The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics learning fosters generally improved reasoning. This is ostensibly done by providing students with access to aspects of mathematical epistemology, which are taken to have some value beyond mathematics itself. The evidential basis both for learning mathematical epistemology and for its influence beyond the mathematics classroom are relatively thin, in part because they are hard to define and operationalize for research. In this paper, I will identify some challenges inherent in studying whether mathematical epistemology might contribute to productive reasoning beyond mathematics and proffer particular aspects of mathematical epistemology that could be useful for instruction and research thereupon. Given that mathematicians and many policy makers believe in the power of mathematical epistemology to improve people's general reasoning, this appears a worthwhile avenue for investigation, even if the challenge is daunting.