Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones.
But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines recently laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones.
Subjective and objective probability emerge at the end of the day as seamlessly interjoined: nothing like this was ever achieved in classical physics. Philosophically it is unprecedented; it will be of interest to philosophers even if quantum mechanics turns out to be false, and the Everett interpretation consigned to physical irrelevance; for the philosophical difficulty with probability has always been to find any conception of what chances are, in physical terms, that makes sence of the role that they play in our rational lives.
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