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www.logicalparadoxes.com/index.html

 

Solution of Hempel’s paradox.

Concisely. An evidence e confirms a hypothesis h iff P(h/e)>P(h). Let us consider the hypothesis h=“all ravens are black” in  the most current context; the value P of its probability calculated on the observation of some ravens, all black, is by far higher than the value P’ calculated on the observation of some non-black individuals, all non-ravens, though h and h’=”all non-black individuals are non-ravens” are logically equivalent. Now (Nicod’s postulate) the new evidence of a non-black non-raven individual (a red apple, say) actually confirms h’, increasing P’ up to P”; but even thus increased, P”<<P, therefore, by definition, h is not at all confirmed by the red apple, because we can already count on its by far higher value P.

Here  is the winning trace for the definitive solution of Hempel’s paradox (in the full respect of classical logic and of Nicod’s postulate). I have similar traces for Goodman’s riddle, McGee’s counter-examples of Modus Ponens, Bértrand’s  polyvalent geometrical probabilities, up to the general solution of logical paradoxes; in fact all these troubles arise from a wrong approach to the various problems.

If some reader is interested in the matter, write to me at italo@italogandolfi.com.