The article reviews recent developments in England in the law of necessity as a defence to crime and calls for its further extension. It argues that the defence of necessity presents the criminal law with difficult questions of competing values and the ordering of harms. English law has taken a nuanced position on the respective roles of the courts and the legislature in the ordering of harms, although the development of the law has been pragmatic rather than coherently theorised. The (...) law has granted necessity some scope as an exculpatory principle in the law of general defences, but it has also respected the primacy of the legislature as the legitimate arbiter of many of the competitions of value that necessity throws up. The recognition of necessity has not been in the form of a single unified defence of that name. Rather it has taken the form of a number of defences, based on a principle of necessity, but with different nomenclature and different rationales. This approach to necessity is defended as right in terms of principle and policy. Any further development of necessity as a general defence should be restricted to two contexts, namely those of emergencies, and of conflicts of duty, where a danger of death or serious injury is present. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sophie, Greta, Cuiyuan, and Feminist DesireStories by Ding Ling, Alice Munro, and Eileen ChangYuhui Bao (bio) and Ian Dennis (bio)Desire has a history and, for a literary criticism inflected by mimetic theory, novelistic prose fiction offers a privileged view of its unfolding. We study novelistic fiction, as opposed to various romance genres, to grasp that history, for what its authors have been able to see, understand, and dramatize—this (...) is the procedural model, indeed the authority established by René Girard and that has largely governed such criticism thereafter.1 But of the three short fictions we consider here—two Chinese and one Canadian—only two are fully novelistic in character, in that they attempt to describe and diagnose—rather than merely express—emergent and changing desires. Students of Girard, of course, recognize here the distinction between the romanesque and romantique. to which one might add the understandings of genre developed by a number of other theorists.2However, we might also concede that all fictions are invariably and to some degree romantic—some desire, necessarily mediated, is always operative, in writers and readers alike, before or even as it is demystified, if indeed it is. Furthermore, a passionate fictional commitment to that which Girard boldly [End Page 131] designated the mensonge romantique may actually reveal or clarify, at least for later readers, that which the author seeks half- or unconsciously to conceal. It is with this possibility in mind that we propose to consider our other subject fiction, "Miss Sophie's Diary" (莎菲女士的日记 sha fei nv shi de ri ji; 1927) by the pioneering Chinese woman writer Ding Ling (丁玲 ding ling).3 "Miss Sophie's Diary," to be clear, is no simple romance; it is at least hybrid, and in its brave if perhaps only partially successful pursuit of the truth of desire, subtly revelatory. Miss Sophie (莎菲 sha fei), chronically ill with tuberculosis and half-separated from a human world she both longs for and despises, with her aggrieved sense of superiority and desperate, shameful longing for those she passionately feels to be her inferiors, with her loquacious rationalizing and constant, perverse reversals of attitude, is a kind of Dostoyevskian "underground woman," afflicted as well with a touch of the "nausea" later made prestigious by J.-P. Sartre.4 She is clearly a harbinger of her own culture's precipitation into the world of internally mediated, indeed, metaphysical desire, what we might also call the market world, the modernity Girard credits the great European novelists from Stendhal onward with diagnosing. This story has long been described as an unprecedented and "frank" revelation "of a Chinese woman's sexual feelings and contempt for conventional views," expressing an "outspoken and unrelenting individualism."5 At the same time, it has been seen as a product of the fatally compromised and ultimately unsuccessful May Fourth literary movement,6 and not necessarily representative of its author's overall fictional production. From an orthodox Girardian critical perspective, however, the crucial interpretative question might be the degree to which Ding Ling is aware of the sources of the newly enfranchised desires her heroine wrestles with, or, as we might also put it, the degree of separation between the author's understanding and that of Miss Sophie. But such a question is perhaps easily enough answered. Ding Ling clearly does not share Girard's "novelistic" perspective on the operation of desire. But from our current perspective, does her best-known work nonetheless