On the Formal Consistency of the Principal Principle

Rédei and Gyenis suggest that Lewis’s Principal Principle is meaningful only if it satisfies certain consistency conditions: starting from any assignment of credences to some algebra of events, we must always be able to extend our algebra with events as “the value of the objective chance of event E is p” and assign credences to such events in a consistent manner. I show that this extension is possible. However, I also argue that this requirement is unnecessary: the Principal Principle concerns subjective beliefs about objective chance; hence, events concerning those probabilities are meant to be in the algebra initially.