Probability theory: the logic of science

This is a remarkable book by a remarkable scientist. E. T. Jaynes was a physicist, principally theoretical, who found himself driven to spend much of his life advocating, defending and developing a particular view of probability theory. His interest was triggered in the 1950s by the role of probability in quantum mechanics, the theory that supersedes Newton’s physics on subatomic scales. Quantum mechanics predicts certain things only probabilistically. The theory is a huge success—the predictions it does make have been verified to unprecedented accuracy. But Jaynes realised that to go further, and penetrate the interpretative fog that surrounded quantum theory, a more coherent understanding of probability was needed than he had been taught. Jaynes effectively took the probability p(X |Y ) to represent how strongly the binary proposition X is implied to be true upon supposing that proposition Y is true. The value ofp(X |Y ) depends on relations that are known between the things to which both propositions refer. Jaynes was deeply impressed by a short 1946 paper by the physicist R. T. Cox, (Cox, 1946) which derived the sum and product rules—the ‘laws of probability’—from the laws of Boolean algebra for propositions. From the sum and product rules follows Bayes’ theorem for incorporating the truth of proposition B into what we know about proposition A, given prior informationC phrased propositionally: