SCIENTIFIC INFERENCE SCIENTIFIC INFERENCE by HAROLD JEFFREYS M. A., D. Sc., F R. S. CAMBRIDGE AT THE UNIVERSITY PRESS 1931 CONTENTS Preface .,....., P a g e vii Chapter I LOGIC AND SCIENTIFIC INFERENCE ... i Chapter II PROBABILITY 8 Chapter III SAMPLING 24 Chapter IV QUANTITATIVE LAWS 36 Chapter V ERRORS 52 Chapter VI PHYSICAL MAGNITUDES 84 Chapter VII MENSURATION 107 Chapter VIII NEWTONIAN DYNAMICS 131 Chapter IX LIGHT AND RELATIVITY 159 VI CONTENTS Chapter X MISCELLANEOUS QUESTIONS . . . page 191 Chapter XI OTHER THEORIES OF SCIENTIFIC KNOWLEDGE . 218 Appendix I PROBABILITY IN LOGIC AND PURE MATHEMATICS . 229 Appendix II INFINITE NUMBERS 232 Appendix III THE ANALYTIC TREATMENT OF THE SINE AND COSINE 237 Lemmas 240 Index 245 PREFACE THE present work had its beginnings in a series of papers published jointly some years ago by Dr Dorothy Wrinch and myself. Both before and since that time several books pur porting to give analyses of the principles of scientific inquiry have appeared, but it seems to me that none of them gives adequate attention to the chief guiding principle of both scientific and everyday knowledge that it is possible to learn from experience and to make inferences from it beyond the data directly known by sensation. Discussions from the philosophical and logical point of view have tended to the con clusion that this principle cannot be justified by logic alone, which is true, and have left it at that. In discussions by physi cists, on the other hand, it hardly seems to be noticed that such a principle exists. In the present work the principle is frankly adopted as a primitive postulate and its consequences are developed. It is found to lead to an explanation and a justification of the high probabilities attached in practice to simple quantitative laws, and thereby to a recasting of the processes involved in description. As illustrations of the actual relations of scientific laws to experience it is shown how the sciences of mensuration and dynamics may be developed. I have been stimulated to an interest in the subject myself on account of the fact that in my work in the subjects of cosmo gony and geophysics it has habitually been necessary to apply physical laws far beyond their original range of verification in both time and distance, and the problems involved in such extrapolation have therefore always been prominent. My thanks are due to the staff of the Cambridge Univer sity Press for their care and courtesy also to Dr Wrinch and Mr M. H. A. Newman, who have read the whole in proof and suggested many improvements. HAROLD JEFFREYS ST JOHNS COLLEGE CAMBRIDGE January 1931 CHAPTER I LOGIC AND SCIENTIFIC INFERENCE Contrariwise, continued Tweedledee, if it was so, it might be and if it were so, it would be but as it isnt, it aint. Thats logic. LEWIS CARROLL, Through the Looking Glass 1-1. The fundamental problem of this work is the question of the nature of scientific inference. The data available to the scientific worker, as well as to the man in the street, are com posed of two classes. The first class consists of the crude data provided by the senses. These will be called sensations. The second class consists of general principles, which determine how the information provided by the senses is to be treated. It is actually treated in two different ways, which may be called description and inference. Description, in the strict sense, would involve only the cataloguing and classification of sensations already experienced. Inference is the use of sen sations already experienced to derive information about sen sations not yet experienced, to construct physical objects, and to describe the past and future of these physical objects. For pure description only an application of the principles of classification and the properties of classes is required these are purely logical ideas. Inference requires much more...