Just a quick rebuttal of the author's specific points: (1) Given a set of elements X, E(X) = \sum{x \in X} xp(x). The problem the author mentioned is solved, s

Just a quick rebuttal of the author's specific points: (1) Given a set of elements X, E(X) = \sum{x \in X} xp(x). The problem the author mentioned is solved, since we are now summing over all elements in X rather than using the input variable inappropriately. (2) Given sets of elements X and Y, and the set of ALL elements O, then p(X), p(Y), and p(X|Y) are all computed in the same manner. p(X) is shorthand for p(X|O) -- so we are now given three analogous functions, p(X|O), p(Y|O), and p(X|Y). So, Bayes' can be used to compute all three in the exact same manner, if you so wish. The above rebuttals are obviously discrete, but there are analogous continuous variable scenarios.