In recent literature on vagueness, writers have noted that more ‘plentiful’ theories of properties – those that postulate genuine properties corresponding to the classically vague predicates like ‘bald’ and ‘heap’ – appear straightforwardly committed to ontic vagueness. In this paper, however, I will argue that worries of ontic vagueness are not specific to ‘plentiful’ accounts of properties. The classically ‘sparse’ theories of properties – Universals and tropes – will, I contend, be subject to similar difficulties.

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

The standard definition of vagueness is in terms of borderline cases. But what is a borderline case? The obvious answer is that a borderline case is one which neither falls under the predicate in question nor does not fall under the predicate. One problem with this definition is that it presupposes that borderline cases involve gaps and not gluts. A definition of vagueness should not prejudice the question of how best to deal with it, and yet the standard definition rules (...) out a paraconsistent approach to vagueness right from the start (such an approach insists that vagueness involves gluts not gaps). In this paper, we explore some of the ways in which vagueness might be spelled out and consider problems for each of them. In the end, we propose a non-question begging definition of vagueness and discuss some of the advantages and shortcomings of this alternative. (shrink)

In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution.

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is (...) an inconsistency view on vagueness. (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)

By offering the statement, "the truth or truths we accept determine what our lives are and will be," the authors of this volume explore the contemporary world and all of its contradictions, from starvation, AIDS, and illiteracy to digital technology, the human genome project, and the financial markets of Wall Street and Tokyo. This engaging, accessible text examines the truth propounded by a range of philosophies, such as critical theory, existentialism, feminism, and nihilism, discussing their practical applications and offering responses (...) to the questions asked. (shrink)

Our concept of truth is governed by two principles. The.

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 timely book 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)

The present offers a pragmatic solution of the Heap Paradox, based on the idea that vague predicates are “indexical” in the sense that their denotation does not only depend on the context of their use, but it is a function of the context. The analysis is based on the following three claims. The borderlines of vague terms are undetermined in the sense that though they may be determined in some contexts, they may differ from one context to the next. Vagueness (...) serves the important communicative function, enabling speakers to identify entities as objects (as things we can talk about) in terms of some quantitative differences between the “object” and its background in the context. Thus, in some contexts we can naturally partition the group of men uniquely so as to distinguish the bald from the not-bald. Whether a man with a given hair number is among the bald in a given context depends not only on his own hair number but also on the hair number of others in that context. This provides the background for the claim that when we assert that John is bald, we presuppose that there is a unique demarcation to the bald in that context. I consider the truth of the Paradox’s statements in contexts where the presupposition is true and in contexts where it is false. The analysis yields that the contradiction is avoided because though each of the statements is often true, never are all the sentences in the Paradox true together. (shrink)

I argue that both demonstratives and vague predicates are instances of some more general linguistic phenomena, which could take quite different forms. My argument consists in constructing three natural-like langauges, and using their intelligibility to argue for conclusions about languages such as English.

I argue for an account of vagueness according to which the root of vagueness lies not in the type of semantic-value that is best associated with an expression, but in the type of linguistic practice that renders the expression meaningful. I suggest, in particular, that conventions about how to use sentences involving attributions of vague predicates to borderline cases prevail to a lesser degree than conventions about how to use sentences involving attributions of vague predicates to clear cases.

In ‘Something to Do with Vagueness ...’, Linda Burns defends an analogy between the informational and the borderline-case variety of vagueness. She argues that the latter is in fact less extraordinary and less disastrous than people in the tradition of Michael Dummett and Crispin Wright have told us. However, her account involves presuppositions that cannot be taken for granted. Here is to take a closer look at some of these presuppositions and argue hat they may--when left unguarded--undermine much of Burns’ (...) general account. (shrink)

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)

On the epistemic view of vagueness, a vague expression has sharp boundaries whose location speakers of the language cannot recognize. The paper argues that one of the deepest sources of resistance to the epistemic view is the idea that all truths are cognitively accessible from truths in a language for natural science, conceived as precise, in a sense explained. The implications of the epistemic view for issues about the relations between vague predicates and scientific predicates are investigated.

It is a great pleasure to have the opportunity to contribute to this volume dedicated to the critical celebration of Stephen Schiffer’s very considerable philosophical achievements. My focus will be on his recent work on vagueness.1 The broad direction of Schiffer’s researches in this area has been to give priority to what we may call the characterisation problem: the problem of saying what the vagueness of expressions of natural language consists in or, more specifically – since Schiffer takes it as (...) a given that the vagueness he is targeting consist in a propensity of vague expressions to give rise to borderline cases —the problem of saying what being a borderline case of the concept expressed by a vague expression consists in. This has not been a main preoccupation of most of the work in the field since the vagueness “boom” started in the mid 1970s. There has been a tendency to jump straight into devising semantic theories for vague languages, usually aimed at twin desiderata of saving classical logic and dissolving the various paradoxes of vagueness, with a principal focus on the standard sorites, and occasional glances at the Forced March, and others.2 Of course, such work has inevitably implicated commitment to broad conceptions of vagueness, and of borderline cases, of various kinds. The classical epistemicist approach, for example, conceives of borderline cases as instances whose correct classification in terms of the relevant concept is, for reasons it attempts to explain, unknowable. Semantic indeterminist approaches, by contrast, tend (often implicitly) to conceive of borderline cases as items to which the concept in question neither applies nor fails to apply and as coming about because our practice with the concept leaves it, in effect, merely partially defined and so ‘gappy’. A variation on this, still semantic indeterminist, regards vagueness as consisting in a phenomenon akin to divided reference, whereby a predicate, for example, may be associated with a range of extensionally distinct best candidates to be the property it refers to; borderline cases are then items which exemplify some but not all of these properties.. (shrink)

