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)

In spite of its success, Neo-Darwinism is faced with major conceptual barriers to further progress, deriving directly from its metaphysical foundations. Most importantly, neo-Darwinism fails to recognize a fundamental cause of evolutionary change, “niche construction”. This failure restricts the generality of evolutionary theory, and introduces inaccuracies. It also hinders the integration of evolutionary biology with neighbouring disciplines, including ecosystem ecology, developmental biology, and the human sciences. Ecology is forced to become a divided discipline, developmental biology is stubbornly difficult to reconcile (...) with evolutionary theory, and the majority of biologists and social scientists are still unhappy with evolutionary accounts of human behaviour. The incorporation of niche construction as both a cause and a product of evolution removes these disciplinary boundaries while greatly generalizing the explanatory power of evolutionary theory. (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...

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)

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

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)

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)

Perhaps only Tar Baby is as enigmatic and compelling a figure from Afro-American mythic discourse as is that oxymoron, the Signifying Monkey.3 The ironic reversal of a received racist image of the black as simianlike, the Signifying Monkey—he who dwells at the margins of discourse, ever punning, ever troping, ever embodying the ambiguities of language—is our trope for repetition and revision, indeed, is our trope of chiasmus itself, repeating and simultaneously reversing in one deft, discursive act. If Vico and Burke, (...) or Nietzsche, Paul de Man, and Harold Bloom, are correct in identifying “master tropes,” then we might think of these as the “master’s tropes,” and of signifying as the slave’s trope, the trope of tropes, as Bloom characterizes metalepsis, “a trope-reversing trope, a figure of a figure.” Signifying is a trope that subsumes other rhetorical tropes, including metaphor, metonymy, synecdoche, and irony, and also hyberbole, litotes, and metalepsis. To this list, we could easily add aporia, chiasmus, and catachresis, all of which are used in the ritual of signifying.The black tradition has its own subdivisions of signifying, which we could readily identify with the typology of figures received from classical and medieval rhetoric, as Bloom has done with his “maps of misprision.” In black discourse “signifying” means modes of figuration itself. When one signifies, as Kimberly W. Benston puns, one “tropes-a-dope.” The black rhetorical tropes subsumed under signifying would include “marking,” “loud-talking,” “specifying,” “testifying,” “calling out”, “sounding,” “rapping,” and “playing the dozens.”4 3. On Tar Baby, see Ralph Ellison, “Hidden Man and Complex Fate: A Writer’s Experience in the United States,” Shadow and Act, p. 147, and Toni Morrison, Tar Baby. On the black as quasi-simian, see Jean Bodin, Method for the Easy Comprehension of History, trans. Beatrice Reynolds, p. 105; Aristotle Historia Animalium 606b; Thomas Herbert, Some Years Travels, pp. 16-17; and John Locke, An Essay Concerning Human Understanding, 8th ed., 2 vols., 2:53.4. Geneva Smitherman defines these and other black tropes and then traces their use in several black texts. Smitherman’s work, like that of Claudia Mitchell-Kernan and Abrahams, is especially significant for literary theory. See Smitherman, Talkin and Testifyin: The Language of Black America, pp. 101-66. See also nn. 13 and 14 below. (shrink)

So, on 22 July 1865, under the title ‘Philosophy and Punch’, did England's premier comic weekly greet the election of J. S. Mill as MP for Westminster. Mill held his seat for only one term, until the general election of 1868, when his Whig-Liberal colleague Robert Wellesley Grosvenor was re-elected, but Mill was replaced by the loser in 1865, the Conservative W. H. Smith, Jr., who, though he never went to sea, became the ruler of the Queen's navy. The reasons (...) for that reversal have engaged the attention of many, including Mill himself; I should like to introduce into the discussion material from an ignored source, the comic weeklies, which took a continued and close look at Mill's behaviour during his parliamentary years. While this evidence generally does not disconfirm earlier judgments—including my own— it does more than merely add to the induction. First, it shows how different political stances led journals to focus on different aspects of Mill's parliamentary career, and to adopt different rhetorical strategies in portraying him in picture and word. Second, it demonstrates how the hardening of party allegiances during the parliament of 1865–68, which accelerated in the preparatory campaigns for the general election of 1868, affected Mill adversely. Third, it suggests strongly that it was not his ‘crotchets’ or ‘whims’, especially women's suffrage and proportional representation, that damaged his chances for re-election, but his advocacy of causes unpopular with the majority of Liberals as well as with Conservatives. (shrink)