The motion of the mind is conveyed along a cloud of meaning.~ There is this paradox that we get to meaning only when we strip the meaning from symbols.
David BerlinskiCommentators who today talk of 'The Dark Ages' when faith instead of reason was said to ruthlessly rule, have for their animadversions only the excuse of perfect ignorance. Both Aquinas' intellectual gifts and his religious nature were of a kind that is no longer commonly seen in the Western world.
David BerlinskiAn axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.
David BerlinskiArithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.
David Berlinski