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14. Science / C. Induction / 6. Bayes's Theorem

[equation showing probability of an inductive truth]

16 ideas
The probability of two events is the first probability times the second probability assuming the first [Bayes]
Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey ,by Davidson]
Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey]
Probabilities can only be assessed relative to some evidence [Dancy,J]
Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]
Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
Bayes seems to rule out prior evidence, since that has a probability of one [Lipton]
Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton]
A hypothesis is confirmed if an unlikely prediction comes true [Lipton]
Explanation may be an important part of implementing Bayes's Theorem [Lipton]
Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton]
Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz]
Bayesian inference is forced to rely on approximations [Thagard]
Bayes produces weird results if the prior probabilities are bizarre [Sider]
Bayesianism claims to find rationality and truth in induction, and show how science works [Bird]
Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]