I read that too a some time ago and he makes a really basic error, which made me lose some respect for him (If I was able to catch that error surely he should have, and if he didn’t, then he should have heard a correction and corrected it by now).
The error is the assumption that what Bayes does is compare between H and !H, or to take his example, ‘the sun is powered by nuclear fusion’ VS ‘the sun is not powered by nuclear fusion’. What the math really says you should do, is compare all possible hypothesis, so the term !H isn’t itself an explanation/hypothesis, it’s the sum of all other explanations/hypotheses.
I think Abram Demski (which, unlike me, is actually qualified to talk about this stuff) talked about this error in Bayes’ Law is About Multiple Hypothesis Testing (though not directly referring to Deutsch).
I don’t know if Bayes and Deutsch view of explanation actually conflict. It feels to me like he kinda wants them to conflict.
Wow, this is honestly baffling. It sounds as if Deutsch doesn’t know about the generalised form of Bayes’ theorem (I’m sure he does know, which makes me feel worse).
P(Hi|E)=P(E|Hi)P(Hi)ΣjP(E|Hj)P(Hj)
You make an excellent point. Bayes’ theorem can be applied to all possible hypotheses, not just H and ¬H.
If a top physicist can be this biased, then I cannot be surprised by anything anymore.
I read that too a some time ago and he makes a really basic error, which made me lose some respect for him (If I was able to catch that error surely he should have, and if he didn’t, then he should have heard a correction and corrected it by now).
The error is the assumption that what Bayes does is compare between H and !H, or to take his example, ‘the sun is powered by nuclear fusion’ VS ‘the sun is not powered by nuclear fusion’. What the math really says you should do, is compare all possible hypothesis, so the term !H isn’t itself an explanation/hypothesis, it’s the sum of all other explanations/hypotheses.
I think Abram Demski (which, unlike me, is actually qualified to talk about this stuff) talked about this error in Bayes’ Law is About Multiple Hypothesis Testing (though not directly referring to Deutsch).
I don’t know if Bayes and Deutsch view of explanation actually conflict. It feels to me like he kinda wants them to conflict.
Wow, this is honestly baffling. It sounds as if Deutsch doesn’t know about the generalised form of Bayes’ theorem (I’m sure he does know, which makes me feel worse).
P(Hi|E)=P(E|Hi)P(Hi)ΣjP(E|Hj)P(Hj)You make an excellent point. Bayes’ theorem can be applied to all possible hypotheses, not just H and ¬H.
If a top physicist can be this biased, then I cannot be surprised by anything anymore.
Thank you very much for your response Yoav Ravid.