In the Bayesian view, you can never really make absolute positive statements about truth anyway. Without a simplicity prior you would need some other kind of distribution. Even for computable theories, I don’t think you can ever have a uniform distribution over possible explanations (math people, feel free to correct me on this if I’m wrong!); you could have some kind of perverse non-uniform but non-simplicity-based distribution, I suppose, but I would bet some money that it would perform very badly.
Damn, I didn’t intend to hit that Retract button. Stupid mobile. In case it wasn’t clear, I do stand by this comment aside from the corrections offered by JoshuaZ.
Consistency forces you to have a simplicity based prior if you have a counteable set of non-overlapping hypotheses described using some finite collection of symbols (and some other minor conditions to ensure non-pathology). See prior discussion here. See also here for related issues.
In the Bayesian view, you can never really make absolute positive statements about truth anyway. Without a simplicity prior you would need some other kind of distribution. Even for computable theories, I don’t think you can ever have a uniform distribution over possible explanations (math people, feel free to correct me on this if I’m wrong!); you could have some kind of perverse non-uniform but non-simplicity-based distribution, I suppose, but I would bet some money that it would perform very badly.
Damn, I didn’t intend to hit that Retract button. Stupid mobile. In case it wasn’t clear, I do stand by this comment aside from the corrections offered by JoshuaZ.
Consistency forces you to have a simplicity based prior if you have a counteable set of non-overlapping hypotheses described using some finite collection of symbols (and some other minor conditions to ensure non-pathology). See prior discussion here. See also here for related issues.
You can act “as if” by just using the likelihood ratios and not operating with prior and posterior probabilities.