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Bayes set out his theory of probability in Essay towards solving a problem in the doctrine of chances published in the Philosophical Transactions of the Royal Society of London in 1764. His conclusions were accepted by Laplace in a 1781 memoir, rediscovered by Condorcet (as Laplace mentions), and remained unchallenged until Boole questioned them in the Laws of Thought . Since then Bayes' techniques have been subject to controversy.
Bayes also wrote an article An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (1736) attacking Berkeley for his attack on the logical foundations of the calculus.
Bayes was elected a Fellow of the Royal Society in 1742 despite the fact that at that time he had no published works on mathematics, indeed none were published in his lifetime.
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