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

#### [equation showing probability of an inductive truth]

19 ideas
 14280 The probability of two events is the first probability times the second probability assuming the first [Bayes]
 22656 Trying to assess probabilities by mere calculation is absurd and impossible [James]
 19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
 19155 Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson]
 2751 Probabilities can only be assessed relative to some evidence [Dancy,J]
 2798 Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]
 2799 Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
 16801 A hypothesis is confirmed if an unlikely prediction comes true [Lipton]
 16802 Bayes seems to rule out prior evidence, since that has a probability of one [Lipton]
 16803 Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton]
 16837 Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton]
 16839 Explanation may be an important part of implementing Bayes's Theorem [Lipton]
 6372 Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz]
 17600 Bayesian inference is forced to rely on approximations [Thagard]
 14990 Bayes produces weird results if the prior probabilities are bizarre [Sider]
 6798 Bayesianism claims to find rationality and truth in induction, and show how science works [Bird]
 22178 If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
 17943 Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
 22365 The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger]