We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, emphasises (...) its refined composition and rigorous internal structure. (shrink)

Thomas S. Kuhn's singular voice was stilled by cancer on June 17, 1996, some 49 years after his initial encounters with past science had drawn him into a career in the history and philosophy of science. One of the most widely-read and influential academics of the 20th century, Kuhn was educated at Harvard University, where he received an S.B. in Physics in 1943 and a Ph.D. in the subject in 1949. He remained there until 1956, first as a Junior Fellow (...) in the Society of Fellows from 1948 to 1951, when he in effect retrained himself as a historian of science, and then as an Assistant Professor of General Education and History of Science. He joined the faculty of the University of California, Berkeley, in 1956, becoming Professor of History of Science in 1961. From 1964 to 1979 he was on the faculty of the History of Science Program of Princeton University, and from 1972 to 1979 also a member of the Institute for Advanced Study. He moved to the Department of Linguistics and Philosophy of Massachusetts Institute of Technology in 1979, where he became Professor Emeritus in 1991. He was President of the History of Science Society in 1968—70 and of the Philosophy of Science Association in 1988–90. He received the George Sarton Medal of the History of Science Society in 1982 and the John Desmond Bernal Award of the Society for the Social Studies of Science in 1983. (shrink)

The book demonstrates for the first time that transculturality – the mixed constitution of cultures – is by no means only a characteristic of the present, but has de facto determined the composition of cultures since time immemorial. This is demonstated using examples from the arts across all cultures and continents.

This book is about the interrelationship between nature, semiosis, metarepresentation and (self-)consciousness, and the role played by metarepresentation in ...

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

Among the most influential and well-known experiments of the 19th century was the generation and detection of electromagnetic radiation by Heinrich Hertz in 1887–1888, work that bears favorable comparison for experimental ingenuity and influence with that by Michael Faraday in the 1830s and 1840s. In what follows, we pursue issues raised by what Hertz did in his experimental space to produce and to detect what proved to be an extraordinarily subtle effect. Though he did provide evidence for the existence of (...) such radiation that other investigators found compelling, nevertheless Hertz’s data and the conclusions he drew from it ran counter to the claim of Maxwell’s electrodynamics that electric waves in air and wires travel at the same speed. Since subsequent experiments eventually suggested otherwise, the question arises of just what took place in Hertz’s. The difficulties attendant on designing, deploying, and interpreting novel apparatus go far in explaining his results, which were nevertheless sufficiently convincing that other investigators, and Hertz himself, soon took up the challenge of further investigation based on his initial designs. (shrink)

Kirchhoff’s 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens’ principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff’s work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel’s results (...) by means of Green’s theorem and function under specific boundary conditions. In the late 1880s, Poincaré uncovered an inconsistency between Kirchhoff’s conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff’s theory—even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation that, however, did not match experimental data better than Kirchhoff’s theory. After all, Kirchhoff’s formula worked quite well in a specific approximation regime. Finally, in 1964, Marchand and Wolf employed the transformation of Kirchhoff’s surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff’s original formulation from Poincaré’s paradox. (shrink)

Most recent work on the nature of experiment in physics has focused on "big science"--the large-scale research addressed in Andrew Pickering's Constructing Quarks and Peter Galison's How Experiments End. This book examines small-scale experiment in physics, in particular the relation between theory and practice. The contributors focus on interactions among the people, materials, and ideas involved in experiments--factors that have been relatively neglected in science studies. The first half of the book is primarily philosophical, with contributions from Andrew Pickering, Peter (...) Galison, Hans Radder, Brian Baigrie, and Yves Gingras. Among the issues they address are the resources deployed by theoreticians and experimenters, the boundaries that constrain theory and practice, the limits of objectivity, the reproducibility of results, and the intentions of researchers. The second half is devoted to historical case studies in the practice of physics from the early nineteenth to the early twentieth century. These chapters address failed as well as successful experimental work ranging from Victorian astronomy through Hertz's investigation of cathode rays to Trouton's attempt to harness the ether. Contributors to this section are Jed Z. Buchwald, Giora Hon, Margaret Morrison, Simon Schaffer, and Andrew Warwick. With a lucid introduction by Ian Hacking, and original articles by noted scholars in the history and philosophy of science, this book is poised to become a significant source on the nature of small-scale experiment in physics. (shrink)

Incommensurability between successive scientific theories—the impossibility of empirical evidence dictating the choice between them—was Thomas Kuhn's most controversial proposal. Toward defending it, he directed much effort over his last 30 years into formulating precise conditions under which two theories would be undeniably incommensurable with one another. His first step, in the late 1960s, was to argue that incommensurability must result when two theories involve incompatible taxonomies. The problem he then struggled with, never obtaining a solution that he found entirely satisfactory, (...) was how to extend this initial line of thought to sciences like physics in which taxonomy is not so transparently dominant as it is, for example, in chemistry. This paper reconsiders incommensurability in the light of examples in which evidence historically did and did not carry over continuously from old laws and theories to new ones. The transition from ray to wave optics early in the nineteenth century, we argue, is especially informative in this regard. The evidence for the theory of polarization within ray optics did not carry over to wave optics, so that this transition can be regarded as a prototypical case of discontinuity of evidence, and hence of incommensurability in the way Kuhn wanted. Yet the evidence for classic geometric optics did carry over to wave optics, notwithstanding the fundamental conceptual readjustment that Fresnel's wave theory required. (shrink)