offer, however imperfectly, certain now-recognizable insights into historical processes of desire that our other two writers more fully realize?"Miss Sophie's Diary" is famous in China for the delicacy, depth, and explicitness with which those bold and passionate sexual desires of Sophie are exposed, even as such desires are (perhaps reassuringly) defeated, or at least revealed as illusory. Clearly the story reflects a period of cultural and personal crisis. "I was extremely confused at that time," she wrote in a later phase of self-critique. "On one hand, I was radically rebellious, believing blindly in social revolution; on the other hand, I indulged myself in a petty bourgeoisie sense, departing from revolution, so I was trapped in loneliness, struggle and misery [End... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"'Twas Nature Gnaw'd Them to This Resolution":Byron's Poetry and Mimetic DesireIan Dennis (bio)1. IntroductionWe all know Lord Byron, I presume. Know him as a paradigmatic object of cultural desire, as the quintessentially romantic individualist whose haughtily transgressive rejection of his society turned him into one of its most compelling models and objects, the endlessly provocative rival of a multitude of young men to follow—and they are still following—all (...) to differing degrees blind to or writhing in the anxieties of his influence. I myself belong to that somewhat smaller group that actually reads his poetry.Having passed through the little deification of celebrity, Byron was on something of a downslope of fame, and knew it, before he put the matter past all doubt by dying almost-young for liberty in Greece in 1824. Perhaps not surprisingly, given all this, he developed into something of an expert on desire. Almost alone among the major Romantics, he came to understand this most basic force in human experience not only as mediated and mimetic but as increasingly a function of a new kind of market whose commanding value was apparent autonomy from the market. It is not too hard to see how he figured this out. Those whom Byron defied adored him; those whose petty gratifications he evaded in spectacular suffering emulated him; those to whose desires he declared himself indifferent desired him—as few have ever been desired. For all his very real faults he was an intelligent man and an observant one. He reflected on what had happened to him.2. Reading Byron's Poetry for Nature and DesireIn his earlier poetry the natural scene, at least in Byron's privileged experiences of it, acts as an ally against other people. It is a source of his difference from and thus his indifference to the rest of us—an apparent replacement for, rather than object of, mediated desire. [End Page 115]Almost the first words of the preface to his fame-making Childe Harold's Pilgrimage (1812) tell us that the poem was "written, for the most part, amidst the scenes which it attempts to describe" and a coy disquisition on the identity of the Childe—who is and is not Byron—follows close on the heels of a spate of place-name dropping. They are sexy places, too, hard to get to, exotic, naturally beautiful, and dangerous. Soon the note of human pollution is of course sounded—man "mars" the beauties of Cintra that the hero is experiencing (1980–1993, 1.15)1—reminding us of the prototypical alliance between the alienated Romantic solitary and the unspoiled, or spoiled natural world, alike menaced by sociality, by the Other. This alliance is powerfully reinforced by an identification with the bovine victim of the Cadiz bull-ring, vivid sacrifice at the center of—in the young poet's chilling phrase—"the silent circle's peopled walls" (1.75). Does man scapegoat nature? There could hardly be a handier metaphor. And the Childe makes common cause.Mainly, though, "Dear Nature" is the particular solace of her "never-wean'd" favorite son, the one who never "pollutes her path," he who, as he rather complacently notes, "mark'd her when none other hath" (2.27). Byron does at least make good on such a claim by going to Albania, a wild, inaccessible place which he, with some justification, boasts "all admire, but many dread to view" (2.43). He writes some stirring descriptive poetry, leavened with occasional homilies on the smallness and nastiness of man and the grandeur and beauty of nature, sentiments that would not sound out of character on the lips of young backpacking, development-deploring kindred spirits of a later age. Again, it is to be remembered that the first besmirchment of the natural world to be complained of is not material, but social, in particular by the Romantic rebel's own society—not chemicals and chainsaws but the poisonous presence of overly familiar people and practices. The language of protest remains much the same after the products of industrial economic activity are added to the score, and indeed a good part of... (shrink)

