Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.
David BerlinskiAlthough every novel is derived directly from another novel, there is really only one novel, the Quixote.
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 BerlinskiSome philosophers see into themselves, and some into their times; still others forge an alliance with the future.
David Berlinski