On Wednesday, July 22, 2015 at 11:22:57 PM UTC+5:30, Oscar Benjamin wrote: > On Wed, 22 Jul 2015 at 18:01 Steven D'Aprano <st...@pearwood.info> wrote: > > > > I think that the critical factor there is that it is all in the past tense. > > Today, I believe, the vast majority of mathematicians fall into two camps: > > > > (1) Those who just use numbers without worrying about defining them in some > > deep or fundamental sense; > > > > Probably. I'd say that worrying too much about the true essence of numbers is > just Platonism. Numbers are a construct (a very useful one). There are many > other constructs used within mathematics and there are numerous ways to > connect them or define them in terms of each other. Usually these are > referred to as "connections" or sometimes more formally as "isomorphisms" and > they can be useful but don't need to have any metaphysical meaning.
Philosophers-of-mathematics decry platonism. However from my experience (I am not a professional mathematician, though Ive known good ones) most practicing-mathematicians proceed on the assumption that they *discover* math and not that they *invent* it. To me this says that though they may not know the meaning or spelling of platonism, they all layman-adhere to it. tl;dr To me (as unprofessional a musician as mathematician) I find it arbitrary that Newton *discovered* gravity whereas Beethoven *composed* the 9th symphony. Maybe Beethoven was sent my God to write Ode-to-Joy and reunite Europe? -- https://mail.python.org/mailman/listinfo/python-list