This article reports three experiments that investigated the relationship between working memory capacity and syllogistic and five-term series spatial inference. A series of complex and simple verbal and spatial working memory measures were employed. Correlational analyses showed that verbal and spatial working memory span tasks consistently predicted syllogistic and spatial reasoning performance. A confirmatory factor analysis showed that three factors best accounted for the data--a verbal, a spatial, and a general factor. Syllogistic reasoning performance loaded all three factors, whilst spatial (...) reasoning loaded only the general factor. The implications of these findings are discussed in the context of reasoning theories and contemporary accounts of the structure of working memory. (shrink)

In this paper several problems are raised concerning Ian Barbour's four ways of interrelating science and religion—Conflict, Independence, Dialogue, and Integration—as put forward in such publications as his highly influential Religion in an Age of Science (1990) and widely adopted by other writers in this field. The authors argue that this taxonomy is not very useful or analytically helpful, especially to historians seeking to understand past engagements between science and religion.

A study is reported which focused on the problem-solving strategies employed by expert electronics engineers pursuing a real-world task: integrated-circuit design. Verbal protocol data were analysed so as to reveal aspects of the organisation and sequencing of ongoing design activity. These analyses indicated that the designers were implementing a highly systematic solution-development strategy which deviated only a small degree from a normatively optimal top-down and breadth-first method. Although some of the observed deviation could be described as opportunistic in nature, much (...) of it reflected the rapid depth-first exploration of tentative solution ideas. We argue that switches from a predominantly breadth-first mode of problem solving to depth-first or opportunistic modes may be an important aspect of the expert's strategic knowledge about how to conduct the design process effectively when faced with difficulties, uncertainties, and design impasses. (shrink)

The aim of the present research was to develop a difficulty model for logical reasoning problems involving complex ordered arrays used in the Graduate Record Examination. The approach used involved breaking down the problems into their basic cognitive elements such as the complexity of the rules used, the number of mental models required to represent the problem, and question type. Weightings for these different elements were derived from two experimental studies and from the reasoning literature. Based on these weights, difficulty (...) models were developed which were then tested against new data. The models had excellent predictive validity and showed the relative influence of rule based factors and factors relating to the number of underlying models. Different difficulty models were needed for different question types, suggesting that people used a variety of approaches and, at a wider level, that both mental models and mental rules may be used in reasoning. (shrink)

Although rational choice theory has enjoyed only modest predictive success, it provides a powerful explanatory mechanism for social processes involving strategic interaction among individuals and it stimulates interesting empirical inquiries. Rather than present competing theories to compare against rational choice, Don Green and Ian Shapiro have merely alluded to alternative explanatory variables such as culture, institutions, and social norms, without showing either how these factors can be incorporated into a more powerful theory, or how they are inconsistent with rational choice (...) theory. It is likely that any eventual theory of the origin and maintenance of social institutions, norms, and values will have to reserve a central place for rational action. (shrink)

Intellectual humility is a hot topic. One of the key questions the literature is exploring is definitional: What is intellectual humility? In their recent paper, “Intellectual Humility: Owning our Limitations,” Dennis Whitcomb, Heather Battaly, Jason Baehr, and Daniel Howard-Snyder have proposed an answer: Intellectual humility is “proper attentiveness to, and owning of, one’s intellectual limitations”. I highlight some limitations of the limitations-owning account of intellectual humility. And in conclusion, I suggest that ultimately these are not limitations that any viable (...) account of intellectual humility should own and that Whitcomb et al. should revise their view accordingly. (shrink)

