Anti-quantum zealots are like childrenI agree with what he says, except for "intrinsically probabilistic in character". There is no proof that the universe is intrinsically probabilistic. Quantum mechanics describes the universe, but is not intrinsically probabilistic. It is not helpful to think of either as being intrinsically probabilistic.
The more I interact with them, the more I feel that the people who keep on talking about hidden variables, many worlds, pilot waves, mechanisms of collapses etc. – people who refuse to understand that the most fundamental description of the Universe is intrinsically probabilistic in character – resemble children who just can't live with the insight that the tooth fairy was just an illusion, a trick, an approximation in which playful parents are equated with the most divine layer of the Cosmos.
Mathematically, probability is always understood in terms of an underlying measure space. But thinking about that underlying measure space leads to talking about hidden variables and all the other concepts that Lumo rights decries. There is no underlying measure space, as I explain in my FQXi essay.
I would rather say that our most fundamental description of the Universe gives a Hilbert space formalism for predicting observations, but we have no complete mathematization of the Universe itself.