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A SERIES OF VOLUMES FOR THE PROMOTION OF SCIENTIFIC RESEARCH AND EDUCATIONAL PROGRESS
SCIENCE AND EDUCATION. A series of volumes for the promotion of scientific research and educational progress.
Volume I. The Foundations of Science. By H. POINCARÉ. Containing the authorised English translation by George Bruce Halsted of "Science and Hypothesis," "The Value of Science," and "Science and Method."
Volume II. Medical Research and Education. By Richard Mills Pearce, William H. Welch, W. H. Howell, Franklin P. Mall, Lewellys F. Barker, Charles S. Minot, W. B. Cannon, W. T. Councilman Theobald Smith, G. N. Stewart, C. M. Jackson, E. P. Lyon, James B. Herrick, John M. Dodson, C. R. Bardeen, W. Ophuls, S. J. Meltzer, James Ewing, W. W. Keen, Henry H. Donaldson, Christian A. Herter, and Henry P. Bowditch.
Volume III. University Control. By J. MCKEEN CATTELL and other authors.
AMERICAN MEN OF SCIENCE. A Biographical Directory.
SCIENCE. A weekly journal devoted to the advancement of science. The official organ of the American Association for the Advancement of Science.
THE POPULAR SCIENCE MONTHLY. A monthly magazine devoted to the diffusion of science.
THE AMERICAN NATURALIST. A monthly journal devoted to the biological sciences, with special reference to the factors of evolution.
SCIENCE AND HYPOTHESIS THE VALUE OF SCIENCE SCIENCE AND METHOD
AUTHORIZED TRANSLATION BY GEORGE BRUCE HALSTED
WITH A SPECIAL PREFACE BY POINCARÉ, AND AN INTRODUCTION BY JOSIAH ROYCE, HARVARD UNIVERSITY
THE SCIENCE PRESS NEW YORK AND GARRISON, N. Y. 1913
PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA.
PAGE Henri Poincaré ix Author's Preface to the Translation 3
CHAPTER I.--On the Nature of Mathematical Reasoning 31 Syllogistic Deduction 31 Verification and Proof 32 Elements of Arithmetic 33 Reasoning by Recurrence 37 Induction 40 Mathematical Construction 41
CHAPTER II.--Mathematical Magnitude and Experience 43 Definition of Incommensurables 44 The Physical Continuum 46 Creation of the Mathematical Continuum 46 Measurable Magnitude 49 Various Remarks (Curves without Tangents) 50 The Physical Continuum of Several Dimensions 52 The Mathematical Continuum of Several Dimensions 53