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His equation is that for Universal Inductive Inference. It is correct. Fully bayesian but incomputable.

I never disagreed with the equation (of course it's correct). My point is that the prior always comes first, even in UII. You're not simply picking the hypothesis that best explains the data (assuming by best explains you mean has the greatest likelihood P(O|T)), otherwise you just end up with the hypothesis containing a lookup table of all previous data. You need to take into account your confidence in the hypothesis before the data arrived (e.g. based on the complexity/size of programs expressing that hypothesis for UII).

Ah. Your use of not true made it look like an outright dismissal of his whole statement. As for the order of when to pick the prior, I think what is more important is that the data not influence your choice of prior. If you were some oracular machine you could see the data and generate hypothesis and priors for them independent of the data and still not fall for the problem you state.

And then there is the problem of how do you form sensible hypotheses without at least knowing the shape of the data first. The form of these hypotheses are themselves a restriction on the possible space. I think that is what the GGP was getting at.

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