This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.

Anthology of eleven essays by mathematician Hermann Weyl, originally published 1930s-50s.

Hermann Weyl was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in (...) any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World and Mind and Nature, each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life. (shrink)

A new study of the mathematical-physical mode of cognition.

"-- Norman Sieroka, ETH Zurich"This is an important complement to Weyl's Philosophy of Mathematics and Natural Science because most of the pieces in this new..

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Cette section contient les recensions que Rudolf Carnap, Moritz Schlick et Hermann Weyl ont données de l’ouvrage de Hugo Dingler : Physik und Hypothese. Versuch einer induktiven Wissenschaftslehre nebst einer kris­tischen Analyse der Fundamente der Relativitätstheorie [Dingler 1921]. Elles sont traduites par Christophe Bouriau en collaboration avec Oliver Sehlaudt et Gerhard Heinzmann.

Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.

Dedicated to Dana Scott on his sixtieth birthday.It is common knowledge that for a short while Hermann Weyl joined Brouwer in his pursuit of a revision of mathematics according to intuitionistic principles. There is, however, little in the literature that sheds light on Weyl's role and in particular on Brouwer's reaction to Weyl's allegiance to the cause of intuitionism. This short episode certainly raises a number of questions: what made Weyl give up his own program, (...) spelled out in “Das Kontinuum”, how did Weyl come to be so well-informed about Brouwer's new intuitionism, in what respect did Weyl's intuitionism differ from Brouwer's intuitionism, what did Brouwer think of Weyl's views,…? To some of these questions at least partial answers can be put forward on the basis of some of the available correspondence and notes. The present paper will concentrate mostly on the historical issues of the intuitionistic episode in Weyl's career.Weyl entered the foundational controversy with a bang in 1920 with his sensational paper “On the new foundational crisis in mathematics”. He had already made a name for himself in the foundations of mathematics in 1918 with his monograph “The Continuum” [18]; this contained in addition to a technical logical-mathematical construction of the continuum, a fairly extensive discussion of the shortcomings of the traditional construction of the continuum on the basis of arbitrary—and hence also impredicative—Dedekind cuts. (shrink)

Hermann Weyl was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben in the general relativistic framework for the Dirac equation. He preserved the (...) central idea of gauge as a “purely infinitesimal” aspect of symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations. (shrink)

In what seems to have been his last paper, Insight and Reflection (1954), Hermann Weyl provides an illuminating sketch of his intellectual development, and describes the principal influences—scientific and philosophical—exerted on him in the course of his career as a mathematician. Of the latter the most important in the earlier stages was Husserl’s phenomenology. In Weyl’s work of 1918-22 we find much evidence of the great influence Husserl’s ideas had on Weyl’s philosophical outlook—one need merely glance (...) through the pages of Space-Time-Matter or The Continuum to see it. Witness, for example, the following passages from the former. (shrink)

Hermann Weyl as a founding father of field theory in relativistic physics and quantum theory always stressed the internal logic of mathematical and physical theories. In line with his stance in the foundations of mathematics, Weyl advocated a constructivist approach in physics and geometry. An attempt is made here to present a unified picture of Weyl's conception of space-time theories from Riemann to Minkowski. The emphasis is on the mathematical foundations of physics and the foundational significance (...) of a constructivist philosophical point of view. I conclude with some remarks on Weyl's broader philosophical views. (shrink)

"J’aborderai ici de biais la question de l’ «École de l’ETH» dans l’œuvre de Gaston Bachelard, et plus spécifiquement de la figure spectrale d’Hermann Weyl.".

The work addresses the problem of the relationship between science and philosophy in the work of Hermann Weyl. The author begins by discussing Weylls Gottingen tradition. Contrary to standard accounts of this tradition, Edmund Husserl and Georg Cantor are included. The influence of this tradition on Weyl is then illustrated by an examination of Weyl's early philosophy of mathematics. Here Weyl attempts to use Husserl's early phenomenology to amalgamate the thought of Felix Klein, David Hilbert (...) and Cantor. Weyl's "phenomenological period," in which he wrote The Continuum and Space-Time-Matter, is then discussed in detail. The work reveals that for Weyl, philosophy and science, guided by the same telos to construct an objective picture of the world, are involved in a dialectic in which each serves as a corrective and limitation of the other. (shrink)

MATHEMATICS AND PHILOSOPHY ARE CLOSELY LINKED, and several great mathematicians who were at the same time great philosophers come to mind— Pythagoras, Descartes and Leibniz, for instance. One great mathematician of the modern era in whose thinking philosophy played a major role was Hermann Weyl (1885–1955), whose work encompassed analysis, number theory, topology, differential geometry, relativity theory, quantum mechanics, and mathematical logic. His many writings are informed by a vast erudition, an acute philosophical awareness, and even, on occasion, (...) a certain playfulness. No matter what the subject may be—mathematics, physics, philosophy—Weyl’s writing fascinates both by the depth of insight it reveals and by its startling departures from academic convention. Who else would have the daring to liken (as he does in the discussion of Space and Time in his Philosophy of Mathematics and Natural Science), a coordinate system to “the residue of the annihilation of the ego”1? Or then (somewhat further on in the same discussion) to express the belief in the impossibility of a completely objective account of individual consciousness by the assertion “...it is shattered by Judas’ desperate outcry, ‘Why did I have to be Judas?’”2. (shrink)