OK. I don’t recall hearing any Bayesian praising low probability theories, but no doubt you’ve heard more of them than me.
The greater P(E|A) is compared to P(E|B), the more A benefits compared to B.
Yes but that only helps you deal with wishy washy theories. There’s plenty of theories which predict stuff with 100% probability. Science has to deal with those. This doesn’t help deal with them.
Examples include Newton’s Laws and Quantum Theory. They don’t say they happen sometimes but always, and that’s important. Good scientific theories are always like that. Even when they have a restricted, non-universal domain, it’s 100% within the domain.
Physics is currently thought to be deterministic. And even if physics was random, we would say that e.g. motion happens randomly 100% of the time, or whatever the law is. We would expect a law of motion with a call to a random function to still always be what happens.
PS Since you seem to have an interest in math, I’d be curious about your thoughts on this:
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.
OK. I don’t recall hearing any Bayesian praising low probability theories, but no doubt you’ve heard more of them than me.
It seems obvious that low probability theories are good. Since probabilities must add up to 100%, there can be only a few high-probability theories and, when one is true, there is not much work to be done in finding it, since it is already so likely. telling someone to look among low-probability theories is like telling them to look among nonapples when looking for possible products to sell, and it provides no way of distinguishing good low-prior theories, like quantum mechanics, from bad ones, like astrology.
Unfortunately, I cannot read that article, as it is behind a paywall. If you have access to it, perhaps you could email it to me at endoself (at) yahoo (dot) com .
ETA:
Yes but that only helps you deal with wishy washy theories. There’s plenty of theories which predict stuff with 100% probability. Science has to deal with those. This doesn’t help deal with them.
I was only talking about Popper’s idea of theories with high content. That particular analysis was not meant to address theories that predicted certain outcomes with probability 1.
OK. I don’t recall hearing any Bayesian praising low probability theories, but no doubt you’ve heard more of them than me.
Yes but that only helps you deal with wishy washy theories. There’s plenty of theories which predict stuff with 100% probability. Science has to deal with those. This doesn’t help deal with them.
Examples include Newton’s Laws and Quantum Theory. They don’t say they happen sometimes but always, and that’s important. Good scientific theories are always like that. Even when they have a restricted, non-universal domain, it’s 100% within the domain.
Physics is currently thought to be deterministic. And even if physics was random, we would say that e.g. motion happens randomly 100% of the time, or whatever the law is. We would expect a law of motion with a call to a random function to still always be what happens.
PS Since you seem to have an interest in math, I’d be curious about your thoughts on this:
http://scholar.google.com/scholar?cluster=10839009135739435828&hl=en&as_sdt=0,5
There’s an improved version in Popper’s book The World of Parmenides but that may be harder for you to get.
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?
It seems obvious that low probability theories are good. Since probabilities must add up to 100%, there can be only a few high-probability theories and, when one is true, there is not much work to be done in finding it, since it is already so likely. telling someone to look among low-probability theories is like telling them to look among nonapples when looking for possible products to sell, and it provides no way of distinguishing good low-prior theories, like quantum mechanics, from bad ones, like astrology.
Unfortunately, I cannot read that article, as it is behind a paywall. If you have access to it, perhaps you could email it to me at endoself (at) yahoo (dot) com .
ETA:
I was only talking about Popper’s idea of theories with high content. That particular analysis was not meant to address theories that predicted certain outcomes with probability 1.