In this collection of essays one of the preeminent philosophers of science writing offers a reinterpretation of the enduring significance of logical positivism, the revolutionary philosophical movement centered around the Vienna Circle in the 1920s and 30s. Michael Friedman argues that the logical positivists were radicals not by presenting a new version of empiricism but rather by offering a new conception of a priori knowledge and its role in empirical knowledge. This collection will be mandatory reading for any philosopher or (...) historian of science interested in the history of logical positivism in particular or the evolution of modern philosophy in general. (shrink)

Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in (...) mathematics from the early nineteenth century. Much of history is in the details, and much of good history is in tone, emphasis, and the drawing together of different strands. Without being Whiggish, Ferreirós is never far from major synthetic themes, themes that in the main work toward balance and pull back from excesses of emphasis of some recent histories. The main criticism of the book would have to be on matters of broad interpretation. Yet, Ferreirós brings a considerable mathematical acuity and expertise to his enterprise, and this makes his viewpoints the more compelling.” . (shrink)

This essay takes a close look at specially selected features of the Göttingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Göttingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Göttingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation (...) of a special atmosphere that served as a model for several other important centers for mathematical research. Göttingen exemplified a dynamic new way of doing mathematics within a highly competitive community in which the spoken word often carried more weight than did information conveyed in written texts. This oral dimension of the Göttingen culture played an important, till now overlooked role in the early development of Einstein's general theory of relativity. (shrink)

In the history of mathematics and natural philosophy Jacobi's contribution to theoretical mechanics is known as a part of the higher calculus in the tradition of Lagrange: accepted as mathematically important, it was denied to have any substantial physical or philosophical relevance. His last lectures on analytical mechanics, given in 1847–1848, three years before his death, and not yet published, show this view to be no longer tenable. These lectures are the most detailed and genuine source on Jacobi's views concerning (...) the foundations of mechanics. In particular, his criticism of the principles of mechanics is unprecedented for its time and anticipates some of Poincaré's views, published about fifty years later. The prehistory of Jacobi's Analytical Mechanics, a description of its content in general and an outline of his criticism, are presented in this paper. (shrink)

79. This study of the interaction between mechanics and differential geometry does not pretend to be exhaustive. In particular, there is probably more to be said about the mathematical side of the history from Darboux to Ricci and Levi Civita and beyond. Statistical mechanics may also be of interest and there is definitely more to be said about Hertz (I plan to continue in this direction) and about Poincaré's geometric and topological reasonings for example about the three body problem [Poincaré (...) 1890] (cf. also [Poincaré 1993], [Andersson 1994] and [Barrow-Green 1994]). Moreover, it would be interesting to find out how the 19th century ideas discussed here influenced the developments in the 20th century. Einstein himself is a hotly debated case. Yet, despite these shortcommings, I hope that this paper has shown that the interactions between mechanics and differential geometry is not a 20th century invention. Klein's view (see my Introduction) that Riemannian geometry grew out of mechanics, more specifically the principle of least action, cannot be maintained. On the other hand, when Riemannian geometry became known around 1870 it was immediately used in mechanics by Lipschitz. He began a continued tradition in this field, which had several elements in common with the new view of mechanics conceived by the physicists and explicitly carried out by Hertz. Before 1870 we found only scattered interactions between differential geometry and mechanics and only direct ones for systems of two or three degrees of freedom. For more degrees of freedom the geometrical ideas were in some interesting cases taken over by analogy, but these analogies did not lead to formal introduction of geometries of more than three dimensions. (shrink)

This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent role in the transformation of mechanics in the nineteenth century. Such understanding permits a separation from linguistic and arbitrary conventions, thus highlighting its epistemic features and not transforming fundamental principles into mere arbitrary agreements. After addressing the main references in the literature discussing the role of convention (...) in mechanics, we analyze its classical use as a concept originating from law. Then we explain its use by Carl G. Jacobi, Ferdinand F. Reech, and J. Henri Poincaré. Here we also show how their uses conform to the features analyzed regarding conventions in jurisprudence. Finally, we try to explain how the use of this concept, among other factors, contributed to the transformation of mechanics. (shrink)

With over 150 alphabetically arranged entries about key scientists, concepts, discoveries, technological innovations, and learned institutions, the Oxford Guide to Physics and Astronomy traces the history of physics and astronomy from the Renaissance to the present. For students, teachers, historians, scientists, and readers of popular science books such as Galileo's Daughter, this guide deciphers the methods and philosophies of physics and astronomy as well as the historical periods from which they emerged. Meant to serve the lay reader and the professional (...) alike, this book can be turned to for the answer to how scientists learned to measure the speed of light, or consulted for neat, careful summaries of topics as complicated as quantum field theory and as vast as the universe. The entries, each written by a noted scholar and edited by J. L. Heilbron, Professor of History and Vice Chancellor, Emeritus, University of California, Berkeley, reflect the most up-to-date research and discuss the applications of the scientific disciplines to the wider world of religion, law, war, art and literature. No other source on these two branches of science is as informative or as inviting. Thoroughly cross-referenced and accented by dozens of black and white illustrations, the Oxford Guide to Physics and Astronomy is the source to turn to for anyone looking for a quick explanation of alchemy, x-rays and any type of matter or energy in between. (shrink)