The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age, very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of (...) mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga. (shrink)

This response to a variety of criticisms of _Charles Peirce and Modern Science_ restates and attempts to clarify and explain major themes of the book.

The following paragraphs were written not for print publication but for oral delivery on a celebratory occasion; their many unsupported assertions, some commonplace and some controversial, were made not to prove a thesis but to suggest a point of view—a perspective on Peirce's thought that might be taken, or not, as one wishes. The suggestion is that some difficulties are resolved and some things fall into place if we view his philosophy in its several relations to modern science. For that (...) purpose, his idea of science is of central importance and it is that idea only that I discuss here. Although drawn from the historical fact of modern science, Peirce's concept of science is unusual, radical, and difficult. In... (shrink)

My purpose in what follows is not so much to defend the basic principle of utilitarianism as to indicate the form of it which seems most promising as a basic moral and political position. I shall take the principle of utility as offering a criterion for two different sorts of evaluation: first, the merits of acts of government, social policies, and social institutions, and secondly, the ultimate moral evaluation of the actions of individuals. I do not take it as implying (...) that the individual should live his life on the basis of constant evaluations of this sort. For there are different levels of decision making each with its appropriate criteria. For example, we each inevitably make many of our decisions from the point of view of our own personal self-fulfilment and this cannot regularly take a directly utilitarian form, nor should the utilitarian want it to do so. His claim is at most that we should sometimes review our life from the point of view of a kind of impersonal moral truth of a universalistic utilitarian character. (shrink)

In this book, T. L. Short corrects widespread misconceptions of Peirce's theory of signs and demonstrates its relevance to contemporary analytic philosophy of language, mind and science. Peirce's theory of mind, naturalistic but nonreductive, bears on debates of Fodor and Millikan, among others. His theory of inquiry avoids foundationalism and subjectivism, while his account of reference anticipated views of Kripke and Putnam. Peirce's realism falls between 'internal' and 'metaphysical' realism and is more satisfactory than either. His pragmatism is not verificationism; (...) rather, it identifies meaning with potential growth of knowledge. Short distinguishes Peirce's mature theory of signs from his better-known but paradoxical early theory. He develops the mature theory systematically on the basis of Peirce's phenomenological categories and concept of final causation. The latter is distinguished from recent and similar views, such as Brandon's, and is shown to be grounded in forms of explanation adopted in modern science. (shrink)

As the editor noted in the last number Freddie Ayer, or Professor Sir Alfred Ayer, played a considerable part in launching the vast enterprise of the Bentham edition. It is fitting, therefore, that something be said in Utilitas about his achievement as a philosopher and the extent to which he falls within the same broad empiricist and utilitarian tradition to which Bentham and J. S. Mill belonged.

In the postscript to The Varieties of Religious Experience William James distinguishes two types of belief in the supernatural, conceived as an essential component in religion, crass or piecemeal supernaturalism, on the one hand, and refined supernaturalism on the other.

As is well known, many editors, following Valckenaer, reject the bracketed line altogether; but the omission leaves the opening clause with a very unsatisfactory ending. μπρέποντας αίθέρι, heavily stressed by its position, seems to form little less than an anticlimax, unless we assume that the stars could hardly be expected to shine in the sky. On the other hand, when line 7 is added, έμπρέποντας αίθέρ στέρας brings out clearly the fact that only certain conspicuous stars or constellations are meant—those (...) which serve as guides to the operations of agriculture and navigation, such as the Pleiades, Arcturus, and Orion, as we may see from Hesiod, Op. 609 onwards. (shrink)