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)

In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding validity in those different domains. Indeed, (...) as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

Evan's influential argument against vague objects (_Analysis<D>, 1978) has a parallel directed against contingent identity. I argue that Noonan failed in his attempt to accept Evans's argument but save contingent identity by establishing a disanalogy between the two arguments (in The Philosophical Quarterly 1991). Instead, I suggest an alternative way to block the argument against contingent identity and argue that its analogue provides a satisfactory response to Evans's original argument.

Can supervaluationism successfully handle indirect speech reports? This chapter considers, and rejects, Schiffer’s claim that they cannot. One alleged problem with indirect speech reports is that the truth of “Carla said that Bob is tall” implausibly requires that Carla said all of a huge number of precise things (i.e. that Bob was over n feet tall, for values of n corresponding to precisifications of “tall”). The paper shows why the supervaluationist is not committed to this. Vague singular terms are no (...) particular problem for supervaluationism within indirect speech reports, it is argued, but there remain some issues surrounding certain vague demonstratives. The supervaluationist has good responses available, however, and any remaining questions face all theories of vagueness and are more appropriately addressed within a theory of demonstratives rather than a theory of vagueness. (shrink)

A framework of degrees of belief, or credences, is often advocated to model our uncertainty about how things are or will turn out. It has also been employed in relation to the kind of uncertainty or indefiniteness that arises due to vagueness, such as when we consider “a is F” in a case where a is borderline F. How should we understand degrees of belief when we take into account both these phenomena? Can the right kind of theory of the (...) semantics of vagueness help us answer this? Nicholas J.J. Smith defends a unified account, according to which “degree of belief is expected truth-value”; this builds on his Degree Theory of vagueness that offers an account of the semantics and logic of vagueness in terms of degrees of truth. I argue that his account fails. Degree theories of vagueness do not help us understand degrees of belief and, I argue, we shouldn’t expect a theory of vagueness to yield a detailed uniform story about this. The route from the semantics to psychological states needn’t be straightforward or uniform even before we attempt to combine vagueness with probabilistic uncertainty. (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)

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? (...) This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of “verities”. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain. (shrink)

Logical Pluralists maintain that there is more than one genuine/true logical consequence relation. This paper seeks to understand what the position could amount to and some of the challenges faced by its formulation and defence. I consider in detail Beall and Restall’s Logical Pluralism—which seeks to accommodate radically different logics by stressing the way that they each fit a general form, the Generalised Tarski Thesis (GTT)—arguing against the claim that different instances of GTT are admissible precisifications of logical consequence. I (...) then consider what it is to endorse a logic within a pluralist framework and criticise the options Beall and Restall entertain. A case study involving many-valued logics is examined. I next turn to issues of the applications of different logics and questions of which logic a pluralist should use in particular contexts. A dilemma regarding the applicability of admissible logics is tackled and it is argued that application is a red herring in relation to both understanding and defending a plausible form of logical pluralism. In the final section, I consider other ways to be and not to be a logical pluralist by examining analogous positions in debates over religious pluralism: this, I maintain, illustrates further limitations and challenges for a very general logical pluralism. Certain less wide-ranging pluralist positions are more plausible in both cases, I suggest, but assessment of those positions needs to be undertaken on a case-by-case basis. (shrink)

According to an increasingly popular view, the source of logical necessity is to be found in the essences of logical entities. One might be tempted to extend the view further in using it to tackle fundamental questions surrounding logical consequence. This chapter enquires: how does a view according to which the facts about logical consequence are determined by the essences of logical entities look in detail? Are there any more or less obvious problems arising for such a view? The chapter (...) uncovers a prima facie result in favour of logical pluralism. However, it then goes on to raise some concerns for this result. It argues that, considered generally, it is difficult to see how essence could do all of the requisite work alone. The chapter also shows how considering things from the perspective of disputes between particular rival logics makes an interesting and important difference to the picture of things presented by the essentialist account. (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)

This piece gives an overview of the supervaluationist theory of vagueness. According to that theory, a sentence is true if and only if it is true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The article presents the view and some of its merits and briefly compares it with other theories of vagueness. It raises issues about higher-order vagueness and the definitely operator (...) and about the supervaluationist's accounts of truth and validity. (shrink)

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)

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)

This paper explores several different accounts of validity within the supervaluationist framework that coincide in the absence of the D operator but differ once that operator is introduced. It argues that the alternatives have different advantages and suggests a form of a pluralism about notions of validity within the supervaluationist framework.

This paper asks whether a good philosophical account of something can ever be circular. It explores the kind of circumstances in which an account of F might involve F itself while still serving the functions of and meeting the requirements on a philosophical account. The paper discusses two criteria for acceptable circularity, based on ideas from Humberstone 1997. And it illustrates the surprisingly wide variety of kinds of accounts in which circularity need not be bad.

