 Isaac Levi (1991) has clarified the nature of this idealization by pointing out that a belief set consists of the sentences that someone is committed to believe, not those that she actually believes in. According to Levi, we are doxastically committed to believe in all the logical consequences of our beliefs, but typically our performance does not live up to this commitment. The belief set is the set of the agent’s epistemic commitments, and therefore larger than the set of her actually held beliefs.