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Mind and Nature

Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics

Edited and with an introduction by Peter Pesic
Copyright Date: 2009
Pages: 272
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  • Book Info
    Mind and Nature
    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 Natureis 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the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished.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) andMind 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.

    eISBN: 978-1-4008-3332-0
    Subjects: Mathematics, General Science, Physics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Introduction
    (pp. 1-19)
    Peter Pesic

    “It’s a crying shame that Weyl is leaving Zurich. He is a great master.”¹ Thus Albert Einstein described Hermann Weyl (1885–1955), who remains a legendary figure, “one of the greatest mathematicians of the first half of the twentieth century .... No other mathematician could claim to have initiated more of the theories that are now being explored,” as Michael Atiyah put it.² Weyl deserves far wider renown not only for his importance in mathematics and physics but also because of his deep philosophical concerns and thoughtful writing. To that end, this anthology gathers together some of Weyl’s most important...

  4. 1 Electricity and Gravitation 1921
    (pp. 20-24)

    Modern physics renders it probable that the only fundamental forces in Nature are those which have their origin in gravitation and in the electromagnetic field. After the effects proceeding from the electromagnetic field had been coordinated by Faraday and Maxwell into laws of striking simplicity and clearness, it became necessary to attempt to explain gravitation also on the basis of electromagnetism, or at least to fit it into its proper place in the scheme of electromagnetic laws, in order to arrive at a unification of ideas. This was actually done by H. A. Lorentz, G. Mie, and others, although the...

  5. 2 Two Letters by Einstein and Weyl on a Metaphysical Question 1922
    (pp. 25-28)

    Berlin, June 7,1922

    Haberlandstrasse 5

    Dear Sir, Your “Question to Mr. Langevin” provokes me to give an answer. Regarding the general questions that interest you, relativity theory changes nothing at all in the state of affairs because it signifies nothing but an improvement and modification of the basis of the physical-causal world-picture without a change in its fundamental point of view. This is a kind of logical system for representing space-time events in which mental essences (will, feeling, etc.) do not apply directly. To avoid a collision between the various sorts of “realities” that physics and psychology deal with, Spinoza...

  6. 3 Time Relations in the Cosmos, Proper Time, Lived Time, and Metaphysical Time 1927
    (pp. 29-33)

    1. The possible space-time locations or world points form a four-dimensional continuum in the mathematical sense. This already is said to describe a definitestructurein this medium of the external world, if one believes that a splitting of the world into anabsolute spaceand anabsolute timehas an objective meaning in the sense of saying about two separated, strictly limited space-time events that they take place at the same place (for different times) or the same time (for different places). All world points at equal times form a three-dimensionalstratum,all world points at the same place...

  7. 4 The Open World: Three Lectures on the Metaphysical Implications of Science 1932
    (pp. 34-82)

    One common thought holds together the following three lectures: Modern science, insofar as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed but pointing beyond itself. Or, as FranzWerfel expresses it in pregnant wording in one of his poems,

    “Diese Welt ist nicht die Welt allein.”

    Science finds itself compelled, at once by the epistemological, the physical and the constructive-mathematical aspect of its own methods and results, to recognize this situation. It remains to be added that science can do...

  8. 5 Mind and Nature 1934
    (pp. 83-150)

    It shall be the purpose of these lectures to trace a characteristic outline of the mathematical-physical mode of cognition. In doing this I should like to place one theme foremost: the structure of our scientific cognition of the world is decisively determined by the fact that this world does not exist in itself, but is merely encountered by us as an object in the correlative variance of subject and object. The world exists only as that met with by an ego, as one appearing to a consciousness; the consciousness in this function does not belong to the world, but stands...

  9. [Illustrations]
    (pp. 151-161)
  10. 6 Address at the Princeton Bicentennial Conference 1946
    (pp. 162-174)

    During the past three days the various speakers of this conference have discussed the actual state and current problems of our science in all its various branches, and have tried to prolong the lines beyond the present into the future. Will you now lend me your ear for a brief spell in which I shall evoke the past and let my memory roam over same of the outstanding mathematical events of my lifetime? I have reached the age where one likes “to the sessions of sweet silent thought, to summon up remembrance of things past,” and is prone to believe...

  11. 7 Man and the Foundations of Science ca. 1949
    (pp. 175-193)

    One does not miss the mark badly by fixing as the birth date of our science and our philosophy that day when Democritus spoke the following words ringing down the ages: “Sweet and bitter; cold and warm, as well as the colors, all these things exist but in opinion and not in reality(nomōi, ou physei);what really exist are unchangeable particles, atoms, and their motions in empty space.” Indeed, reflecting philosophy is impossible as long as the standpoint of naive realism stands unquestioned, constructive science is impossible as long as one accepts all phenomena at their face value. The...

  12. 8 The Unity of Knowledge 1954
    (pp. 194-203)

    The present solemn occasion on which I am given the honor to address you on our general theme “The Unity of Knowledge” reminds me, you will presently see why, of another Bicentennial Conference, held fourteen years ago by our neighborly university in the city of Brotherly Love. The words with which I started there a talk on “The Mathematical Way of Thinking” sound like an anticipation of today’s topic; I repeat them: “By the mental process of thinking we try to ascertain truth; it is our mind’s effort to bring about its own enlightenment by evidence. Hence, just as truth...

  13. 9 Insight and Reflection 1955
    (pp. 204-222)

    I should like to take this opportunity of describing the part which philosophical reflection, along with scientific insight, has played in my life. Although my work has centered on mathematical research, with occasional detours into theoretical physics, I was always feeling the urge to render a reflective account of the meaning and goal of that research. In a lecture on “The Levels of Infinity,” following upon a discussion of constructive mathematics and reflective metamathematics, I once described their mutual relation in this fashion:

    In the intellectual life of man we find discernibly separated, on the one hand, a sphere of...

  14. Notes
    (pp. 223-240)
  15. References
    (pp. 241-252)
  16. Acknowledgments
    (pp. 253-254)
  17. Index
    (pp. 255-261)