The article you sent me is mathematically sound, but Popper draws the wrong conclusion from it. He has already accepted that P(H|E) can be greater than P(H). That’s all that’s necessary for induction: updating probability distribution. The stuff he says at the end about H ← E being countersupported by E does not prevent decision making based on the new distribution.
Setting aside Popper’s point for a minute, p(h|e) > p(h) is not sufficient for induction.
The reason it is not sufficient is that infinitely many h gain probability for any e. The problem of dealing with those remains unaddressed. And it would be incorrect and biased to selectively pick some pet theory from that infinite set and talk about how it’s supported.
The article you sent me is mathematically sound, but Popper draws the wrong conclusion from it. He has already accepted that P(H|E) can be greater than P(H). That’s all that’s necessary for induction: updating probability distribution. The stuff he says at the end about H ← E being countersupported by E does not prevent decision making based on the new distribution.
Setting aside Popper’s point for a minute, p(h|e) > p(h) is not sufficient for induction.
The reason it is not sufficient is that infinitely many h gain probability for any e. The problem of dealing with those remains unaddressed. And it would be incorrect and biased to selectively pick some pet theory from that infinite set and talk about how it’s supported.
Do you see what I’m getting at?
Yes, that is what the Solomonoff prior is for. It gives numbers to all the P(H_i).
And what is the argument for that prior? Why is it not arbitrary and often incorrect?
And whatever argument you give, I’ll also be curious: what method of arguing are you using? Deduction? Induction? Something else?
I tried to present it, but was obviously very unclear. If you read http://lesswrong.com/lw/jk/burdensome_details/ , http://lesswrong.com/lw/jn/how_much_evidence_does_it_take/ , and http://lesswrong.com/lw/jp/occams_razor/ , it’s basically a formalization of those ideas, with a tiny amount of handwaving.
Deduction.
Deduction requires premises to function. Where did you get the premises?