A theory of vagueness gives a model of vague language and of reasoning within the language. Among the models that have been offered are Degree Theorists’ numerical models that assign values between 0 and 1 to sentences, rather than simply modelling sentences as true or false. In this paper, I ask whether we can benefit from employing a rich, well-understood numerical framework, while ignoring those aspects of it that impute a level of mathematical precision that is not present in the (...) modelled phenomenon of vagueness. Can we ignore apparent implications for the phenomena by pointing out that it is just a model and that the unwanted features are mere artefacts? I explore the distinction between representors and artefacts and criticise the strategy of appealing to features as mere artefacts in defence of a theory. I focus largely on theories using numerical resources, but also consider other, related theories and strategies, including theories appealing to non-linear structures. (shrink)

According to columnar higher-order vagueness, all orders of vagueness coincide: any borderline case is a borderline borderline case, and a third-order borderline case, etc. Bobzien has worked out many details of such a theory and models it with a modal logic closely related to S4. I take up a range of questions about the framework and argue that it is not suitable for modelling the structure of vagueness and higher-order vagueness.

If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns (...) a heap into a non-heap, but we can never know exactly which one it is. (shrink)

This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in (...) response to Keefe’s paper. In addition, the audio of the session, which is available online, becomes inaudible at the beginning of my reply to Keefe’s comments due to a technical defect. The following is a full version of my remarks. (shrink)

Many philosophers, I suspect, are partial to supervaluational theories of vagueness. And with good reason. Its rivals all seem to promise metaphysical mysteries concerning hitherto unnoticed, and perhaps unnoticeable, sharp boundaries around our concepts, or radical revision in our logical practices. And not only have philosophers been so tempted. The texts are a little unclear, but it seems several economists can be read as adopting supervaluational solutions to the difficulties raised by vagueness in economic concepts. Given its popularity, and plausibility, (...) supervaluationism deserves a book-length defence. Yet this is the first such book in the philosophical canon. (shrink)

Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that theories of vagueness based upon fuzzy logic and set theory rest on a confusion: once we have assigned a number to an object to represent (for example) its *height*, there is no distinct purpose left to be served by assigning a number to the object to represent its *degree of tallness*; she claims that ``any numbers assigned in an attempt to capture the vagueness of `tall' do no (...) more than serve as another measure of height.'' In this paper I defend fuzzy theories of vagueness against Keefe's attack. I show that the numbers that we assign to objects to measure (for example) heights serve a quite distinct purpose from the numbers that fuzzy theories of vagueness assign to objects to measure degrees of tallness: the two sorts of assignment are both *formally* and *conceptually* distinct; the fuzzy approach to vagueness is well-motivated and free of confusion. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

Michael Tye responds to the problem of higher-order vagueness for his trivalent semantics by maintaining that truth-value predicates are “vaguely vague”: it’s indeterminate, on his view, whether they have borderline cases and therefore indeterminate whether every sentence is true, false, or indefinite. Rosanna Keefe objects (1) that Tye’s argument for this claim tacitly assumes that every sentence is true, false, or indefinite, and (2) that the conclusion is any case not viable. I argue – contra (1) – that (...) Tye’s argument needn’t make that assumption. A version of her objection is in fact better directed against other arguments Tye advances, though Tye can absorb this criticism without abandoning his position’s core. On the other hand, Keefe’s second objection does hit the mark: embracing ‘vaguely vague’ truth-value predicates undermines Tye’s ability to support validity claims needed to defend his position. To see this, however, we must develop Keefe’s remarks further than she does. (shrink)

A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’: 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety (...) of options available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advo... (shrink)

A festschrift for Dorothy Edgington, containing contributions from Cleo Condoravdi, Dorothy Edgington, Kit Fine, Alan Hájek, John Hawthorne, Sabine Iatridou, Nick Jones, Rosanna Keefe, Angelika Kratzer, David Over, Daniel Rothschild, Robert Stalnaker, Scott Sturgeon, and Timothy Williamson.

Theories of spatial cognition are derived from many sources. Psychologists are concerned with determining the features of the mind which, in combination with external inputs, produce our spatialized experience. A review of philosophical and other approaches has convinced us that the brain must come equipped to impose a three-dimensional Euclidean framework on experience – our analysis suggests that object re-identification may require such a framework. We identify this absolute, nonegocentric, spatial framework with a specific neural system centered in the hippocampus.A (...) consideration of the kinds of behaviours in which such a spatial mapping system would be important is followed by an analysis of the anatomy and physiology of this system, with special emphasis on the place-coded neurons recorded in the hippocampus of freely moving rats. A tentative physiological model for the hippocampal cognitive map is proposed. A review of lesion studies, in tasks as diverse as discrimination learning, avoidance, and extinction, shows that the cognitive map notion can adequately explain much of the data.The model is extended to humans by the assumption that spatial maps are built in one hemisphere, semantic maps in the other. The latter provide a semantic deep structure within which discourse comprehension and production can be achieved. Evidence from the study of amnesic patients, briefly reviewed, is consistent with this extension. (shrink)

