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Single Idea 6372

[filed under theme 14. Science / C. Induction / 6. Bayes's Theorem ]

Full Idea

It follows from the probability calculus that every tautology has probability 1; it then follows in Bayesian epistemology that we are justified in believing every tautology.

Gist of Idea

Since every tautology has a probability of 1, should we believe all tautologies?

Source

J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §4.3.1.5)

Book Ref

Pollock,J.L./Cruz,J: 'Contemporary Theories of Knowledge (2nd)' [Rowman and Littlefield 1999], p.105

A Reaction

If I say 'a bachelor is a small ant' you wouldn't believe it, but if I said 'I define a bachelor as a small ant' you would have to believe it. 'Bachelors are unmarried' men is a description of English usage, so is not really a simple tautology.

The 19 ideas with the same theme [equation showing probability of an inductive truth]:

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]
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]
16801 A hypothesis is confirmed if an unlikely prediction comes true [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]