Produced by Juliet Sutherland, Andrew D. Hwang, and the Online Distributed Proofreading Team at http://www.pgdp.net. Transcriber's Note Minor typographical errors and irregularities have been corrected. Footnotes have been numbered sequentially within chapters and moved to the end of each chapter. THE LOGIC OF CHANCE AN ESSAY ON THE FOUNDATIONS AND PROVINCE OF THE THEORY OF PROBABILITY, WITH ESPECIAL REFERENCE TO ITS LOGICAL BEARINGS AND ITS APPLICATION TO MORAL AND SOCIAL SCIENCE AND TO STATISTICS, BY JOHN VENN, Sc.D., F.R.S., FELLOW AND LECTURER IN THE MORAL SCIENCES, GONVILLE AND CAIUS COLLEGE, CAMBRIDGE. LATE EXAMINER IN LOGIC AND MORAL PHILOSOPHY IN THE UNIVERSITY OF LONDON. "So careful of the type she seems So careless of the single life." _THIRD EDITION, RE-WRITTEN AND ENLARGED._ London: MACMILLAN AND CO. AND NEW YORK 1888 [_All Rights reserved._] _First Edition printed_ 1866. _Second Edition_ 1876. _Third Edition_ 1888. PREFACE TO FIRST EDITION Any work on Probability by a Cambridge man will be so likely to have its scope and its general treatment of the subject prejudged, that it may be well to state at the outset that the following Essay is in no sense mathematical. Not only, to quote a common but often delusive assurance, will 'no knowledge of mathematics beyond the simple rules of Arithmetic' be required to understand these pages, but it is not intended that any such knowledge should be acquired by the process of reading them. Of the two or three occasions on which algebraical formulæ occur they will not be found to form any essential part of the text. The science of Probability occupies at present a somewhat anomalous position. It is impossible, I think, not to observe in it some of the marks and consequent disadvantages of a _sectional_ study. By a small body of ardent students it has been cultivated with great assiduity, and the results they have obtained will always be reckoned among the most extraordinary products of mathematical genius. But by the general body of thinking men its principles seem to be regarded with indifference or suspicion. Such persons may admire the ingenuity displayed, and be struck with the profundity of many of the calculations, but there seems to them, if I may so express it, an _unreality_ about the whole treatment of the subject. To many persons the mention of Probability suggests little else than the notion of a set of rules, very ingenious and profound rules no doubt, with which mathematicians amuse themselves by setting and solving puzzles.