Philosophical or empirical incommensurability of frequentist versus Bayesian thinking

Frequentists and Bayesians disagree about the soundness of performing calculations based, in an important part, on prior information. The disagreement goes back to a basic philosophical disagreement about how to conceptualize the meaning of probability. As frequentists and Bayesians use the term differently, there is a basic philosophical incommensurability. However, this philosophical incommensurability need not imply an empirical incommensurability. It is possible for there to be, simultaneously, philosophical incommensurability and empirical commensurability. This possibility implies consequences that this article discusses.