 A corollary of this is that in mathematics many of the “proofs” are not really proofs in the full sense of the word (that is, demonstrations that proceed deductively from apodictic premises via unquestionable rules of inference to certain conclusions) and that many of the “refutations” are not really refutations either, since something rather like the “refuted” thesis often survives the refutation and arises refreshed and invigorated from the dialectical process.