The question of the boundaries of human understanding and the explanation of these cognitive limits is raised. Non-trivial epistemic limits are shown to be the implication of standard sensory, behavioural, and external theories about the nature of thought. The hypothesis of cognitive transcendence, the idea that certain philosophical questions are unanswerable given our epistemic capacities, is proposed, and it is claimed that the existence of such questions is just what theory would predict; but it is denied that what is transcended is thereby non-natural (‘transcendental naturalism’). A theory of the structure of our theoretical capacities is sketched in the light of Chomsky’s theses about our grasp of number theory, which McGinn calls the ‘CALM (Combinatorial Atomism with Lawlike Mappings) conjecture’: if something conforms to CALM principles we can understand it; we cannot understand what does not.
Keywords: CALM conjecture, Chomsky, cognitive limits, cognitive transcendence, epistemic limits, transcendental naturalism,