On a Question in the Theory of Probabilities. (Including a letter from Professor Boole).” In Philosophical Magazine, Series 4, Volume 23, No. 155, 1862, pages 361-365.
Cayley, A[rthur].

Spine slightly chipped, otherwise fine. Complete issue in original printed wrappers, uncut and unopened. Octavo. (Item ID: 7075)


In October, 1853, a few months before the publication of The Laws of Thought, Boole’s theory of probability and in particular his treatment of independent causes was criticized by Arthur Cayley, a brilliant mathematician and close friend of Boole, who later developed matrix calculus. Boole replied in a short article, stating that he had a more general approach to the problem, which would be fully developed in The Laws of Thought. It was not. As soon as The Laws of Thought was published, it was attacked by Wilbraham, who argued convincingly that Boole introduced unnecessary assumptions and that those assumptions distorted the results. Boole had labored for several years to overcome the difficulties expressed by Wilbraham, but not too successfully (Keynes, p. 188). In the above paper, Cayley tries to settle the dispute and summarizes the remaining differences between him and Boole. He incorporates a letter from Boole which stubbornly defends Boole’s initial assumptions. Two of the greatest mathematicians of the nineteenth century struggled to define the notion of “independent-causes,” a problem that modern statisticians still find perplexing.

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