Abstract. In the Theory of Evolution one separates "the fact of evolution" (that species have evolved) from "the theory of evolution" (natural selection, mutations). Softcore critics accept the fact but attack the theory, often replacing it by things divine (hardcore critics attack even the fact).
In my talk I will formalize in precise terms what I believe is the undisputed "fact" of probability - that stochastic things happen. I will then discuss three theories "explaining" that fact: a tautological theory which explains nothing at all, the classical "Kolmogorov" theory (aka "fiction") and the Quantum Probability theory which seems to be the one really running our universe. I will give a beautiful example that underlines the difference between the classical and the quantum theories and discuss the (proper) inclusion of the former by the latter.
This is a service talk. Everything I will talk about is well known and nothing is original, and I will make every effort to make the talk accessible to anyone not afraid of diagonalizing a matrix.
This page is http://www.math.toronto.edu/~drorbn/Talks/UofT-031208/UofT-031208.html.