The PI holds that, given no reason for preferring any of a set of alternatives over any other, all are equally probable. There are cases in which the PI can seemingly be used to justify incompatible probability assignments, due to different ways of conceptualizing the same set of possibilities. These conflicts can generally be resolved by appealing to the principle that the PI should be applied to the most explanatorily fundamental hypotheses. This has applications to the Problem of Induction as well as the mystery of entropy.
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