Bruno wrote: * ( - "...are true independently of you, matter, universe, bibles, etc. *- ) * No theorem of math, even of intuitionist math makes any sense, without such belief*..." * *WHO'S BELIEF?* or rather: *WHAT"S BELIEF*? does a snail believe that 2+13=15, or a rock? I bet for the answer it is: *h u m a n s . - or - maybe: super-human intelligence. * So it is US, humans, (at least) who ought to believe the numbers. Most of us do. It's OK.
John On 7/26/10, Bruno Marchal <marc...@ulb.ac.be> wrote: > > > On 26 Jul 2010, at 18:22, Brent Meeker wrote: > > On 7/26/2010 6:24 AM, Brian Tenneson wrote: >> >>> >>> Does this mean that sets of numbers are inventions or just particular >>> numbers are inventions? >>> If the latter, then there must be a largest number which is, to me, >>> counterintuitive. >>> >>> Numbers existed before 10,000 years ago when they were first understood >>> by humans to some extent. There was a specific number of atoms in the >>> universe one day before any numbers were understood by humans, for example. >>> >> >> But there weren't an infinite number of atoms (or anything else). >> > > > But arithmetical realism does not ask for an infinite number. All finite > numbers is quite enough. You need only to believe that statement like > > s(s(0)) + s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) = > s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) (commonly written 2 + 13 = > 15) > > are true independently of you, matter, universe, bibles, etc. > > No theorem of math, even of intuitionist math makes any sense, without such > belief. You can threw Pythagorus theorem in the trash. > > Only ultrafinitists are not arithmetical realist. But it is impossible for > them to say so, because the cognitive abilities you need to say that you do > NOT believe in arithmetical realism needs arithmetical realism. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-l...@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com<everything-list%2bunsubscr...@googlegroups.com> > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