This article provides background material to help readers appreciate three speeches printed in this issue, given by Stefan Morawski, Dennis Smith and Hans Joas on the occasion of the presentation to Zygmunt Bauman of a Festschrift in March 1996 in Leeds. The article describes: relevant details of Polish history concerning cultural patriotism, anti-state attitudes, the role of Jews in the communist state apparatus and anti-Semitism, focusing on post-1945; the peculiarities of the indigenous British sociology tradition and the part played (...) by exiles in shaping it; a profile of the `successful outsider'; and the implications of Bauman's recent work on the Holocaust for the Sonderweg thesis about German history and the Historikerstreit, which are also sketched. It concludes that far from being a `homeless intellectual', Bauman has two homes, perhaps reflecting the wider integrating process of Eastern and Western Europe, until recently separated by a gulf. (shrink)

The writings of Ian Barbour and Arthur Peacocke can be construed as initial contributions to a Lakatosian research program on the relation between theology and science, the core theory of which is the thesis that theology belongs at the top of a nonreducible hierarchy of sciences. The positive heuristic of this program involves showing that theology and the sciences have enough in common epistemologically to be so related and arguing for nonreducibility. The author in this essay “rationally reconstructs” some of (...) her philosophical work as a contribution to these tasks. (shrink)

I’m going to argue that omniscience is impossible and therefore that there is no God. The argument turns on the notion of grounding. After illustrating and clarifying that notion, I’ll start the argument in earnest. The first step will be to lay out five claims, one of which is the claim that there is an omniscient being, and the other four of which are claims about grounding. I’ll prove that these five claims are jointly inconsistent. Then I’ll argue for the (...) truth of each of them except the claim that there is an omniscient being. From these arguments it follows that there are no omniscient beings and thus that there is no God. (shrink)

This paper argues that epistemologists should theorize about wisdom and critically examines a number of attempts to do as much. It then builds and argues for a particular theory of what wisdom is.

Plato of Athens, who laid the foundations of the Western philosophical tradition and in range and depth ranks among its greatest practitioners, was born to a prosperous and politically active family circa 427 BC. In early life an admirer of Socrates, Plato later founded the first institution of higher learning in the West, the Academy, among whose many notable alumni was Aristotle. Traditionally ascribed to Plato are thirty-five dialogues developing Socrates' dialectic method and composed with great stylistic virtuosity, together with (...) the Apology and thirteen letters. The four works in this volume recount the circumstances of Socrates' trial and execution in 399 BC. In Euthyphro, set in the weeks before the trial, Socrates and Euthyphro attempt to define holiness. In Apology, Socrates answers his accusers at trial and unapologetically defends his philosophical career. In Crito, a discussion of justice and injustice explains Socrates' refusal of Crito's offer to finance his escape from prison. And in Phaedo, Socrates discusses the concept of an afterlife and offers arguments for the immortality of the soul. This edition, which replaces the original Loeb edition by Harold North Fowler, offers text, translation, and annotation that are fully current with modern scholarship." -- Publisher's description. (shrink)

Democracy and justice are often mutually antagonistic ideas, but in this innovative book Ian Shapiro shows how and why they should be pursued together. Justice must be sought democratically if it is to garner legitimacy in the modern world, he claims, and democracy must be justice-promoting if it is to sustain allegiance over time. _Democratic Justice_ meets these criteria, offering an attractive vision of a practical path to a better future. Wherever power is exercised in human affairs, Shapiro argues, the (...) lack of democracy will be experienced as injustice. The challenge is to democratize social relations so as to diminish injustice, but to do this in ways that are compatible with people’s values and goals. Shapiro shows how this can be done in different phases of the human life cycle, from childhood through the adult worlds of work and domestic life, retirement, old age, and approaching death. He spells out the implications for pressing debates about authority over children, the law of marriage and divorce, population control, governing the firm, basic income guarantees, health insurance, retirement policies, and decisions made by and for the infirm elderly. This refreshing encounter between political philosophy and practical politics will interest all those who aspire to bequeath a more just world to our children than the one we have inherited. (shrink)

This article critically examines numerous attempts to build a knowledge-first ethics of belief. These theories specify a number of potential "knowledge norms for belief".

