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The Logic of Chance

John Venn
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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In reading John Venn’s The Logic of Chance, one is struck by two things almost from the outset:

  1. The English language, as it is used to describe mathematics, has undergone some changes since 1888 when this book first appeared.
  2. Venn was a master of written English (and definitely much more than “that diagram guy”).

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 ( 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.


Part I.
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
IX. Induction
X. Chance, Causation, and Design
XI. Material and Formal Logic
XII. Consequences of the Distinctions of the Previous Chapter
XIII. On Modality
XIV. Fallacies
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