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Posts Tagged ‘the problem of induction’

Salmon and Corroboration

In bartley, critical rationalism, induction, popper, salmon on 22/06/2011 at 2:14 am

If inductive evidence is ampliative evidence, then it is clear what would count as a successful outcome of the inductivist project. Given hypothesis h, and evidence e, one must show that evidence e makes p(h if e, e), greater than p(h if e). Evidence e can be anything one cares to name, including repeated sightings of white swans, black raven, or blue hats.

Popper and Miller proved in 1983 that, following from the rules of probability, no e can satisfy this requirement. Until this proof is answered, inductivists are tilting at windmills.

” … if the hypothesis h logically implies the evidence e in the presence b [background knowledge] (so that he is equivalent to h) then p(h, eb) is proportional to p(h, b) … suppose that e is some such evidence statement as ‘All swans in Vienna in 1986 are white’, h  the supposedly inductive generalization ‘All swans are white’ and k the counterinductive generalization ‘All swans are black, except those in Vienna in 1986, which are white’. Then p(h, eb) = p(h, b)/p(k, b). No matter how h and k generalize on the evidence e, this evidence is unable to disturb the ration of their probabilities …. Supporting evidence points in all directions at once, and therefore points usefully in no direction. (Popper & Miller, Why Probabilistic Support is not Inductive, Phil. Trans. of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 321, No. 1562 (Apr. 30, 1987))

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