The Logical Firmament

ABSTRACT This essay asks a new question: When someone with a firm understanding of basic operations nevertheless remains ignorant of a complex logical or mathematical truth, precisely what kind of information are they missing? I introduce “catenary truths,” a significant component of this non‐omniscient shortfall. Traditional epistemologies of the a priori don't extend to catenary knowledge, so I offer a novel proposal for how we acquire catenary information. The proposal answers Benacerraf‐inspired worries about access to abstracta by showing how processes of reasoning instantiate catenary truths. The proposal also sheds new light on whether logic is ampliative, how a calculation is like an experiment, higher‐order doubts about deductive reasoning, the inconceivability of logically impossible worlds, and commonalities between mathematical and moral intuition.