I wrote a backlink to here from OB. I am not yet expert enough to do an evaluation of this. I do think however that it is an important and interesting question that mjgeddes asks. As an active (although at a low level) rationalist I think it is important to try to at least to some extent follow what expert philosophers of science actually find out of how we can obtain reasonably reliable knowledge. The dominating theory of how science proceeds seems to be the hypothetico-deductive model, somewhat informally described. No formalised model for the scientific process seems so far has been able to answer to serious criticism of in the philosophy of science community. "Bayesianism" seems to be a serious candidate for such a formalised model but seems still to be developed further if it should be able to anser all serious criticism. The recent article by Gelman and Shalizi is of course just the latest in a tradition of bayesian-critique. A classic article is Glymour "Why I am Not a Bayesian" (also in the reference list of Gelman and Shalizi). That is from 1980 so probably a lot has happened since then. I myself am not up-to-date with most of development, but it seems to be an import topic to discuss here on Less Wrong that seems to be quite bayesianistically oriented.