The causal reason that Bayes’ theorem is in the article is because Luke wrote that part before I was involved. If I had written it from scratch, I probably wouldn’t have included it.
But I think it’s reasonable to include it because this is an article for laymen, and Bayes’ theorem is a really important piece to have your knowledge of rationality built around. Furthermore, the discovery of Solomonoff induction was motivated by the search for objective priors, which is a Bayes’ theorem thing.
But you’re exactly correct that hypotheses either match or they don’t. The updating of probabilities occurs when you renormalize after eliminating hypotheses. Also, I’ve thought about it for a while and concluded that no modification is needed to represent probabilistic hypotheses. I may write a piece later about how Bayes’ theorem is consistent with Solomonoff induction.
You are pretty much correct.
The causal reason that Bayes’ theorem is in the article is because Luke wrote that part before I was involved. If I had written it from scratch, I probably wouldn’t have included it.
But I think it’s reasonable to include it because this is an article for laymen, and Bayes’ theorem is a really important piece to have your knowledge of rationality built around. Furthermore, the discovery of Solomonoff induction was motivated by the search for objective priors, which is a Bayes’ theorem thing.
But you’re exactly correct that hypotheses either match or they don’t. The updating of probabilities occurs when you renormalize after eliminating hypotheses. Also, I’ve thought about it for a while and concluded that no modification is needed to represent probabilistic hypotheses. I may write a piece later about how Bayes’ theorem is consistent with Solomonoff induction.