In the philosophy of probability there are two central questions we are concerned with.

The first is: what is the correct formal theory of probability? Orthodoxy has it that Kolmogorov’s axioms are the correct axioms of probability. However, we shall see that there are good reasons to consider alternative axiom systems. The second central question is: what do probability statements mean? Are probabilities “out there” in the world, as frequencies, propensities, or some other objective feature of reality, or are probabilities “in the head,” as subjective degrees of belief? We will survey some of the answers that philosophers, mathematicians and physicists have given to these questions.

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