Rational Self-Doubt - Philosophy

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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
SolutionsTyped theory?Re-CalWon’t do the jobP f (q) = P i (q/P i (q) = x . PR(q/P i (q) = x) = y) = y The class of propositions is not a set.But then probability must be definable on proper classes.It is:Rubin, Herman, A new approach to the foundations of probability.1969 Foundations of Mathematics (Symposium CommemoratingKurt Gödel, Columbus, Ohio, 1966) pp. 46--50 Springer, New York35
Page 1 and 2: Rational Self-DoubtSherri RoushDepa
Page 4 and 5: Judgmental Self-DoubtSecond-guessin
Page 6 and 7: Evidence about q vs. evidence about
Page 8 and 9: Terms - 1 st - and 2 nd - order evi
Page 10 and 11: What is the rational thing to do?1)
Page 12 and 13: Second-Order ProbabilitiesA second-
Page 14 and 15: The Principle that Gets in the WayP
Page 16 and 17: Restricted Self-Respect (RSR)P(q/P(
Page 18 and 19: Unrestricted Self-Respect (USR)P(q/
Page 20 and 21: Expressing the QuandaryExplicitly:P
Page 22 and 23: Expressing the QuandaryExplicitly:P
Page 24 and 25: Principal PrincipleP(q/PR(q) = y .
Page 26 and 27: What’s good for the goose is good
Page 28 and 29: Calibration and Re-calibrationCal(s
Page 30 and 31: Taking StockSupposed reasons to ign
Page 32 and 33: Incoherence of Cal?1. P(q) = x,2. P
Page 36 and 37: Taking StockSupposed reasons to ign
Page 38 and 39: Regress and PathologyRe-CalP f (q)
Page 40 and 41: Regress and Pathology - NoRe-CalP f
Page 42 and 43: Distorting in the long run?The (Pri
Page 44 and 45: Likelihood Ratio Convergence Theore
Page 46 and 47: PointSeidenfeld: Why bother with th
Page 48 and 49: Re-Cal Re-capNews about reliability
Page 50: Assume:P(q) = xP(P(q) = x) = 1By de

Rational Self-Doubt - Philosophy

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