The theory of probability can be formulated in set-theoretical terms. Or in the language of propositional logic. 'The difference between the two approaches is important, since they assign probabilities to different kinds of things. If we use the first set of axioms we assign probabilities to events, that is, things that take place in the external world. The second set assigns probabilities to linguistic entities, viz. propositions'.
Peterson, M. 2009. An introduction to decision theory. Cambridge: University Press, 121.
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