An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and stories (...) to show how mathematics meets basic human desires and cultivates virtues essential for human flourishing. Readers will explore mathematical concepts-- and see how mathematical thinking can even fulfill such longings as for love, play, freedom, justice, and community. Some lessons come from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher Jackson's letters to the author appear throughout the book and show how this intellectual pursuit can-- and must-- be open to all. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The View from GadshillFrancis SparshottII once had a furious confrontation with that learned and passionate scholar, the late Milton C. Nahm. He had been giving a paper that involved Falstaff—I forget how, but it included the familiar appeal to the fat knight as the comic spirit of untrammelled life, so that the newly crowned Hal’s final repudiation—“I know thee not, old man”—chills the audience as a denial of humanity (...) in favor of impersonal administration. But I told Nahm that I could not see Falstaff that way. As a boy, if I cycled home from Gravesend to Rochester I had to pass over the North Downs at Gadshill. And it is at Gadshill, when we first meet him, that Falstaff’s gang is planning to waylay a band of innocent travelers. I could never take kindly to a man who made a living mugging and rolling people like me. Nahm was contemptuous of my incompetence to deal with literature: I was prevented from appreciating the portrait of the comic monster, appalling but breathtaking, by my inhibited and inhibiting moralism. But I insisted that I saw no reason why one should abandon one’s identity or one’s morality while one was watching a play or reading a book.Nahm would have been right if I had been insensitive to Falstaff’s outrageousness, his unscrupulous energy and vivacity, his wit and candor. But I think my appreciation was sharpened rather than nullified by my awareness of the real menace Falstaff represents to people who happen not to be his pals. And I think Nahm’s enthusiasm blinded him to something else that Shakespeare wrote into the part. At that very first meeting, we find Falstaff trying to negotiate for himself a position of power or privilege when the young prince shall succeed to the throne. And it is just this negotiation that Falstaff is trying to resume [End Page 398] from the sidewalk at the end, when the new king brushes him off. Nahm did not notice this because it did not occur to him that Henry V was going to be a real king with real power over real people, just as it did not occur to him that Falstaff’s robbed and brutalized pilgrim victims would be real people suffering real injury and loss. If my personal angle, the potential victim’s view, had so usurped my vision that it blinded me to whatever else the playwright had made of his character and its situation, it would have made me a bad viewer of the play. But it might have added depth to my understanding and my criticism if it gave me an angle that other viewers and readers could imaginatively share. 1 Since each of us has some sort of angle on everything, sharing perspectives can always be valuable.III have been reminded of my encounter with Nahm by reading Edward W. Said’s Culture and Imperialism. 2 The book appears to start from the position that imperialism is the “determining political horizon of modern Western culture” (p. 60), imperialism being defined as the policy of establishing and maintaining an empire, and an empire as “a relationship... in which one state controls the effective political sovereignty of another political society” (p. 9). Because this is the determining horizon, the right way to think of any “Western” author is as an agent of imperialism, although of course this is most easily shown in the case of authors and works in which the imperial connection is explicit.If there is to be a uniform curriculum and canon for the teaching of English literature everywhere in the world, that canon obviously should not be based on works that assume the rightness and normality of an imperialism that defines most readers of that literature as racially and culturally inferior; such a canon is itself a tacit agent of an offensive and gratuitous imperialism. This much seems clear. But Said’s book then moves off into a hackneyed recitation of the evils that the West (or the north, or the developed world 3 ) inflicts on a world of passive victims, followed by a denunciation of the... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kant without SadeFrancis SparshottErmanno Bencivenga’s discussion of “Kant’s Sadism” rests on a misrepresentation of Kant’s enterprise. 1 It presents Kantian morality as a matter of motivation, so that reason has to be pitted against desire. But Kant’s whole point is that, because the psychological causes of one’s actions can never be ascertained, they are irrelevant to morality. Morality is entirely a matter of the reasons for one’s actions, no (...) matter what one’s feelings. It is true that moral questions arise, morality exists, only for finite rational beings, who have inclinations that are relatively independent of the dictates of reason. But that independence does not mean that one should always act against one’s inclinations.The morality of an action depends on the agent’s “maxim”—the subjective practical principle on which one acts, the reasons one has and can give for thinking that what one is doing is right. Kant’s whole discussion is in terms of maxims. The word does occur twice in Bencivenga’s paper, but his account makes no use of it. When he says that “It is the motives of the action, the motives the person actually has—never mind what evidence we have for them—that confer moral content on the action” (p. 41), he does so in flat contradiction of Kant.The confusion underlying Bencivenga’s misunderstanding is most familiar to English-language Kantians from Schiller’s joke: “Gladly I serve my friends, but alas I do it with pleasure. / Hence I am plagued with doubt that I am not a virtuous person. // —Surely, your only resource is to try to despise them entirely, / and then with aversion do what your duty enjoins you.” 2 Both participants in the exchange think [End Page 151] the morality of an action depends on its psychological causes, not on the reasons the agent has for thinking the action right and doing it. Both are wrong.What is revolutionary in Kant’s position is his contention that all a maxim requires to be moral is that agents should really make it their principle at the time of action—that the agent should really stand by it. That means, obviously, that at that moment the agent should be able consistently to will that everyone should act on it. Kant argues that it also means, less obviously, that doing the right thing should be one’s paramount principle, which involves treating humanity and human freedom as an end in itself—ultimately, treating oneself and others as “law-making members of a kingdom of ends.” Thus, for Kant, morality is entirely a matter of rational consistency.Since rational consistency is all that morality requires, morality lays down no plan of action, but presupposes the familiar world in which people already have plans and purposes. What one wills is always some particular thing. Morality has to do with the principles to be followed in pursuing these objectives. 3 Bencivenga’s contention that “making the well-being of some other human, or of one’s own community, or of humankind the goal of one’s action would be relegating rationality to (at best) an instrumental role, and thus denying any ethical value to that action” is wrong. Kant insists that finite rational beings inevitably pursue happiness, 4 and it is their duty to do so for others and (in a sense) for themselves. 5 A leading contention of the Critique is that happiness, like duty, is a component of the summum bonum. Making a principle of maximizing happiness does not destroy the autonomy of the will; the principle is a principle and subject to the critique of consistency, like other principles. Kant explicitly denies what Bencivenga asserts, that it is merely an empirical matter that humans are desirous as well as rational. On the contrary, it belongs to their essence. 6 What is empirical, as Kant explains at some length, is the specific content of a person’s desires.Neither of Bencivenga’s examples tends to show that morality is opposed to inclination. It is true that if the reason moral agents treat people well is really only that, on each occasion, this is... (shrink)

