Geometry and Chronometry in Philosophical Perspective

Geometry and Chronometry in Philosophical Perspective

Adolf Grünbaum
Copyright Date: 1968
Edition: NED - New edition
Pages: 392
https://www.jstor.org/stable/10.5749/j.ctttvb9v
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  • Book Info
    Geometry and Chronometry in Philosophical Perspective
    Book Description:

    In this volume Professor Grünbaum substantially extends and comments upon his essay “Geometry, Chronometry, and Empiricism,” which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. Smart wrote in Mind (England): “In my opinion Adolf Grünbaum’s paper … supersedes nearly all that has been written on the logical status of physical geometry and chronometry.” The full text of the essay is given here with the author’s extension of it and his discussion of some of the critical comment it has evoked, particularly, a critique published by Hilary Putnam. Adolph Grünbaum is Andrew Mellon Professor of Philosophy at the University of Pittsburgh and the current president of the Philosophy of Science Association.

    eISBN: 978-0-8166-6274-6
    Subjects: General Science

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. PREFACE
    (pp. vii-viii)
    A. G.
  3. Table of Contents
    (pp. ix-xii)
  4. I GEOMETRY, CHRONOMETRY, AND EMPIRICISM
    (pp. 3-146)

    The moment the mathematical discovery of the non-Euclidean geometries had deprived Euclideanism of its claim touniqueness, the triumph of an empiricist account of physical geometry and chronometry seemed assured. Observational findings were presumed capable, at least in principle, of establishing the unique truth of a particular kind of metric geometry. Ironically, however, it soon became clear that the very mathematical discoveries which had heralded the demise of the classical rationalist and Kantian conceptions of geochronometry were a double-edged sword. Critics were quick to marshal these mathematical results against the renascent geometric empiricists who felt emboldened by their victory over...

  5. II GEOMETRY AND PHYSICS
    (pp. 147-194)

    The clash between Newton’s and Riemann’s conceptions of congruence, discussed in §2(i) of Chapter I and,in much greater detail, in §§2 and 3 of Chapter III, bears on the assessment of the physical import of the hypothesis of a universal nocturnal expansion. And I shall offer such an assessment in the light of that clash. But first I need to amend my articulation of Riemann’s idea that in the case of adiscretemanifold, the congruences (and the metric) can be based on thenumberof elements in parts thereof. In Chapter I (p. 12), I stated that for...

  6. III REPLY TO HILARY PUTNAM’S “AN EXAMINATION OF GRUNBAUM’S PHILOSOPHY OF GEOMETRY”
    (pp. 195-372)

    Referring to my philosophical account of physical geometry and chronometry, EL Putnam says: “Griinbaum has in my opinion failed to give a true picture of one of the greatest scientific advances of all time” [37, p. 211].¹ I have not found one single argument in Putnam’s fifty pages that could serve to sustain this judgment. Nay, reflection on fundamentalmathematicalandphysicalerrors on which he rests much of his case has enabled me to uncover substantial new support for my position from the general theory of relativity and from elsewhere in physics.

    The present chapter will endeavor to set...

  7. INDEX
    (pp. 373-378)