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)

The finding that women are attracted to men older than themselves whereas men are attracted to relatively younger women has been explained by social psychologists in terms of economic exchange rooted in traditional sex-role norms. An alternative evolutionary model suggests that males and females follow different reproductive strategies, and predicts a more complex relationship between gender and age preferences. In particular, males' preferences for relatively younger females should be minimal during early mating years, but should become more pronounced as the (...) male gets older. Young females are expected to prefer somewhat older males during their early years and to change less as they age. We briefly review relevant theory and present results of six studies testing this prediction. Study 1 finds support for this gender-differentiated prediction in age preferences expressed in personal advertisements. Study 2 supports the prediction with marriage statistics from two U.S. cities. Study 3 examines the cross-generational robustness of the phenomenon, and finds the same pattern in marriage statistics from 1923. Study 4 replicates Study 1 using matrimonial advertisements from two European countries, and from India. Study 5 finds a consistent pattern in marriages recorded from 1913 through 1939 on a small island in the Philippines. Study 6 reveals the same pattern in singles advertisements placed by financially successful American women and men. We consider the limitations of previous normative and evolutionary explanations of age preferences and discuss the advantages of expanding previous models to include the life history perspective. (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.

The finding that women are attracted to men older than themselves whereas men are attracted to relatively younger women has been explained by social psychologists in terms of economic exchange rooted in traditional sex-role norms. An alternative evolutionary model suggests that males and females follow different reproductive strategies, and predicts a more complex relationship between gender and age preferences. In particular, males' preferences for relatively younger females should be minimal during early mating years, but should become more pronounced as the (...) male gets older. Young females are expected to prefer somewhat older males during their early years and to change less as they age. We briefly review relevant theory and present results of six studies testing this prediction. Study 1 finds support for this gender-differentiated prediction in age preferences expressed in personal advertisements. Study 2 supports the prediction with marriage statistics from two U.S. cities. Study 3 examines the cross-generational robustness of the phenomenon, and finds the same pattern in marriage statistics from 1923. Study 4 replicates Study 1 using matrimonial advertisements from two European countries, and from India. Study 5 finds a consistent pattern in marriages recorded from 1913 through 1939 on a small island in the Philippines. Study 6 reveals the same pattern in singles advertisements placed by financially successful American women and men. We consider the limitations of previous normative and evolutionary explanations of age preferences and discuss the advantages of expanding previous models to include the life history perspective. (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)

The popular and successful rhetorical textbooks produced by the 18th century Scottish philosophical tradition, such as George Campbell's The Philosophy of Rhetoric, Hugh Blair’s Lectures on Rhetoric and Belles Lettres, and Alexander Bain’s English Composition and Rhetoric have been widely accorded a role in the trajectories of 19th and 20th century literary theory. Scholars have generally overlooked them, however, as philosophical works. The selected writings chosen for this volume show how these rhetorical textbooks were a practical extension of the philosophy (...) of language developed by 18th century Scottish philosophers. Francis Hutcheson, Adam Smith, Thomas Reid, Adam Ferguson, Alexander Gerard, and Henry Home, Lord Kames, advanced a radically new paradigm of language as an inherently mediated practice, directed simultaneously to personal and social, moral and aesthetic uses. This Scottish philosophy of rhetoric powerfully influenced the teaching of language and literacy as tools for social and educational innovation. This volume — the first of its kind — offers a wide variety of writings on rhetoric and rhetorical theory, selected in a way that reveals their intimate connection with the Scottish philosophical tradition. (shrink)

British marriage statistics suggest that women of breeding age choose young men. Women past breeding age who could still be raising children extend choices to include older men. After this, women do not marry. The choices of men over 50 are restricted to women between 40 and 55: past breeding but young enough to be raising children; the few men over 50 that marry choose women in this age range.

This paper offers re-assessment of Scottish Common Sense rhetoric and its relationship to pluralist practice and philosophical method. It argues that the rhetorical texts of George Campbell, Hugh Blair, and Alexander Bain can be read as a practical application of Scottish Common Sense philosophy. This offers a novel means of examining the relationship that Scottish rhetoric has to the philosophy of David Hume and also its own innovative philosophy of language. Finally, I argue that Scottish rhetoric makes a unique contribution (...) to rhetorical methodology's key place in the creation of social and moral consensus. (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)

Einon's data support our original claims, although not a claim she seems to assume – of reciprocal attraction between elderly men and 20-year-old women. Implicit in her commentary is an assumption that genetic predispositions are omniscient fitness maximizers. Instead, evolutionary models assume selection-fashioned psychological mechanisms that, in the context of other mechanisms and pressures in past environments, had a positive effect on fitness relative to competing alternatives. The Over & Phillips data fit with our own data on homosexuals, and with (...) the assumption of independent modular mechanisms, rather than any existing sociocultural models. Einon also incorrectly assumes that evolutionary models have overemphasized male choice to the exclusion of female choice. (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)