There is now a widespread accord among philosophers that the vagueness of natural language gives rise to some particularly deep and perplexing problems and paradoxes. It was not always so. For most of the first century of analytical philosophy, vagueness was generally regarded as a marginal, slightly irritating phenomenon, —receiving some attention, to be sure, in parts of the Philosophical Investigations and in the amateur linguistics enjoyed by philosophers in Oxford in the 1950s, but best idealised away in any serious (...) theoretical treatment of meaning, understanding and valid inference. Frege, as is well known, had come to be thoroughly mistrustful of vagueness, supposing that a language fit for the purpose of articulating scientific and mathematical knowledge would have to be purified of it. Later trends in philosophical logic and semantics followed his lead, not indeed in setting about the (futile) task of expurgating vagueness from natural language but by largely restricting theoretical attention to artificial languages in whose workings vagueness was assigned no role. (shrink)

The reason, according to the contextualist, that precise boundaries for expressions like ‘heap’ or ‘tall for a basketball player’ are so difficult to detect is that when two entities are sufficiently similar (or saliently similar), we tend to shift the interpretation of the vague expression so that if one counts as falling in the extension of the property expressed by that expression, so does the other. As a conse- quence, when we look for the boundary of the extension of a (...) vague expression in its penumbra, our very looking has the effect of chang- ing the interpretation of the vague expression so that the boundary is not where we are looking. This accounts for the persuasive force of sorites arguments. (Stanley 2003: 269). (shrink)

According to the view I christen sharpism, when Joe says to his daughter in a perfectly ordinary context ‘The Earth is super-duper old’, his claim has an incredibly discriminating truth condition: although it’s true if the Earth is over 347,342,343 years, 2 days, and 17 nanoseconds old, if the Earth is even a nanosecond younger then his claim has some status other than “just plain true”—but we leave open what that new status might be: false, indeterminate, indeterminately indeterminate, meaningless, just (...) under 100% true, or whatnot. The material point is that the claim changes in truth status (“alethic status”) with a nanosecond change in the Earth’s age. The sharp cutoff might not be a cutoff separating the true from the false, but it is a sharp alethic cutoff nonetheless. It has this sensitive truth condition even though Joe has never made any relevant linguistic stipulations and doesn’t even know what a nanosecond is. Another example: when I say to a visiting speaker, ‘The auditorium where you’ll give your lecture is a short walk from here’, my claim is true if the auditorium is no more than 123 meters, 6 centimeters, and 16 nanometers away. Hence, if it turns out that we were 123 meters, 6 centimeters, and 17 nanometers away from the auditorium, my claim had some status other than true. (shrink)

Jason Stanley has criticized a contextualist solution to the sorites paradox that treats vagueness as a kind of indexicality. His objection rests on a feature of indexicals that seems plausible: that their reference remains fixed in verb phrase ellipsis. But the force of Stanley’s criticism depends on the undefended assumption that vague terms, if they are a special sort of indexical, must function in the same way that more paradigmatic indexicals do. This paper argues that there can be more than (...) one sort of indexicality, that one term might easily have both sorts, and that therefore, and despite Stanley’s worries, vagueness might easily be assimilated to one form. (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)

Contextualism concerning vagueness (hereafter ‘CV’) is a popular response to the puzzle of vagueness.[1] The goal in this paper is to uncover in what ways vagueness may be a particular species of context-sensitivity. The most promising form of CV turns out to be a version of socalled ‘Non-Indexical Contextualism’.[2] In §2, we sketch a generic form of CV (hereafter ‘GCV’). In §3, we distinguish between Truth CV and Content CV. A non-indexical form of CV is a form of Truth CV, (...) while an indexical form of CV is a form of Content CV. In §4, we argue that the theory of vagueness given in Fara (2000) is crucially incomplete but is best seen as a non-indexical form of CV. In §5, we set forth four kinds of error-theory to which CV might be committed. It turns out that Non-Indexical CV is committed to a weaker, and more plausible, error-theory than Indexical CV. In §6, we address a challenge posed by Keefe (2007) to the effect that CV entails that any speech report of what has been said by a particular vague utterance, where the context of utterance and the reporting context are relevantly different, will almost always be inaccurate. While this challenge is prima facie effective against Indexical CV it proves to be less effective against Non-Indexical CV. In §7, we look at two tests for context-sensitivity and assess whether they can be employed against CV. These tests, if cogent, reveal that the only workable form of CV is Non-Indexical CV. (shrink)

