The status of automatized knowledge in his mind is experienced by man as if it
had the direct, effortless, self-evident quality (and certainty) of perceptual
awareness. But it is conceptual knowledge—and its validity depends on the
precision of his concepts, which require as strict a precision of meaning
(i.e., as strict a knowledge of what specific referents they subsume) as the
definitions of mathematical terms. (It is obvious what disasters will follow
if one automatizes errors, contradictions and undefined approximations.)