In this paper, I address the question of whether it is ever permissible to grant a request for physician-aid-in-dying (PAD) from an individual suffering from treatment-resistant depression. I assume for the sake of argument that PAD is sometimes permissible. There are three requirements for PAD: suffering, prognosis, and competence. First, an individual must be suffering from an illness or injury which is sufficient to cause serious, ongoing hardship. Second, one must have exhausted effective treatment options, and one’s prospects for recovery (...) must be poor. Third, the individual must be judged competent to request PAD. I argue that many cases of treatment-resistant depression meet the first two requirements. Thus, the key question concerns the third. I consider four features of depression that might compromise a person’s decision-making capacity. Ultimately, I conclude that PAD requests from depressed patients can be permissibly granted in some circumstances. (shrink)

I start with a critical discussion of some attempts to ground epistemic normativity in curiosity. Then I develop three positive proposals. The first of these proposals is more or less purely philosophical; the second two reside at the interdisciplinary borderline between philosophy and psychology. The proposals are independent and rooted in different literatures. Readers uninterested in the first proposal (and the critical discussion preceding it) may nonetheless be interested in the second two proposals, and vice versa. -/- The proposals are (...) as follows. First I argue that, among several ways in which the notion of curiosity might be used to delineate significant truths from trivial ones, a particular way is the most promising. Second, I argue that curiosity has some underappreciated epistemic roles involving memory. Third, I argue that curiosity has some underappreciated epistemic roles involving coherence. (shrink)

Suppose that you are engaging with someone who is your oppressor, or someone who espouses a heinous view like Nazism or a ridiculous view like flat-earthism. In contexts like these, there is a disparity between you and your interlocutor, a dramatic normative difference across which you are in the right and they are in the wrong. As theorists of humility, we find these contexts puzzling. Humility seems like the *last* thing oppressed people need and the *last* thing we need in (...) dealing with those whose views are heinous or ridiculous. Responding to such people via humility seems uncalled for, even inappropriate. But how could this be, given that humility is a *virtue*? The purpose of the paper is to explore this puzzle. We explain what the puzzle is and then attempt to draw some lessons from it: first, the lesson that the importance of humility is limited in several ways, and second, the lesson that humility nonetheless has several important roles to play, even for people who are in the right in contexts of disparity. (shrink)

The interconnections between self and surroundings in Daoist thought have been explored in the past in a variety of contexts. This paper, however, explores the Daoist version of the relational self from the general perspective of chaos theory and, more specifically, examines the role of the self in creating emergent form and dynamism in nature and society. The fractal self and world merge through the disciplined effort of the sage until the effort becomes effortless. Both self and world are transformed (...) and become one through the emergent moment. This moment represents a new opportunity for subsequent patterns, or attractors, to emerge. We suggest that the self folds itself into the world, creating and being created by a new attractor, or pattern, in the organization of nature, which we argue is Dao. Our current investigation addresses the following aspects of chaos theory and its relation to Daoism: (1) the Daoist notion of wuwei as perfect congruence; (2) yin and yang at the edge of chaos; (3) the emergent nature of the myriad things; and (4) a Daoist warning against fractal disconnections in the world. Finally, we conclude that the self has the potential to become the world. To approach this amplified condition, the self must dedicate itself to and risk open engagement with events across the complexity of nature. Through openly engaging the world, the self is transformed, leaving the world forever changed. (shrink)

This article offers an approach to advance the use of virtue ethics in the training of business managers and leaders, as well as in the education of business students. A thesis is that virtue ethics offers a valuable way to think about how we want to be and what we should strive to become qua businessperson, manager, and leader. The article provides a framework for thinking about virtue ethics in the context of business and leadership, with emphasis on building trust (...) in organizations. It includes a brief summary of Aristotelian virtue ethics, core concepts, and how they apply to management and leadership decision-making. The article concludes with a summary of an approach for teaching a virtue ethics module, which has evolved over the past 20 years. Included are exercises, a survey tool, and a business case as components of the module. The module has been used in corporate training, as well as graduate and undergraduate business education. It is hoped this approach will spur others to explore other ways to bring virtue ethics to business and business education. (shrink)

