On the Formal Consistency of the Principal Principle

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Bana, Gergei
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preprint description
Rédei and Gyenis (2013) suggest that Lewis’s Principal Principle is meaningful only if it satisfies certain consistency conditions: starting from any assignment of subjective probabilities (credences) to some algebra of events, we should always be able to extend our algebra with events of the form “the value of the objective probability (chance) of event E is p” and assign subjective probabilities to such events in a consistent manner. We show that this extension is indeed possible in most cases. However, we also argue that this requirement is not necessary: the Principal Principle concerns subjective believes about objective chance, hence events concerning those probabilities are meant to be in the algebra initially, as Lewis’s text suggests clearly.