Science And Method

SCIE E AND METHOD Henri Poincare S HENRI BY A CIENCE A N D I METHOD BY POINCARE. FRANCIS MAITLAND. PREFACE BERTRAND THOMAS LONDON, TRANSLATED BY WITH T H E HON. RUSSELL, F.R.S. NELSON EDINBURGH, AND DUBLIN, & NEW SONS YORK C O N T E N T S PREFACE INTRODUCTION. I. . T H E . . SCIENTIST . . ^ . ' . . . V . « . . c . . . . 15 . 2 5 . 46 I V . CHANCE II. .5', 9 : SCIENCE. I I . T H E F U T U R E OF MATHEMATICS I I I . MATHEMATICAL DISCOVERY —^ 3 AI^D I. T H E SELECTION OF FACTS .. 64 MATHEMATICAL REASONING. I. T H E RELATIVITY OF SPACE 93 117 I I . M A T H E M A T I C A L DEFINITIONS AND EDUCATION I I I . MATHEMATICS AND LOGIC 143 160 I V . T H E N E W LOGICS 177 V . T H E L A S T EFFORTS OF T H E LOGISTICIANS III. T H E NEW MECHANICS. I. MECHANICS A N D R A D I U M 199 I I . MECHANICS A N D OPTICS 213 I I I . T H E N E W MECHANICS A N D ASTRONOMY . . 235 I. T H E M I L K Y W A Y AND T H E T H E O R Y OF GASES . 253 IV. ASTRONOMICAL SCIENCE. I I . F R E N C H GEODESY 270 GENERAL 284 CONCLUSIONS P R E F A C E . agreement, the most eminent scientific man of his generation—more eminent, one is tempted to think, than any man of science now living. From the mere variety of the subjects which he illuminated, there is certainly no one who can appreciate critically the whole of his work. Some conception of his amazing comprehensiveness may be derived from the obituary number of the Revue de Mitaphysique et de Morale (September 1913), where, in the course of 130 pages, four eminent men—a philosopher, a mathematician, an astronomer, and a physicist—tell in outline the contributions which he made to their several subjects. In all we find the same characteristics — swiftness, comprehensiveness, unexampled lucidity, and the perception of recondite but fertile analogies. Poincare's philosophical writings, of which the present volume is a good example, are not those of a professional philosopher: they are the untrammelled reflections of a broad and cultivated mind upon the procedure and the postulates of scientific discovery. The writing of professional philosophers on such subjects has too often the deadness of merely external description; Poincare's writing, on the contrary, as the reader of this book may see in his account of mathematical invention, has the freshness of actual experience, of vivid, intimate contact with what he is HENRI P o i N C A R ^ was, by general 6 PREFACE describing. There results a certain richness and resonance in his words: the sound emitted is not hollow, but comes from a great mass of which only the polished surface appears. H i s wit, his easy mastery, and his artistic love of concealing the labour of thought, may hide from the non-mathem