In article <firstname.lastname@example.org>, FredJeffries <FredJeffries@gmail.com> wrote:
> On 6/30/2013 1:55 AM, email@example.com wrote:> > > Just the contrary. Cantor knew that natural numbers exist. To know > > that, one does not need axioms unless being a jerk, Bourbakist, > > or matheologian, or a cross-breed of these species. > > One does not use axioms to prove that things exist. One writes down and > clearly communicates axioms in order to clarify proofs and arguments, > to expose previously unexpressed presuppositions in order to find > possible flaws and in order to have civilized conversations.
Every mathematician makes assumptions. The good ones make clear, both to themselves and others, what assumptions they are making.
Even as marginal a mathematician as WM makes assumptions, things he holds to be true without having any explicit proofs of their truth, though collectively they are often mutually contradictory. --