Comment on Conservation of Expected Evidence

Mon, 08 Oct 2012 20:33:11 GMT

You're not really wrong. The thing is that "Occam's razor" is a conceptual principle, not one mathematically defined law. A certain (subjectively very appealing) formulation of it does follow from Bayesianism.

P(AB model) \propto P(AB are correct) and P(A model) \propto P(A is correct). Then P(AB model) <= P(A model).

Your math is a bit off, but I understand what you mean. If we have two sets of models, with no prior information to discriminate between their members, then the prior gives less probability to each model in the larger set than in the smaller one.

More generally, if deciding that model 1 is true gives you more information than deciding that model 2 is true, that means that the maximum entropy given model 1 is lower than that given model 2, which in turn means (under the maximum entropy principle) that model 1 was a-priori less likely.

Anyway, this is all besides the discussion that inspired my previous comment. My point was that even without Popper and Jaynes to enlighten us, science was making progress using other methods of rationality, among which is a myriad of non-Bayesian interpretations of Occam's razor.

Discuss