Bayesian epistemology is broadly concerned with providing norms for rational belief and learning using the mathematics of probability theory. Many authors have worried that the theory is too idealized to accurately describe real agents. In this paper I argue that an emerging program, computable Bayesian epistemology, can describe more realistic agents while retaining sufficient generality. I situate this program by placing it among the ongoing debate about ideal versus bounded rationality. I then present the basics of computable analysis and demonstrate its usefulness by proving a simple result: there are no computable finitely additive probability measures.