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)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (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)

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain features.

Rooted in the field of cathedral studies, this paper draws into dialogue three bodies of knowledge: Edward Bailey’s notion of implicit religion that, among other things, highlights the continuing traction of the Christian tradition and Christian practice within secular societies; David Walker’s notion of the multiple ways through which in secular societies people may relate to the Christian tradition as embodied within the Anglican Church and John Fisher’s notion of spiritual wellbeing as conceptualised in relational terms. Against this conceptual (...) background, this paper draws on data provided by 1234 participants attending one of the Christmas Eve carol services in Liverpool Cathedral to explore the perceived impact of attendance on the spiritual health of people who do not believe in God and yet feel that Liverpool Cathedral is their cathedral, and it is this sense of belonging that brings them back at Christmas time.Contribution: Situated within the science of cathedral studies, this paper links in an original way three fields of discourse: Edward Bailey’s notion of implicit religion, David Walker’s notion of the four ways of belonging to God facilitated by the Anglican Church and John Fisher’s conceptualisation and operationalisation of the notion of spiritual wellbeing. The hypothesis developed from this original integration of theoretical perspectives is then tested empirically on data provided by 404 participants at carol services who do not believe in God. (shrink)

This essay is a review of Edward Feser’s Aquinas: A Beginner’s Guide. In the first part, the author summarizes the book’s five chapters, drawing attention to Feser’s application of Aquinas’s thought to contemporary philosophical problems. Part 2 is dedicated to Feser’s Thomistic analysis of Intelligent Design. The author explains Feser’s case and why Aquinas’s “Fifth Way,” which is often labeled a “design argument,” depends on a philosophy of nature that ID’s methods implicitly reject.

“Principium Sapientiae. Los orígenes del pensamiento filosófico griego” fue publicado póstumamente en 1952 y estaba prácticamente acabado, a salvo de algunos aspectos de los capítulos finales, cuando a Cornford le sobrevino la muerte. La edición ha sido preparada por W. K. C. Guthrie, que ha añadido una breve introducción y un apéndice. “Principium Sapientiae” ofrece una perspectiva general sobre el pensamiento de su autor a la vez que añade material nuevo a los trabajos anteriores. Hoy es ya una obra clásica.

The history of yoga -- Yoga prior to Patañjali -- The Vdic period -- Yoga in the Upanisads -- Yoga in the Mahabharata -- Yoga and Sankhya -- Patañjali's yoga -- Patañjali and the six schools of Indian philosophy -- The Yoga sutras as a text -- The commentaries on the Yoga sutras -- The subject matter of the Yoga sutras -- The dualism of yoga -- The Sankhya metaphysics of the text -- The goals of yoga -- The eight (...) limbs of yoga -- The present translation and commentary -- Meditative absorption -- Practice -- Mystic powers -- Absolute independence. (shrink)

Change happens, sometimes predictably as with demographic patterns, sometimes unpredictably as with the fall of the Berlin Wall, sometimes gradually and sometimes suddenly and violently. Cass R. Su...

Change happens, sometimes predictably as with demographic patterns, sometimes unpredictably as with the fall of the Berlin Wall, sometimes gradually and sometimes suddenly and violently. Cass R. Su...

Quiero examinar dos tesis opuestas acerca de la posibilidad de comprender el arte de otras culturas: 1. La tesis según la cual hay una dificultad inherente e insupera-ble en la comprensión del arte de las culturas distintas de la propia. Esta tesis nace de la creencia de que, puesto que el arte es la expresión de significados y sentimientos que pertenecen a esa cultura, el observador externo no puede ni siquiera empezar a comprender tal arte en cuanto que lo que (...) expresa está fuera de su experiencia. 2. La tesis clásica según la cual el arte es único al ser un "lenguaje" universal; tesis defendida por la noción de Kant de una comunidad del gusto y por la de Hegel de un espíritu universal. (shrink)

Pitanja filozofskog razumijevanja i pravednosti bitno su povezana od samih početaka grčkog filozofiranja. Baš kao što filozofska heremenutika ili hJrmeneiva ima svoj pretfilozofski izvor u grčkome bogu Hermesu, platoničko razumijevanje pravednosti ima ga u božici Dike. U svojoj ambivalentnosti Hermes tako naznačuje mogućnost razumijevanja kao i mogućnosti zavođenja ili zloupotrebe razumijevanja, koje – u horizontu sokratičke i platoničke filozofije – znači zapravo nedostatak razumijevanja. U platoničkoj filozofiji, naime, spoznaja i etički stav blisko su povezani. Ali ako se taj etički stav (...) ponajvećma razumije kao pravičnost, potonja se ne smije razumjeti u ponešto reduciranom značenju slaganja ljudskih djelovanja s državnim zakonima; ono čime se trebamo baviti jest unutarnje slaganje i harmonija čovjeka i njegove duše, a što također znači slaganje čovjeka sa svijetom u kojemu živi. S tog gledišta, potencijalni hermeneutički ‘an-arhizam’ može se ponovno – ovoga puta drukčije – usmjeriti prema pitanju ajrchv i transponirati iz sfere puke teorije u samo biće ljudskoga života, koje se – u platoničkoj filozofiji – tretira kroz pitanje o duši. (shrink)

This essay is a review of Edward Feser’s Aquinas: A Beginner’s Guide. In the first part, the author summarizes the book’s five chapters, drawing attention to Feser’s application of Aquinas’s thought to contemporary philosophical problems. Part 2 is dedicated to Feser’s Thomistic analysis of Intelligent Design (ID). The author explains Feser’s case and why Aquinas’s “Fifth Way,” which is often labeled a “design argument,” depends on a philosophy of nature that ID’s methods implicitly reject.