Rational Self-Doubt - Philosophy

Incoherence of Second-orderPower Set problem:Probability?Assume that the domain of the probability function P is allpropositions of form q, r, etc., and P(q) = x, P(r) = y, and all Booleancombinations thereof.Let S 1 , S 2 , S 3 , … be the subsets of the set of propositions (in the domainof P). For each one, we can construct a distinct proposition (in thedomain of P):P(p) = z if and only if p is a member of S 1 . We’ve just mapped the set of subsets of the propositions into theset of propositions.34