Abstract
The term “probability” is applied to many diverse phenomena, and the existence of a branch of mathematics called “probability theory” suggests that these diverse phenomena can all be understood as applications of the same formal system. Although the different interpretations of probability have many similarities, this similarity is not exact, even at the purely formal level. This chapter shows that the bearers of probability in the propensity, subjective, and logical interpretations of probability are distinct classes of objects, and that this changes the mathematical relations that must hold between conditional and unconditional probabilities. The principles connecting different interpretations of probability have natural modifications that allow the objects of the functions to be different and different relations between conditional and unconditional probability to hold in each.
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