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)

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)

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)

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)

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)

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.

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)

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.

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.

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.

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)

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)

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)

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)

One striking oddity about Democritus and Epicurus is that, even though Epicurus' theory of perception is largely the same as that of Democritus, Democritus and his followers draw skeptical conclusions from this theory of perception, whereas Epicurus declares that all perceptions are true or real. I believe that the dispute between Democritus and Epicurus stems from a question over what sort of ontological status should be assigned to sensible qualities. In this paper, I address three questions: 1) Why were Democritus (...) and his followers skeptical? 2) How did Epicurus modify Democritus' metaphysics in order to avoid these skeptical conclusions? and 3) How successful was he? -/- 1) I argue that Democritus allows only the intrinsic properties of atoms into his ontology, and then runs into skeptical difficulties because of the relativity of perception. 2) I propose that Epicurus modifies Democritus' ontology by allowing dispositional and relational properties as real properties of bodies. Sensible qualities are conceptualized as dispositional properties of bodies to cause certain experiences in percipients. 3) I argue that Epicurus does not run into the same problems as Democritus. Finally, I consider how my interpretation of Epicurus' ontology helps to make sense of his claim that all perceptions are alethes--'true' or 'real.'. (shrink)

Metaphors used to describe new technologies mediate public understanding of the innovations. Analyzing the linguistic, rhetorical, and affective aspects of these metaphors opens the range of issues available for bioethical scrutiny and increases public accountability. This article shows how such a multidisciplinary approach can be useful by looking at a set of texts about one issue, the use of a newly developed technique for genetic modification, CRISPRcas9.

First of all, I want to express my gratitude to the Association for the Advancement of Philosophy and Psychiatry, Philosophy, Psychiatry, & Psychology, and the Karl Jaspers Award Committee for their recognition of my paper "Institution or individuality? Some reflections on the lessons to be learned from personal accounts of recovery from schizophrenia" (Wannberg, 2024). I am also very thankful for Dr. Paul B. Lieberman's (2024) and Pr. Elizabeth Pienkos' (2024) stimulating comments on the paper.In the original paper, I used (...) the case of the first person accounts of recovery from schizophrenia as a paradigm to elucidate the components of subjectivity more generally, as well as their logical relations. My main point... Read More. (shrink)

Appeals to nature are ubiquitous in Epicurean ethics and politics. The foundation of Epicurean ethics is its claim that pleasure is the sole intrinsic good and pain the sole intrinsic evil, and this is supposedly shown by the behavior of infants who have not yet been corrupted, "when nature's judgement is pure and whole." Central to their recommendations about how to attain pleasure is their division between types of desires: the natural and necessary ones, the natural but non-necessary ones, and (...) the vain and empty ones. Elsewhere, the Epicureans talk about the "natural goods" of political power and fame, and they contrast "natural wealth" with wealth as "defined by empty opinion." Finally, in their politics, Epicurus claims that the "the justice of nature is a pledge of reciprocal usefulness, [i.e.,] neither to harm one another nor to be harmed." This paper explores two questions regarding these various appeals to nature. The first is: what is it for these things to be natural, i.e., what notion of "natural" or "nature" is at play here? (Furthermore, is there a single notion being used across these appeals, and if not, how are they related?) The second is: what normative work does a thing's being natural do? That is, what reason, if any, does a desire's being natural give me for pursuing the object of that desire and trying to fulfill that desire, as opposed to not doing so and trying to eliminate it, and similarly for the other appeals to nature? (shrink)

