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.
Any work on Probability by a Cambridge man will be solikely to have its scope and its general treatment of thesubject prejudged, that it may be well to state at the outsetthat the following Essay is in no sense mathematical. Notonly, to quote a common but often delusive assurance, will‘no knowledge of mathematics beyond the simple rules ofArithmetic’ be required to understand these pages, but it isnot intended that any such knowledge should be acquired bythe process of reading them. Of the two or three occasionson which algebraical formulæ occur they will not be found toform any essential part of the text.
The science of Probability occupies at present a somewhatanomalous position. It is impossible, I think, not toobserve in it some of the marks and consequent disadvantagesof a sectional study. By a small body of ardent students ithas been cultivated with great assiduity, and the results theyhave obtained will always be reckoned among the most extraordinaryproducts of mathematical genius. But by thegeneral body of thinking men its principles seem to beregarded with indifference or suspicion. Such persons mayadmire the ingenuity displayed, and be struck with the profundityof many of the calculations, but there seems tovithem, if I may so express it, an unreality about the wholetreatment of the subject. To many persons the mention ofProbability suggests little else than the notion of a set ofrules, very ingenious and profound rules no doubt, with whichmathematicians amuse themselves by setting and solvingpuzzles.
It must be admitted that some ground has been givenfor such an opinion. The examples commonly selected bywriters on the subject, though very well adapted to illustrateits rules, are for the most part of a special and peculiarcharacter, such as those relating to dice and cards. Whenthey have searched for illustrations drawn from the practicalbusiness of life, they have very generally, but unfortunately,hit upon just the sort of instances which, as I shall endeavourto show hereafter, are among the very worst that couldbe chosen for the purpose. It is scarcely possible for anyunprejudiced person to read what has been written about thecredibility of witnesses by eminent writers, without his experiencingan invincible distrust of the principles which theyadopt. To say that the rules of evidence sometimes givenby such writers are broken in