In this paper I offer a critique of the recent popular strategy of giving a contextualist account of vagueness. Such accounts maintain that truth-values of vague sentences can change with changes of context induced by confronting different entities (e.g. different pairs through a sorites series). I claim that appealing to context does not help in solving the sorites paradox, nor does it give us new insights into vagueness per se. Furthermore, the contextual variation to which the contextualist is committed is (...) problematic in various ways. For example, it yields the consequence that much of our everyday (non-soritical) reasoning is fallacious, and it renders us ignorant of what we and others have said. (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)

After a brief account of the problem of higher-order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like ‘borderline red’ and ‘determinately red’ are, or at least can be, vague, but they are different in kind from ‘red’. In particular, ‘borderline red’ and ‘determinately red’ are not colours. These predicates have linguistic components, and invoke notions like ‘competent user of the language’. On my (...) view, so-called ‘higher-order vagueness’ is actually ordinary, first-order vagueness in different predicates. I explore the possibility that, nevertheless, a pernicious regress ensues. (shrink)

In this book, Scott Soames illuminates the notion of truth and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part I addresses crucial background issues, including the identification of the bearers of truth, the basis for distinguishing truth from other notions (like certainty, with which it is often confused), and the formulation of positive responses to well-known forms of philosophical skepticism about truth. Part II explicates the formal theories of Alfred (...) Tarski and Saul Kripke, including their treatments of the Liar paradox, and evaluates the philosophical significance of their work. Part III extends important lessons drawn from Tarski and Kripke into new domains: vague predicates, the Sorites paradox, and the development of a larger, deflationary perspective on truth. Soames aims to integrate and deepen the most significant insights on truth from a variety of sources. He powerfully brings together the best technical work an the most important philosophical reflection on truth and shows how each can illuminate the other. (shrink)

One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...) objection by viewing formalization as a process of building models, not providing descriptions. When we are constructing models, as opposed to accurate descriptions, we often include in the model extra ‘machinery’ of some sort in order to facilitate our manipulation of the model. In other words, while some parts of a model accurately represent actual aspects of the phenomenon being modelled, other parts might be merely artefacts of the particular model. With this distinction in place, the criticisms of Sainsbury and Tye are easily dealt with—the precision of the semantics is artefactual and does not represent any real precision in vague discourse. Although this solution to this problem is independent of any particular semantics a detailed account of how we would distinguish between representor and artefact within Dorothy Edgington's degree-theoretic semantics is presented. (shrink)

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

Degree theories of vagueness build on the observation that vague predicates such as 'tall' and 'red' come in degrees. They employ an infinite-valued logic, where the truth values correspond to degrees of truth and are typically represented by the real numbers in the interval [0,1]. In this paper, the success with which the numerical assignments of such theories can capture the phenomenon of vagueness is assessed by drawing an analogy with the measurement of various physical quantities using real numbers. I (...) argue that degree theories of vagueness are undermined by the failure of the necessary connectedness principle. Moreover, the semantics for the connectives entail that there must be a uniquely correct numerical assignment for the sentences, and this is implausible. Different senses of 'coming in degrees' are then distinguished; I argue that a confusion between them could be the source of the degree theorist's error, and the distinction illuminates the problem cases described earlier in the paper. (shrink)

It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting a (...) many-valued semantics even if one accepts a form of epistemicism. The resulting hybrid view has advantages over both classical epistemicism and traditional many-valued approaches. (shrink)

If there are vague numbers, it would be easier to use numbers as semantic values in a treatment of vagueness while avoiding precise cut-off points. When we assign a particular statement a range of values (less than 1 and greater than 0) there is no precise sharp cut-off point that locates the greatest lower bound or the least upper bound of the interval, I should like to say. Is this possible? “Vague Numbers” stands for awareness of the problem. I do (...) not present a serious theory of vague numbers. I sketch some reasons for using a many-value semantics. These reasons refer to my earlier treatments of determinacy and definitions of higher-order borderline cases. I also sketch how definitions of independence use the determinacy operator. The distinction between actually assigned values and values whose assignments are acceptable helps avoid unwanted precise cut-off points. (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)

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)

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S1 to the effect that 'Bob is bald' is x true, for x in [0,1], there should be a further statement S2 which tells us how true S1 is, and so on---that is, it accommodates higher-order vagueness---without resorting to the claim that the metalanguage (...) in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic---as opposed to the semantics---of vague discourse is classical. I model the extension of a vague predicate P as a BLURRY SET, this being a function which assigns a degree of membership or DEGREE FUNCTION to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence (0.3,0.2), for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature. (shrink)