Quantum Mechanics as a Theory of Probability

We examine two quite different threads in Pitowsky’s approach to the measurement problem that are sometimes associated with his writings. One thread is an attempt to understand quantum mechanics as a probability theory of physical reality. This thread appears in almost all of Pitowsky’s papers (see for example 2003, 2007). We focus here on the ideas he developed jointly with Jeffrey Bub in their paper ‘Two Dogmas About Quantum Mechanics’ (2010) (See also: Bub (1977, 2007, 2016, 2020); Pitowsky (2003, 2007)). In this paper they propose an interpretation in which the quantum probabilities are objective chances determined by the physics of a genuinely indeterministic universe. The other thread is sometimes associated with Pitowsky’s earlier writings on quantum mechanics as a Bayesian theory of quantum probability (Pitowsky 2003) in which the quantum state seems to be a credence function tracking the experience of agents betting on the outcomes of measurements. An extreme form of this thread is the so-called Bayesian approach to quantum mechanics. We argue that in both threads the measurement problem is solved by implicitly adding structure to Hilbert space. In the Bub-Pitowsky approach we show that the claim that decoherence gives rise to an effective Boolean probability space requires adding structure to Hilbert space. With respect to the Bayesian approach to quantum mechanics, we show that it too requires adding structure to Hilbert space, and (moreover) it leads to an extreme form of idealism.