 current 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)
The paper is divided into two parts, each with subsections. In the first part, I shall discuss some matters that have been extensively examined by Kim, namely what the basic types of supervenience are and how they are pairwise logically related; in the course of this discussion, I shall distinguish a weak from a strong notion of global supervenience. In the second part, I shall examine supervenience in a context in which Kim has not: I shall attempt to solve a (...) puzzle that arises when we consider supervenience relations involving vague properties and/or predicates. This is, of course, not a special case of property/predicate supervenience, but the typical one: for virtually all properties/predicates are vague. The two parts of the paper stand independently of each other. Of the discussion in the first part, essentially all that is presupposed in the second is the notion of “world strong supervenience” defined in section 1 of part I. (shrink)
This chapter explores the implications of moral vagueness for non-naturalist metaethical theories like those recently championed by Shafer-Landau, Parfit, and others. It characterizes non-naturalism in terms of its commitment to seven theses: Cognitivism, Correspondence, Atomism, Objectivism, Supervenience, Non-reductivism, and Rationalism. It starts by offering a number of reasons for thinking that moral predicates are vague in the same way in which “red,” “tall,” and “heap” are said to be. It then argues that the moral non-naturalist seeking to countenance moral (...)vagueness faces a dilemma: are moral properties vague, or perfectly sharp? On either horn of the dilemma, serious problems arise for some of the central tenets of non-naturalism: vague properties seem to threaten Objectivism, Supervenience, and Non-reductivism; on the other hand, sharp properties raise problems for Supervenience and Rationalism. The difficulties on each horn of the dilemma are real, and while they may not be insuperable, they do, at the very least, drastically limit the things non-naturalists can consistently say about moral properties, facts, and reasons. (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)
We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it (...) supports the requisite of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference. (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)
Some have argued that the vagueness exhibited by geographic names and descriptions such as ‘Albuquerque’, ‘the Outback’, or ‘Mount Everest’ is ultimately ontological: these terms are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and hold the view that geographic vagueness is exclusively semantic, or conceptual at large. There is no such thing as a vague mountain. Rather, there are many things where we conceive a mountain to be, each with (...) its precise boundary, and when we say ‘Everest’ we are just being vague as to which thing we are referring to. This paper defends this view against some plausible objections. (shrink)
In psychiatry there is no sharp boundary between the normal and the pathological. Although clear cases abound, it is often indeterminate whether a particular condition does or does not qualify as a mental disorder. For example, definitions of ‘subthreshold disorders’ and of the ‘prodromal stages’ of diseases are notoriously contentious. -/- Philosophers and linguists call concepts that lack sharp boundaries, and thus admit of borderline cases, ‘vague’. Although blurred boundaries between the normal and the pathological are a recurrent theme in (...) many publications concerned with the classification of mental disorders, systematic approaches that take into account philosophical reflections on vagueness are rare. This book provides interdisciplinary discussions about vagueness in psychiatry by bringing together scholars from psychiatry, psychology, philosophy, history, and law. It draws together various lines of inquiry into the nature of gradations between mental health and disease and discusses the individual and societal consequences of dealing with blurred boundaries in medical practice, forensic psychiatry, and beyond. -/- Part I starts with an overview chapter that helps readers to navigate through the philosophy of vagueness and through the various debates surrounding demarcation problems in the classification and diagnosis of mental illness. Part II encompasses historical and recent philosophical positions on gradualist approaches to health and disease. Part III approaches the vagueness of present psychiatric classification systems, and the debates concerning their revisions by scrutinizing controversial categories, such as posttraumatic stress disorder, and the difficulties of day-to-day diagnostic and therapeutic practice. Part IV finally focuses on social, moral, and legal implications that arise when being mentally ill is a matter of degree. (shrink)
Signalling games are popular models for studying the evolution of meaning, but typical approaches do not incorporate vagueness as a feature of successful signalling. Complementing recent like-minded models, we describe an aggregate population-level dynamic that describes a process of imitation of successful behaviour under imprecise perception and realization of similar stimuli. Applying this new dynamic to a generalization of Lewis’s signalling games, we show that stochastic imprecision leads to vague, yet by-and-large efficient signal use, and, moreover, that it unifies (...) evolutionary outcomes and helps avoid sub-optimal categorization. The upshot of this is that we see ‘as-if’-generalization at an aggregate level, without agents actually generalizing. _1_ Introduction _2_ Background _2.1_ Sim-max games and conceptual spaces _2.2_ Vagueness in sim-max games and conceptual spaces _2.3_ Vagueness, functional pressure, and transmission biases _3_ Imprecise Imitation _3.1_ Replicator dynamic in behavioural strategies _3.2_ Noise-perturbed conditional imitation _4_ Exploring Imprecise Imitation _4.1_ Setting the stage _4.2_ Simulation set-up _4.3_ Measures of interest _4.4_ Results _5_ Discussion _5.1_ Levels of vagueness _5.2_ Evolutionary benefits of imprecision _5.3_ Related work _6_ Conclusion Appendix. (shrink)
There are three main traditional accounts of vagueness : one takes it as a genuinely metaphysical phenomenon, one takes it as a phenomenon of ignorance, and one takes it as a linguistic or conceptual phenomenon. In this paper I first very briefly present these views, especially the epistemicist and supervaluationist strategies, and shortly point to some well-known problems that the views carry. I then examine a 'statistical epistemicist' account of vagueness that is designed to avoid precisely these problems (...) – it will be a view that provides an account of the phenomenon of vagueness as coming from our linguistic practices, while insisting that meaning supervenes on use, and that our use of vague terms does yield sharp and precise meanings, which we ignore, thus allowing bivalence to hold. (shrink)
This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in respect of truth. (...) The definition is extended to cover vagueness of many-place predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higher-order vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth. (shrink)