We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

Kirsten Walsh has criticized my interpretation of Newton’s view on the certainty of his new science of color, namely, that it shifted through his long career from one of certainty to probabilism. I...

The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)

My talk today will be about Newton’s avowed methodology, and specifically the place of experiment in his conception of science, and how his ideas changed significantly over the course of his career. I also want to look at his actual scientific practice and see how this influenced his views on the nature of the experimental sciences.

Simon Schaffer has published a constructivist analysis of the acceptance of Newton’s theory of color that focuses on Newton’s experiments, the continual controversies over them, and his power and authority. In this article, I show that Schaffer’s account does not agree with the historical evidence. Newton’s theory was accepted much sooner than Schaffer holds, when and in places where Newton had little power; many successfully repeated the experiments and few contested them; and theory mattered more than experiment in acceptance. I (...) also present an alternative account of the acceptance of Newton’s theory that shows that, despite criticism when it was first published in 1672, the theory, or parts of it, gradually came to be accepted by mathematical scientists—including Huygens and Leibniz—and Scottish natural philosophers by the time of the publication of the Opticks in 1704. On the Continent, it was coming to be accepted within a decade or so after its publication, that is, before 1716, when Newton replied to a challenge, purportedly by Leibniz, that Schaffer sees as the crucial conflict that at last gave Newton’s experiments their authority. (shrink)

In developing a new theory of vision in Ad Vitellionem paralipomena Kepler introduced a new optical concept, pictura, which is an image projected on to a screen by a camera obscura. He distinguished this pictura from an imago, the traditional image of medieval optics that existed only in the imagination. By the 1670s a new theory of optical imagery had been developed, and Kepler's pictura and imago became real and virtual images, two aspects of a unified concept of image. The (...) new concept of image developed out of a synthesis of Kepler's determination of the geometrical location of a pictura as the limit, or focus, of refracted pencils of rays and the triangulation used by a single eye to determine the perceived location of an imago. The distinction between real and imaginary images was largely developed by Gilles Personne de Roberval and the Jesuits Francesco Eschinardi and Claude François Milliet Dechales. (shrink)

The book is a collection of essays on the history of science and mathematics, with especial emphasis on Newtonian themes.

Newton se rehusó a usar el término “filosofía experimental”, ampliamente usado en la Inglaterra de la Restauración al comienzo de su carrera, hasta 1712 cuando añadió un pasaje al Escolio General de los Principia que exponía brevemente su metodología anti-hipotética. No obstante, los borradores para la Cuestión 23 de la segunda edición de la Óptica (1706) (que se convertiría en la Cuestión 31 en la tercera edición) muestran que con anterioridad había intentado introducir el término para explicar su metodología. Newton (...) introdujo el término por propósitos polémicos para defender su teoría de la gravedad contra las críticas de los cartesianos y los leibnizianos pero, especialmente en los Principia, contra Leibniz mismo. La "filosofía experimental" tiene poco que ver directamente con el experimento, sino que más bien designa de manera más amplia la ciencia empírica. Los manuscritos de Newton proporcionan la oportunidad de comprender el uso que hace de la “filosofía experimental” y la formulación de su metodología, especialmente de términos claves como “deducir”, “inducción” y “fenómenos”, a comienzos del siglo XVIII. (shrink)

[…] Open the pages of almost any national journal or magazine, and where ten years ago one found only one or another kind of free verse lyric, one now finds well rhymed quatrains, sestinas, villanelles, sonnets, and blank verse dramatic monologues or meditations.1 In a recent issue of the New Criterion, Robert Richman describes this rekindled interest in formal verse among younger poets as a return to the high seriousness, eloquence, and technical fluency that characterized the best achievements of American (...) poetry forty years ago.2 As Mr. Richman numbers me among the younger poets working in form, I ought to be as cheered by these developments as he is. Yet I am anything but cheered. And not because I don’t want to belong to club that would have me as a member, though this may be a part of it; but because I suspect that what Mr. Richman hails as a development may in fact be nothing but a mechanical reaction, and that the new formalists, in rejecting the sins of their experimental fathers may end up merely repeating the sings of their New Critical grandfathers, resuscitating the stodgy, overrefined conventions of the “fifties poem,” conventions which were of course sufficiently narrow and restrictive to provoke rebellion in the first place. Any reform, carried to uncritical extremes by lesser talents who ignore rather than try to assimilate the achievements of their predecessors, will itself require reformation. If James Wright, say, or Robert Bly, produced more than their fair share of imitators, if they even imitate themselves much of the time, they nonetheless have written poems all of us can and ought to learn from. Maybe we have had too much of the “raw” in recent years. But the answer to the raw is not the overcooked. Besides, it’s dangerous to think we have to choose exclusively between free verse and form. The wider the range of styles and forms that we avail ourselves of, the more enriched, more flexible and inclusive our expressive resources will be. It’s as important for those who work in form to be familiar with the experiments and innovatins of the last hundred years as it is for those who work in looser measures to be familiar with traditional verse forms that go back beyond the twentieth century. Alan Shapiro’s most recent book of poems, Happy Hour, was published this year. (shrink)

A collection of essays on the situation of poetry in contemporary American culture, from Shapiro's multiple perspectives as poet (four volumes), teacher of poetry (U. of North Carolina, Greensboro), and reader. A TriQuarterly book. Annotation copyright by Book News, Inc., Portland, OR.

The collected essays in this volume encompass a wide-ranging spectrum of philosophical, scientific, and literary topics as they relate to the theory and strategy of interpretation.

The 300th anniversary of the publication of Isaac Newton’s Opticks in 1704 provides an occasion to review the history of its composition and publication. As a preliminary to presenting that history, Newton’s attitude to publication and response to criticism are examined. Newton’s clashes with Hooke and his presumed role as the cause of the delay in the publication of the Opticks until after his death are also scrutinized. Rather than simply presenting Newton and Hooke as quarrelsome, which they indeed were, (...) they are presented as rivals to be England’s leading optical authority. Although Newton announced his intention to publish a book very much like the Opticks in the winter of 1675–76, he did not begin to write it until 1687. It was composed in various stages, including new experimental investigations, by 1692, except for the part on diffraction. A planned, but unfulfilled, revision of the part on diffraction was responsible for delaying its publication for a number of years. (shrink)

In this astonishingly rich volume, experts in ethics, epistemology, philosophy of mind, political theory, aesthetics, history, critical theory, and hermeneutics bring to light the best philosophical scholarship on what is arguably Nietzsche's most rewarding but most challenging text. Including essays that were commissioned specifically for the volume as well as essays revised and edited by their authors, this collection showcases definitive works that have shaped Nietzsche studies alongside new works of interest to students and experts alike. A lengthy introduction, annotated (...) bibliography, and index make this an extremely useful guide for the classroom and advanced research. (shrink)

These are the abstracts of papers for the conference, History Unveiled Science Unfettered: A Conference in Celebration of James E. McGuire University of Pittsburgh, January 19, 2002.