In this paper, I argue for a social conception of subjectivity, via a philosophical reading of first-person accounts of recovery from schizophrenia, published in the _Schizophrenia Bulletin_. Following the hypothesis that these accounts exemplify a more general tension between, on the one hand, normative and social dimensions of the self, and on the other, experiential and psychological dimensions, the first section of the paper formulates the problem from a philosophical perspective inspired by Ludwig Wittgenstein's grammatical approach. The second section explores (...) and rejects different possible readings (sociologistic, phenomenological, or narrativist readings), as conceiving the subject in too passive a relationship with him or herself, and as leading to overly skeptical conclusions about the claims in the first-person accounts insisting on the notion of recovery as a restoration of a sense of self and as empowerment. The third section suggests that a more positive answer can be given via the idea of a certain _grammar of recovery_ governing these narratives, and sketches out how this relates to the more general philosophical question on subjectivity. (shrink)

People with higher levels of emotional intelligence (EI: adaptive emotional traits, skills and abilities) typically achieve more positive life outcomes, such as psychological wellbeing, educational attainment, and job-related success. Although the underpinning mechanisms linking EI with those outcomes are largely unknown, it has been suggested that EI may work as a ‘stress buffer’. Theoretically, when faced with a stressful situation, emotionally intelligent individuals should show a more adaptive response than those with low EI, such as reduced reactivity (less mood deterioration, (...) less physiological arousal), and faster recovery once the threat has passed. A growing number of studies have begun to investigate that hypothesis in respect to EI measured as both an ability (AEI) and trait (TEI), but results are unclear. To test the ‘stress-buffering’ function of EI, we systematically reviewed experimental studies that explored the relationship between both types of EI and acute stress reactivity or recovery. By searching 4 databases, we identified 45 eligible studies. Results showed that EI was only adaptive in certain contexts, and that findings differed according to stressor type, and how EI was measured. In terms of stress reactivity, TEI related to less mood deterioration during sports-based stressors (e.g. competitions), physical discomfort (e.g. dental procedure), and cognitive stressors (e.g. memory tasks), but did not appear as helpful in other contexts (e.g. speeches). Furthermore, effects of TEI on physiological stress responses, such as heart rate, were inconsistent. Effects of AEI on subjective and objective stress reactivity were often non-significant, with high levels detrimental in some cases. However, data suggest that both higher AEI and TEI relate to faster recovery from acute stress. In conclusion, results provide mixed support for the stress-buffering effect of EI. Limitations and quality of studies are also discussed. Findings could have implications for EI training programmes. (shrink)

Recently, scholars across disciplines raised ethical, legal and social concerns about the notion of human intervention, control, and oversight over Artificial Intelligence (AI) systems. This observation becomes particularly important in the age of ubiquitous computing and the increasing adoption of AI in everyday communication infrastructures. We apply Nicholas Garnham's conceptual perspective on mediation to users who are challenged both individually and societally when interacting with AI-enabled systems. One way to increase user agency are mechanisms to contest faulty or flawed AI (...) systems and their decisions, as well as to request redress. Currently, however, users structurally lack such mechanisms, which increases risks for vulnerable communities, for instance patients interacting with AI healthcare chatbots. To empower users in AI-mediated communication processes, this article introduces the concept of active human agency. We link our concept to contestability and redress mechanism examples and explain why these are necessary to strengthen active human agency. We argue that AI policy should introduce rights for users to swiftly contest or rectify an AI-enabled decision. This right would empower individual autonomy and strengthen fundamental rights in the digital age. We conclude by identifying routes for future theoretical and empirical research on active human agency in times of ubiquitous AI. (shrink)

In this book, Tim O'Keefe reconstructs the theory of freedom of the ancient Greek philosopher Epicurus (341-271/0 BCE). Epicurus' theory has attracted much interest, but our attempts to understand it have been hampered by reading it anachronistically as the discovery of the modern problem of free will and determinism. O'Keefe argues that the sort of freedom which Epicurus wanted to preserve is significantly different from the 'free will' which philosophers debate today, and that in its emphasis on rational (...) action it has much closer affinities with Aristotle's thought than with current preoccupations. His original and provocative book will be of interest to a wide range of readers in Hellenistic philosophy. (shrink)

This book is a survey of how law, language and translation overlap with concepts, crimes and conflicts. It is a transdisciplinary survey exploring the dynamics of colonialism and the globalization of crime. Concepts and conflicts are used here to mean 'conflicting interpretations' engendering real conflicts. Beginning with theoretical issues and hermeneutics in chapter 2, the study moves on to definitions and applications in chapter 3, introducing cattle stealing as a comparative theme and global case study in chapter 4. Cattle stealing (...) is also known in English as 'rustling, duffing, raiding, stock theft, lifting and predatorial larceny.' Crime and punishment are differently perceived depending on cultures and legal systems: 'Captain Starlight' was a legendary 'duffer'; in India 'lifting' a sacred cow is a sacrilegious act. Following the globalization of crime, chapter 5 deals with human rights, ethnic cleansing and genocide. International treaties in translation set the scene for two world wars. Introducing 'unequal treaties' (e.g. Hong Kong), chapter 6 highlights disasters caused by treaties in translation. Cases feature American Indians (the 'trail of broken treaties'), Maoris (Treaty of Waitangi) and East Africa (Treaty of Wuchale). (shrink)