The trouble in physics is that the punchline above was judged to be heretical.
John Norton's paper, "Cosmology and Inductive Inference: A Bayesian Failure" is available here. It is both a pity and a blessing that this was formalized.
(emphasis added)
John Norton talks about the “Bayesian failure” of cosmology and inductive inference. (He admits off the bat that it’s kind of terrifying to have all these cosmologists in the audience.) Basic idea: the Bayesian analysis that cosmologists use all the time is not the right tool. Instead, we should be using “fragments of inductive logics.”
The “Surprising Analysis”: assuming that prior theory is neutral with respect to some feature (e.g. the value of the cosmological constant), we observe a surprising value, and then try to construct a framework to explain it (e.g. the multiverse). This fits in well with standard Bayesian ideas. But that should worry you! What is really the prior probability for observing some quantity? In particular, what if our current theory were not true — would we still be surprised?
We shouldn’t blithely assume that the logic of physical chances (probabilities) is the logic of all analysis. The problem is that this framework has trouble dealing with “neutral evidence” — almost everything is taken as either favoring or disfavoring the hypothesis. We should be talking about whether or not a piece of evidence qualifies as support, not simply calculating probabilities.
The disaster that befell Bayesianism was to cast it in terms of subjective degrees of belief, rather than support. A prior probability distribution is pure opinion. But your choice of that prior can dramatically effect how we interpret particular pieces of evidence.
Example: the Doomsday argument — if we are typical, the universe (or the human race, etc.) will probably not last considerably longer than it already has (or we wouldn’t be typical). All the work in that argument comes from assuming that observers are sampled uniformly. But the fact that 60 billion people have lived so far isn’t really evidence that 100 trillion people won’t eventually live; it’s simply neutral.
Heretical punchline: cosmic parameters can’t be judged as “improbable,” so long as they’re consistent with theory and observation.
PS: at least the beginning of the paper was very readable for me. BTW, this also requires a climbdown from me - I have to admit that philosophers can be useful.
PPS: While the conclusion, as reported by cosmicvariance, is intuitively satisfying ("obvious"), Norton's paper is deep.
