Geometry and Chronometry in Philosophical Perspective

391 Pages·1968·4.94 MB·English

by  Adolf Grunbaum

GEOMETRY AND CHRONOMETRY IN
PHILOSOPHICAL PERSPECTIVE
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GEOMETRY AND
CHRONOMETRY
IN PHILOSOPHICAL PERSPECTIVE
BY
Adolf Grünbaum
UNIVERSITY OF MINNESOTA PRESS • MINNEAPOLIS
© Copyright 1968 by the University of Minnesota. Chapter I © copyright 1962 by
the University of Minnesota. Chapter III © copyright 1968 by Adolf Grünbaum.
All rights reserved. Printed and bound in the United States of America at The
Colonial Press, Inc., Clinton, Massachusetts
Library of Congress Catalog Card Number: 68-22363
PUBLISHED IN GREAT BRITAIN, INDIA, AND PAKISTAN BY THE OXFORD
UNIVERSITY PRESS, LONDON, BOMBAY, AND KARACHI, AND IN CANADA
BY THE COPP CLARK PUBLISHING CO. LIMITED, TORONTO
To my brother, Norbert Grünbaum, M.D., and
my sister, Suzanne Reines
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PREFACE
An essay of mine on the philosophy of geometry and chronometry
appeared in 1962 as part of the third volume of the Minnesota
Studies in the Philosophy of Science (Scientific Explanation, Space,
and Time, edited by H. Feigl and G. Maxwell). This essay prompted
Hilary Putnam to publish a lengthy critique in 1963 in the second
volume of The Delaware Seminar (Philosophy of Science, edited by
B. Baumrin). The kind proposal by the University of Minnesota
Press to reissue my 1962 essay separately provided me with the
welcome opportunity to publish a detailed reply to Putnam (Chapter
III of the present volume) and an extension of the original essay
(Chapter II), along with the 1962 text on which Putnam rested his
critique (which appears here as Chapter I). Chapter II includes some
corrections of the 1962 essay.
Apart from acknowledgments made within the text, I owe an
immense debt to my physicist colleague Allen I. Janis for invaluable
help with points and examples in Chapter III, §§2, 8, and 9. Further-
more, I had the benefit of discussions with Wilfrid Sellars of issues
relating to Chapter II, §1, and with Wesley Salmon of matters
pertaining to the interpretation of Putnam's views. As is evident
from the length of my reply in Chapter III, I am indebted to Putnam
for the great stimulus which his essay afforded me to clarify my
views both to others and to myself, and to Robert S. Cohen and
Wilfrid Sellars for encouragement to write this reply. To a lesser
extent, this also applies to George Schlesinger with respect to Chapter
vii
Viii GEOMETRY AND CHRONOMETRY IN PHILOSOPHICAL PERSPECTIVE
II. I am also obliged to Elizabeth (Mrs. John H.) McMunn for her
excellent preparation of the typescript, to Jeanne Sinnen of the
University of Minnesota Press for her imaginative and painstaking
editing of the entire manuscript, and to Robert Herrick for his
competent compilation of the index. Chapter II draws on material
in my article "The Denial of Absolute Space and the Hypothesis of
a Universal Nocturnal Expansion," published in the Australasian
Journal of Philosophy (May 1967), and I owe thanks to the editors of
that journal for permission to use the material here. Finally I wish
to thank the National Science Foundation for the support of research
and the following publishers for permission to quote from the works
of their authors: University of California Press (Berkeley), publisher
of Newton's Principia, edited by F. Cajori; Cambridge University
Press, publisher of A. N. Whitehead's The Concept of Nature;
Clarendon Press, publisher of E. A. Milne's Modern Cosmology and
the Christian Idea of God; Dover Publications, Inc., publisher of A.
D'Abro's The Evolution of Scientific Thought from Newton to Einstein
and of D. M. Y. Sommerville's The Elements of Non-Euclidean
Geometry, E. P. Dutton and Company and Methuen and Company,
Ltd., publishers of Einstein's Sidelights on Relativity, translated by
G. B. Jeffery and W. Perrett (in which Einstein's essay "Geometry
and Experience" first appeared); and Interscience Publishers, which
issued The Delaware Seminar: Philosophy of Science, in which Put-
nam's essay appeared.
A. G.
University of Pittsburgh
January 1968
CONTENTS
Chapter I. GEOMETRY, CHRONOMETRY,
AND EMPIRICISM
1. Introduction, page 3
2. The Criteria of Rigidity and Isochronism: The Epistemological Status
of Spatial and Temporal Congruence, page 6
(i) The Clash between Newton's and Riemann's Conceptions of Congruence
and the Role of Conventions in Geochronometry, page 6
(ii) Physical Congruence, Testability, and Operationism, page 30
(iii) The Inadequacies of the Nongeometrical Portion of Riemann's Theory
of Manifolds, page 33
3. An Appraisal of R. Carnap's and H. Reichenbach's Philosophy of
Geometry, page 35
(i) The Status of Reichenbach's 'Universal Forces,' and His 'Relativity of
Geometry,' page 35
(ii) Reichenbach's Theory of Equivalent Descriptions, page 51
(iii) An Error in the Carnap-Reichenbach Account of the Definition of Con-
gruence: The Nonuniqueness of Any Definition of Congruence Furnished by
Stipulating a Particular Metric Geometry, page 52
4. Some Chronometric Ramifications of the Conventionality of Con-
gruence, page 59
(i) Newtonian Mechanics, page 59
(ii) The General Theory of Relativity, page 70
(iii) The Cosmology of E. A. Milne, page 73