In reading John Venn’s The Logic of Chance, one is struck by two things almost from the outset:
That having been said, this is not a book from which one could reasonably expect to learn the basic principles of probability theory. The prose is dense and only rewards very careful reading.
But it does so remarkably well. Indeed, at many points in the book, I felt a certain “thrill of discovery” after puzzling out what Venn was describing and connecting it back to something I knew well. For example, the treatment of the Law of Large Numbers is far removed from the compact description found in modern texts, but after careful re-reading, one appreciates encountering this old friend in old language.
Part of the appeal of this approach is a scarcity of equations. Certainly the text would pass any reasonable standard of mathematical rigor, but the explanation of the fundamental principles of probability is accomplished through careful exposition rather than a flood of mathematical notation. In that aspect, this historically significant work is at the same time a refreshing look at its subject.
Mark Bollman (firstname.lastname@example.org) is an assistant professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted.
|Physical Foundations of the Science of Probability|
|I.||The Series of Probability|
|II.||Arrangement and Formation of the Series. Laws of Error.|
|III.||Origin or Process of Causation of the Series|
|IV.||How to Discover and Prove the Series|
|V.||The Conception of Randomness|
|Part II.||Logical Superstructure on the Above Physical Foundations|
|VI.||Measurement of Belief|
|VII.||The Rules of Inference in Probability|
|VIII.||The Rule of Succession|
|X.||Chance, Causation, and Design|
|XI.||Material and Formal Logic|
|XII.||Consequences of the Distinctions of the Previous Chapter|
|Part III.||Various Applications of the Theory of Probability|
|XV.||Insurance and Gambling|
|XVI.||Application of Probability to Testimony|
|XVII.||Credibility of Extraordinary Stories|
|XVIII.||On the Nature and Use of an Average, and on the Different Kinds of Average|
|XIX.||The Theory of the Average as a Means of Approximation to the Truth|