From: Brian Holtz [brian@holtz.org] Sent: Wednesday, April 24, 2002 8:09 AM To: alt.atheism.moderated Subject: Re: finite number of sentences "Paul Holbach" wrote: > > A number like four is a concept which exists explicitly as > > that which is in common to all four-ish acts of contemplation > > and implicitly in the axioms and rules of the mathematical > > system(s) in which it is believed to be producible. > > Do you think classical "intuition" or "mental abstraction" > still play an important role in contemporary mathematics? Are you disagreeing with my statement that the concept "four" exists explicitly as that which is in common to all four-ish acts of contemplation? > can you really contemplate 389.467.347.567-ishness? No, but I can contemplate 389,467,347,567-ishness. :-) > numbers are concepts [and not] entities on a par with > eg electrons and they´re not > idealistic entities beyond spacetime. I agree. > we don´t create numbers but numerical signs Right; by "producible" I of course meant its sense of "exhibitable" rather than "creatable". > > You omit the (in my judgment preferred) option of Logicism: > > the thesis that mathematics can be derived from or reduced to > > pure logic. > > the logicist program of Frege [..] was over after Russell [..] But Russell himself continued to believe that mathematics can be derived from or reduced to logic. The existence of Russell's paradox hardly implies that one of Platonism or Constructivism must be true. -- brian@holtz.org http://humanknowledge.net