This article was prepared for a conference in Girona, Spain, on Standards of Proof and Scientific Evidence. The article demonstrates, first, the analytical power under certain limiting assumptions of treating burdens of persuasion as conventional probability measures. It then demonstrates the remarkable inadequacy of that conceptualization once the limiting assumptions are relaxed as empirical descriptions of the relevant phenomena, and further that this inadequacy suggests that the analytical tools being employed misconceive rather than enlighten the object of inquiry. Alternative ways of analyzing the objects of inquiry are briefly proposed and discussed.