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In the last five years of his life Itamar Pitowsky developed the idea thatthe formal structure of quantum theory should be thought of as a Bayesianprobability theory adapted to the empirical situation that Nature's events justso happen to conform to a non-Boolean algebra. QBism too takes a Bayesianstance on the probabilities of quantum theory, but its probabilities are thepersonal degrees of belief a sufficiently-schooled agent holds for theconsequences of her actions on the external world. Thus QBism has two levels ofthe personal where the Pitowskyan view has one. The differences go further.Most important for the technical side of both views is the quantum mechanicalBorn Rule, but in the Pitowskyan development it is a theorem, not a postulate,arising in the way of Gleason from the primary empirical assumption of anon-Boolean algebra. QBism on the other hand strives to develop a way to thinkof the Born Rule in a pre-algebraic setting, so that it itself may be taken asthe primary empirical statement of the theory. In other words, the hope inQBism is that, suitably understood, the Born Rule is quantum theory's mostfundamental postulate, with the Hilbert space formalism (along with itsperceived connection to a non-Boolean event structure) arising onlysecondarily. This paper will avail of Pitowsky's program, along with itsextensions in the work of Jeffrey Bub and William Demopoulos, to betterexplicate QBism's aims and goals.

Are Non-Boolean Event Structures the Precedence or Consequence of Quantum Probability?