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Author: Julien Bernard
Publisher: Springer Nature
ISBN: 3030115275
Category : Science
Languages : en
Pages : 433
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Book Description
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
Author: Julien Bernard
Publisher: Springer Nature
ISBN: 3030115275
Category : Science
Languages : en
Pages : 433
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Book Description
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.
Author: Hermann Weyl
Publisher:
ISBN:
Category : Relativity (Physics)
Languages : en
Pages : 380
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Book Description
Author: Hermann Weyl
Publisher: Princeton University Press
ISBN: 1400833329
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Hermann Weyl (1885-1955) 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 (1932) and Mind and Nature (1934), 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.
Author: Claus Beisbart
Publisher: Springer Nature
ISBN: 3030477827
Category : Mathematics
Languages : en
Pages : 277
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Book Description
This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory.
Author: Erhard Scholz
Publisher: Birkhäuser
ISBN: 3034882785
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Historical interest and studies of Weyl's role in the interplay between 20th-century mathematics, physics and philosophy have been increasing since the middle 1980s, triggered by different activities at the occasion of the centenary of his birth in 1985, and are far from being exhausted. The present book takes Weyl's "Raum - Zeit - Materie" (Space - Time - Matter) as center of concentration and starting field for a broader look at his work. The contributions in the first part of this volume discuss Weyl's deep involvement in relativity, cosmology and matter theories between the classical unified field theories and quantum physics from the perspective of a creative mind struggling against theories of nature restricted by the view of classical determinism. In the second part of this volume, a broad and detailed introduction is given to Weyl's work in the mathematical sciences in general and in philosophy. It covers the whole range of Weyl's mathematical and physical interests: real analysis, complex function theory and Riemann surfaces, elementary ergodic theory, foundations of mathematics, differential geometry, general relativity, Lie groups, quantum mechanics, and number theory.
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 048613167X
Category : Mathematics
Languages : en
Pages : 210
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Book Description
This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
Author: Harald A. Wiltsche
Publisher: Springer Nature
ISBN: 3030469735
Category : Science
Languages : en
Pages : 258
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Book Description
This book offers fresh perspective on the role of phenomenology in the philosophy of physics which opens new avenues for discussion among physicists, "standard" philosophers of physics and philosophers with phenomenological leanings. Much has been written on the interrelations between philosophy and physics in the late 19th and early 20th century, and on the emergence of philosophy of science as an autonomous philosophical sub-discipline. This book is about the under-explored role of phenomenology in the development and the philosophical interpretation of 20th century physics. Part 1 examines questions about the origins and value of phenomenological approaches to physics. Does the work of classical phenomenologists such as Husserl, Merleau-Ponty or Heidegger contain elements of systematic value to both the practice and our philosophical understanding of physics? How did classical phenomenology influence “standard” philosophy of science in the Anglo-American and other traditions? Part 2 probes questions on the role of phenomenology in the philosophies of physics and science: - Can phenomenology help to solve “Wigner’s puzzle”, the problem of the "unreasonable effectiveness" of mathematics in describing, explaining and predicting empirical phenomena? - Does phenomenology allow better understanding of the principle of gauge invariance at the core of the standard model of contemporary particle physics? - Does the phenomenological notion of “Lifeworld” stand in opposition to the “scientific metaphysics” movement, or is there potential for dialogue? Part 3 examines the measurement problem. Is the solution outlined by Fritz London and Edmond Bauer merely a re-statement of von Neumann’s view, or should it be regarded as a distinctively phenomenological take on the measurement problem? Is phenomenology a serious contender in continuing discussions of foundational questions of quantum mechanics? Can other interpretational frameworks such as quantum Bayesianism benefit from implementing phenomenological notions such as constitution or horizonal intentionality?
Author: Stefania Centrone
Publisher: Springer
ISBN: 9402411321
Category : Philosophy
Languages : en
Pages : 541
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Book Description
Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486266931
Category : Mathematics
Languages : en
Pages : 258
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Book Description
Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.
Author: M. Capek
Publisher: Springer
ISBN: 9401017271
Category : Science
Languages : en
Pages : 593
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Book Description
