From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in (...) which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study. (shrink)

With this issue History and Philosophy of Logic begins its twenty-fifth year of publication. In the years since its founding, by virtue of its high standards and broad scope of coverage, it has bec...

This article critiques efforts to develop curriculum materials that pursue reflective, issues-centered inquiry in the social studies. It finds significant problems in applying rationale to practice. Reviewing Harold Rugg’s 1930s textbooks and materials from the New Social Studies in the 1960s and 70s reveals problems with bias and frame of reference in content selection and presentation. A more recent effort, Reasoning with Democratic Values, controls for these problems but in the process drains the material of emotional impact, relevance, and substantive (...) engagement with the issues. It is questionable whether any of the reviewed materials can meet the goals of their rationales. To develop our students’ abilities to reason independently about ethical issues, it may be unavoidable that we first engage them with emotionally charged material colored by our own frames of reference. If so, careful rationale-building with students is an imperative prerequisite. (shrink)

After John Dewey, Addison W. Moore was recognized as the chief spokesman for the instrumentalist version of pragmatism. Never before available, this complete collection of Moore's work contains dozens of philosophical articles, essays, book reviews, writings by other philosophers, and reviews of his work, together with his book, Pragmatism and its Critics (1910).

Recent reports of the discovery of a “God module” in the human brain derive from the fact that epileptic seizures in the left temporal lobe are associated with ecstatic feelings sometimes described as an experience of the presence of God. The brain area involved has been described as either (a) the seat of an innate human faculty for experiencing the divine or (b) the seat of religious delusions. In fact, religious experience is extremely various and involves many parts of the (...) brain, including some that are prehuman in their evolutionary history and some that are characteristically human. In the continuing integration of such experiences, spiritual formation takes place. Thus the entire human brain might be described as a “God module.” Such a process is only possible because of the brain's complexity. The human brain is the most complex entity for its size that we know of. As used here, complexity is a specialized term denoting the presence of a web of interlinked and significant connections—the more intricate the web, the more complex the entity. Complex systems develop only in a milieu that provides both lawfulness and freedom, and they tend to be self‐organizing, becoming more complex and more effective as a result of both inward and outward experience. The evidence suggests that both personal growth and spiritual growth are processes of complexification of character, and of the brain itself. This thesis is tested in light of the work of William James and James W. Fowler. (shrink)

Book reviewed in this article: The Insanity Defense and the Trial of John W. Hinckley, Jr. By Lincoln Caplan.

Material acquisition—buying, inheriting, being given—and nonmaterial—learning a word, assimilating a form—have been likened, and in both, meaningful acquisition cannot take place without a taxonomy, a scheme of categories into which the acquired element can be fitted. Then with these elements—both material and nonmaterial—we create a world or build and project a self, the painter and the interior decorator equally manipulating the elements in a vocabulary. The coarseness of such an outlook seems to bludgeon away long-established fine distinctions. We need not (...) deny, however, that there may be a kind of "indifference" in regard to "the real existence of the thing" which allows us "to play the part of judge in matters of taste," as Kant would have it,1 we need not deny the existence of an "aesthetic attitude: it is just that such indifference and such an attitude probably don't have much to do with our day-to-day experience of artifacts and perhaps needn't. The "aesthetic attitude" was not long ago defined by Jerome Stolnitz as "disinterested and sympathetic attention to and contemplation of any object of awareness whatever, for its own sake alone."2 Stolnitz is at pains to distinguish the aesthetic attitude from "interests" with which it may be preferable to confuse it. "One of them," he writes, "is the interest in owning a work of art for the sake of pride or prestige". And again, "Another nonaesthetic interest is the 'cognitive,' i.e., the interest in gaining knowledge about an object". Both these interests sound rather acquisitive, and let us consider the "aesthetic attitude" as somehow tied in everyday practice to the bundle of "acquiring" activities. · 1. Immanuel Kant, The Critique of Judgment, trans. James Creed Meredith, p. 43.· 2. Jerome Stolnitz, Aesthetics and the Philosophy of Art Criticism, excerpted in Introductory Readings in Aesthetics, ed. John Hospers, p. 19; all further citations in text. Hiram W. Woodward, Jr. is a lecturer in the department of the history of art at the University of Michigan. He is editor of Eighty Works in the University of Michigan Museum of Art: A Handbook and coeditor of Barabudur: History and Significance of a Buddhist Monument. (shrink)

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Gödel) herausgegebenen "Ergebnisse eines Mathematischen Kolloquiums" zählen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beiträgen von Menger, Gödel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreisträger Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Gödel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst. Außerdem enthält der (...) Band einen biographischen Aufsatz über Karl Menger sowie einen von Menger verfassten Überblick über die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums. (shrink)

Taxation and government policy related to it have only episodic appearance in classical Protestant ethical sources. Of the early sixteenth century reformers, Luther gave most attention to the subject, justifying taxation in general as necessary for the just service of government to the public good and calling the princes to spend tax monies for that good rather than their own luxury. Calvin made much the same claims but called more clearly for official church scrutiny of all government than did Luther. (...) Two centuries later John Wesley criticized English tax policy, appealing to standards of economic efficiency and compassion for the poor with little reference overtly to theology. The churches of colonial and post-revolutionary America developed no systematic, theologically rooted rationale for taxation ethics, either; but official Protestant denominational concern for such ethics has grown measurably in the most recent fifteen years. After a survey of these recent national church statements, and on the basis of them and the slender Protestant heritage on this issue, we end by posing four questions which we see as worthy of much serious thinking by contemporary American Protestant ethicists and church bodies. (shrink)

This is the first book to offer the best essays, articles, and speeches on ethics and intelligence that demonstrate the complex moral dilemmas in intelligence collection, analysis, and operations. Some are recently declassified and never before published, and all are written by authors whose backgrounds are as varied as their insights, including Robert M. Gates, former Director of the Central Intelligence Agency; John P. Langan, the Joseph Cardinal Bernardin Professor of Catholic Social Thought at the Kennedy Institute of Ethics, (...) Georgetown University; and Loch K. Johnson, Regents Professor of Political Science at the University of Georgia and recipient of the Owens Award for contributions to the understanding of U.S. intelligence activities. Creating the foundation for the study of ethics and intelligence by filling in the gap between warfare and philosophy, this is a valuable collection of literature for building an ethical code that is not dependent on any specific agency, department, or country. (shrink)