I’m saying that Solomonoff induction doesn’t contradict Bayes’ theorem. The purpose of Solomonoff induction was to find an objective prior, but then after they discovered it, it included a way of updating too. Bayes’ theorem turned out to be redundant. But since we’re pretty sure Bayes’ theorem is correct, it’s nice to see that they don’t contradict.
Solomonoff induction is more than a choice of priors. It’s also a method of finding all possible hypotheses, and a method of computing likelihoods. It’s an entire system of reasoning.
I guess I made conversational assumption that when Bayes name is used rather than ‘Aristotelian logic’, it speaks of non-binary probabilities rather than the limit in which Bayes does not contradict Aristotelian logic of the form ‘if hypothesis does not match data exactly, hypothesis is wrong’.
Huh? All of that applies to any choice of priors whatsoever, not just Solomonoff’s. Or am I missing something?
I’m saying that Solomonoff induction doesn’t contradict Bayes’ theorem. The purpose of Solomonoff induction was to find an objective prior, but then after they discovered it, it included a way of updating too. Bayes’ theorem turned out to be redundant. But since we’re pretty sure Bayes’ theorem is correct, it’s nice to see that they don’t contradict.
Solomonoff induction as opposed to what? Is there any choice of priors which does contradict Bayes’ theorem?
Solomonoff induction is more than a choice of priors. It’s also a method of finding all possible hypotheses, and a method of computing likelihoods. It’s an entire system of reasoning.
Worth also noting possible misunderstanding from 0 and 1 are not probabilities .
I guess I made conversational assumption that when Bayes name is used rather than ‘Aristotelian logic’, it speaks of non-binary probabilities rather than the limit in which Bayes does not contradict Aristotelian logic of the form ‘if hypothesis does not match data exactly, hypothesis is wrong’.