i don't no hume belief so i can't compare but...
ultrafinitism must reject induction because, otherwise it is trivial to prove '2^1024' exists (use 'p(x) = x exists') . however, induction is a useful way of designing proving procedures (i.e.e programs) that may or may not finish b4 the universe xplode. ne way we r happy 2 use induction principle as SYMBOL MANIPULATE, which is diferent from beliefing that it acts on real tryly existing objects
it is true that ultrafine men do not wish 2 separate platonic reality numbers 4rom physical real numbers--but it does not make us said that physics knowledge is doubtworthy because, we are O.K. with throw out knowledge! in fact u might say that is all we do ! reject ur facts!! |