David Furley's work on the cosmologies of classical antiquity is structured around what he calls "two pictures of the world." The first picture, defended by both Plato and Aristotle, portrays the universe, or all that there is (to pan), as identical with our particular ordered world-system. Thus, the adherents of this view claim that the universe is finite and unique. The second system, defended by Leucippus and Democritus, portrays an infinite universe within which our particular kosmos is only one of (...) countless kosmoi. Aristotle's argument in De caelo I.9 that the world is necessarily unique is an important contribution to this debate. This argument holds interest because it shows Aristotle wrestling with an apparent inconsistency in his own philosophy, as deeply-held convictions within his cosmology collide with an equally deeply-held conviction within his metaphysics. The following three principles, each of which Aristotle appears committed to, are inconsistent: -/- The cosmic uniqueness principle. The world is necessarily unique. The cosmic form principle. The world is an ordered, structured unity. As such, the world has a form. The possibility of multiple instantiation principle. For all F, if F is a form, it is possible that there exist multiple Fs. In De caelo I.9, Aristotle argues that we can establish the uniqueness of the universe, reject the multiple instantiation principle, yet still retain the distinction between 'this world' and 'world in general,' if the following is true (as it is): the world takes up all the matter that exists. Aristotle illustrates this argument with one of the stranger analogies in his corpus: imagine an aquiline nose that takes up all the flesh in the universe. If this were so, then there could not exist any other aquiline objects whatsoever. (For this reason, we dub the De caelo I.9 argument the 'Cosmic Nose argument.') This paper is an interpretation of how this argument is supposed to proceed and an assessment of its success. The first section states the problem Aristotle is confronted with, sorts through Aristotle's various statements of the Cosmic Nose argument, which exhibit some sloppiness, and reconstructs charitably a single argument. We also spend some time examining the significance of Aristotle's example of a gigantic aquiline nose. We argue that, even charitably reconstructed, the argument appears to commit a serious modal fallacy. The remainder of the paper explores whether this modal fallacy can be overcome. We conclude that, although not a cogent argument for the uniqueness of the world (as this would require a significant revision of our current astronomy), the Cosmic Nose argument does succeed on its own terms. However, it should not be regarded as a free-standing argument for the uniqueness of the world. Instead, it depends crucially on the earlier argument in De caelo I.8 for the universe's uniqueness; De caelo I.9 should be viewed as an attempt to extend the conclusion of De caelo I.8 and to show how this conclusion can be made consistent with Aristotle's metaphysical principles about the nature of form. (shrink)

In Outlines of Pyrrhonism, Sextus Empiricus takes pains to differentiate the skeptical way of life from other positions with which it is often confused, and in the course of this discussion he briefly explains how skepticism differs from Cyrenaicism. Surprisingly, Sextus does not mention an important apparent difference between the two. The Cyrenaics have a positive epistemic commitment--that we can apprehend our own affections. Although we cannot know whether the honey is really sweet, we can know infallibly that right now (...) we are being sweetened. By contrast, Sextus says explicitly that, as skeptics, Pyrrhonists apprehend nothing whatsoever. A case can (and has) been made that Sextus does not mention this difference because, on this matter, there really isn't an important difference between the two: the skeptic is perfectly able to report how things appear to him, e.g., that the honey seems sweet, and it is crucial for the skeptic that he not abolish the appearances. But, I argue, what the skeptics are doing when they report how things appear to them is importantly different from the sort of immediate, infallible apprehension of one's own affections claimed by the Cyrenaics, as the latter involves theoretical commitments regarding the nature of one's affections that the skeptic eschews. (shrink)

Overview of Epicurean physics and epistemology, ending with a critical discussion of Cicero's report on Epicurean theology.

Anaxarchus accompanied Pyrrho on Alexander the Great’s expedition to India and was known as “the Happy Man” because of his impassivity and contentment. Our sources on his philosophy are limited and largely consist of anecdotes about his interactions with Pyrrho and Alexander, but they allow us to reconstruct a distinctive ethical position. It overlaps with several disparate ethical traditions but is not merely a hodge-podge; it hangs together as a unified whole. Like Pyrrho, he asserts that things are indifferent in (...) value and that realizing this indifference leads to contentment. But this doctrine of indifference is rooted in Democritean atomism. And in his pursuit of pleasure and dismissiveness of conventional standards of what is just, noble, and pious, Anaxarchus is closer to fifth century thinkers such as Aristippus, Antiphon, and Critias. (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)