Epistemology is normative. This normativity has been widely recognized for a long time, but it has recently come into direct focus as a central topic of discussion. The result is a recent and large turn towards focusing on epistemic value. I’ll start by describing some of the history and motivations of this recent value turn. Then I’ll categorize the work within the value turn into three strands, and I’ll discuss the main writings in those strands. Finally, I’ll explore some themes (...) that are ripe for further development. (shrink)

In The Elm and the Expert, Jerry Fodor tries to reconcile three philosophical positions he is presently committed to: a computational theory of mind, intentional realism and a denotational theory of meaning. One problem he faces is this: a denotational semantics, according to which the meaning of a singular term like a name is exhausted by its referent, seems to rule out there being true intentional generalizations, or generalizations which advert to the contents of a subject's mental states. That there (...) are such true generalizations is a major element in Fodor's intentional realism. Accordingly, Fodor is forced to find a way of dissolving this apparent incompatibility. This paper looks at his attempts to do so and concludes that they fail. (shrink)

Classic studies of explanation, such as those of Hempel and Bromberger, took it for granted that an explanation-seeking question of the form "Why P?" should be understood as asking about the proposition P. This view has been recently challenged by Bas van Fraassen and Alan Garfinkel. They acknowledge that some questions have the surface form "Why P?", but they hold that a correct reading for why-questions should take the form "Why P (rather than Q)?", where Q is a contrasting alternative. (...) This contrast theory is discussed here. It is argued that, properly understood, the contrast theory and the propositional approach can and should give equivalent readings to why-questions. (shrink)

This study proposes a conceptual model to explain persistent, accepted-as-normal corporate wrongdoing (hereafter banality of wrongdoing), particularly for high performance organizations. The model describes five explanatory variables: the culture of competition, ends-biased leadership, missionary zeal, legitimizing myth, and the corporate cocoon. Our thesis is that the nature of competition drives both legitimate and illegitimate goal-seeking to adopt an iconoclastic (rule-breaking) orientation. High performance organizations are favorable hosts for wrongdoing because high performance requires aggressive behavior at the ethical margins of what (...) is acceptable. The way leadership reacts to competition sets the stage for ethical or unethical cultures to develop. Ends-biased leadership will project strong vision, using ideology and legitimizing myth as tools to inspire and motivate. The resulting missionary zeal justifies using questionable means because of the perceived value of the end. One critical method for building strong culture is creating a sense of being separate and apart from the ordinary. This cocoon effect may create a self-referential value system that is significantly at odds with mainstream culture and in which wrongdoing is banal. We intend an empirical study of the variables described in this model. (shrink)

Abstract:This study explores a phenomenon that has been shown to adversely affect managers’ decisions—competitive irrationality. Managers are irrationally competitive in their decisions when they focus on damaging the profits of competitors, rather than improving their own profit performance. Studies by Armstrong and Collopy (1996) and Griffith and Rust (1997) suggest that the phenomenon is common but not universal. We examine the question of why some individuals exhibit competitive irrationality when making decisions, while others do not by focusing on four aspects (...) of moral philosophy—deontological orientation, cognitive moral development, idealism, and relativism. Results suggest that individuals high in deontological orientation, high in cognitive moral development, high in idealism, and low in relativism will be less competitively irrational than those who are not. (shrink)

How to draw the line between depression-as-disorder and non-pathological depressive symptoms continues to be a contested issue in psychiatry. Relatively few philosophers have waded into this debate, but the tools of philosophical analysis are quite relevant to it. In this paper, I defend a particular answer to this question, the Contextual approach.On this view, depression is a disorder if and only if it is a disproportionate response to a justifying cause or else is unconnected to any justifying cause. I present (...) four objections to this approach and then defend it from them. Along the way, I explain why it matters whether we get this question right. (shrink)

