I actually contest that the indoor ornithologist is collecting information on the raven hypothesis. Not just limited information, no information, no information. See, there are two hidden statements here.
1) A raven is a type of bird.
2) There are no birds in my house.
If, indeed, we aren't certain if all ravens are birds, or if I have a parakeet, then the indoor ornithologist can contribute to the cause of science by reporting on the status of non black objects that they have lying around.
Suppose an alien offers a billion tons of gold if humanity can correctly answer the question, "are all zxcbfs black?" We ask the alien to repeat that,, because we didn't quite catch that last bit.
Then they hand every human a magic wand that detects if an object is a zxcbfs or not.
Initially, you should scan everything in your house, everything in your yard. Every result is something.
The paradox seems to flip back and forth between the two scenarios, one where we know a great deal about ravens, and one where we pretend raven is some mysterious category never before conceived by humans.
Investing pink slippers only makes sense if you think they might be a raven.
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.
I actually contest that the indoor ornithologist is collecting information on the raven hypothesis. Not just limited information, no information, no information. See, there are two hidden statements here.
1) A raven is a type of bird.
2) There are no birds in my house.
If, indeed, we aren't certain if all ravens are birds, or if I have a parakeet, then the indoor ornithologist can contribute to the cause of science by reporting on the status of non black objects that they have lying around.
Suppose an alien offers a billion tons of gold if humanity can correctly answer the question, "are all zxcbfs black?" We ask the alien to repeat that,, because we didn't quite catch that last bit.
Then they hand every human a magic wand that detects if an object is a zxcbfs or not.
Initially, you should scan everything in your house, everything in your yard. Every result is something.
The paradox seems to flip back and forth between the two scenarios, one where we know a great deal about ravens, and one where we pretend raven is some mysterious category never before conceived by humans.
Investing pink slippers only makes sense if you think they might be a raven.
I'm on a phone, so my formatting is trash, sorry.
Soluttion 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.