Here’s a nice snippet from a 2009 article by Kass that I read yesterday:
According to my understanding, laid out above, statistical pragmatism has two main features: it is eclectic and it emphasizes the assumptions that connect statistical models with observed data. The pragmatic view acknowledges that both sides of the frequentist-Bayesian debate made important points. Bayesians scoffed at the artificiality in using sampling from a finite population to motivate all of inference, and in using long-run behavior to define characteristics of procedures. Within the theoretical world, posterior probabilities are more direct, and therefore seemed to offer much stronger inferences. Frequentists bristled, pointing to the subjectivity of prior distributions, to which Bayesians responded by treating subjectivity as a virtue on the grounds that all inferences are subjective. While there is a kernel of truth in this observation — we are all human beings, making our own judgments — subjectivism was never satisfying as a logical framework: an important purpose of the scientific enterprise is to go beyond personal decision-making. In fact, the dance around prior distributions has been a bit of a distraction and, it seems to me, the really troubling point for frequentists has been the Bayesian claim to a philosophical high ground, where compelling inferences could be delivered at negligible logical cost. Frequentists have always felt that no such thing should be possible. I believe this feeling has its origins in the gap between models and data, which is neither frequentist nor Bayesian. Statistical pragmatism avoids this irritation by acknowledging explicitly the tenuous connection between the real and theoretical worlds. As a result, its inferences are necessarily subjunctive. We speak of what would be inferred if our assumptions were to hold. The inferential bridge is traversed, by both frequentist and Bayesian methods, when we act as if the data were generated by random variables.