This is a major contribution to the theory of rational choice which will be of particular interest to philosophers and economists. The author sets out the foundations of rational choice, and then sketches a dynamic choice framework in which principles of ordering and independence follow from a number of apparently plausible conditions. However, there is potential conflict among these conditions, and when they are weakened to avoid it the usual foundations of rational choice no longer prevail. The thrust of the (...) argument is to suggest that the theory of rational choice is less deterministic than many suppose. (shrink)

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

Plato is perhaps the best known and most widely studied of all the ancient Greek philosophers. A pupil of Socrates and teacher of Aristotle, his ideas have inspired and influenced scholars of nearly every era. His famous series of dialogues have become a standard part of the western philosophical canon – from the Euthyphro and Gorgias of his early period, the Republic, Phaedrus and Symposium of his middle period, to the Theaetetus and Laws of his late period.The Routledge Library Edition (...) makes available in a single set an outstanding range of scholarship devoted to Plato’s philosophical work. Routledge Library Editions:Plato makes available in a single set an outstanding range of scholarship devoted to Plato’s philosophical work. The 21 volumes provide detailed analysis of his writings and philosophical ideas. From the classic works of Francis Cornford, G. C. Field and A.E. Taylor to more recent approaches and interpretations, Routledge Library Editions: Plato provides libraries and scholars with a century of outstanding scholarship on this key philosopher. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.