The Paradox of Luminosity*

ABSTRACT We explore the consequences of a natural and well‐motivated modeling assumption of Bayesian epistemology, according to which the objects of credence are sentences in the agent's language. We show that this assumption is inconsistent with two further natural Bayesian idealizations: those of Logical Perfection (the logical‐deductive consistency and closure of the sentences in which the agent is certain) and of perfect access to (i.e., certainty regarding) the presence or absence of certainty in any particular sentence in the agent's language—an assumption we call “Luminosity.” That is, it turns out that a luminous agent is an irrational agent. After presenting our main result and some related impossibility results concerning variations on Logical Perfection and Luminosity, we briefly examine the range of candidate solutions to the puzzles that these results present us with.