The paper attempts to provide a basis for exploring the continued relevance of Catholic social teaching to business ethics, byinterpreting the historic development of a Catholic work ethic and the traditions of Catholic social teaching in light of contemporary discussions of economic globalization, notably those of Robert Reich and Peter Drucker. The paper argues that the Catholic work ethic and the Church’s tradition of social teaching has evolved dynamically in response to the structural changes involved in the history of modern (...) economic development, and thus is well poised to speak to the ethical challenges implicit in the advent of a knowledge-based society. In order to test this thesis, the author sketches an approach to the ethical challenge of corporate downsizing that he believes illustrates the continued relevance of Catholic social teaching to business ethics. (shrink)

Timothy Williamson has a marvelously precise account of epistemic justification in terms of knowledge and probability. I argue that the account runs aground on certain cases involving the probability values 0 and 1.

Recent philosophy features remarkably little work on the nature of wisdom. The following is a bibliography of that work, or at least the important-seeming parts of it that I’ve managed to uncover. I’ve also included some work from the history of philosophy, and from a few neighboring fields. Suggested additions would be very appreciated.

This paper takes as its starting point the conjoining of the perceived and conceived spaces of what Soja (1996) calls Thirdspace and what Lefebvre calls ‘lived space’ to launch a discussion about ideas surrounding contemporary concepts of community. The sites under discussion are the ubiquitous shopping malls and the enclave estates or master planned communities (mpcs) which, it is argued, by their design offer only ‘illusions of community.’ The claim in this paper is that within these spaces of control are (...) spatialities of resistance–vagrant spaces-that can, under certain circumstances, point to the—poverty of participation—in the community experience. (shrink)

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version (...) of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

In this dissertation I defend a Kantian notion of the given. I show that something akin to Kant's theory of intuition is necessary to make sense of the normative role perception has in forming perceptual knowledge. ;Perceptual judgments require guidance from the objects they represent. I argue that this normative aspect of perception can be explained only by appeal to a non-conceptual content caused by the object perceived. But isn't this to appeal to the mythical given? I show that it (...) is not by comparing it to the result of Sellars' famous Myth of the Given argument. Contrary to the generally accepted view, what follows from Sellars' argument is not that the given is a myth, but rather that what is immediately present to mind cannot be known. This result leaves an explanatory option which the Sellars' critique does not consider. The given might be a part of knowledge while not itself being independently knowable. ;However, because the possibility of an immediate cognitive content is thought to have been foreclosed by the Sellars argument, much subsequent epistemology has overlooked this alternative. One widespread response has been to embrace coherence theories according to which justification is regarded as a relation between beliefs. These theories regard perception as a thoroughly causal phenomenon and consequently allow no role for perception in the justification of perceptual or other beliefs. ;I argue that in perceptual contexts only perception can decide the case between equally coherent conceptual determinations. But according to the coherentist this kind of justificatory function could not involve perception since perception is a thoroughly causal phenomenon. Against this view, I argue that some notion of the given, one which circumvents Sellars' criticism, is necessary to account for the normative role perception plays in perceptual belief. I show that Kant's notion of sensible intuition circumvents the Sellars critique. The idea of the given is redeemed in Kant's account, since it makes possible a theory of the normative role that perception plays in knowledge. (shrink)

For any normative domain, we can theorize about what is good in that domain. Such theories include utilitarianism, a view about what is good morally. But there are many domains other than the moral; these include the prudential, the aesthetic, and the intellectual or epistemic. In this last domain, it is good to be knowledgeable and bad to ignore evidence, quite apart from the morality, prudence, and aesthetics of these things. This dissertation builds a theory that stands to the epistemic (...) domain as utilitarianism stands to the moral domain. It builds an epistemic value theory. (shrink)