2010/8/2 Brent Meeker <meeke...@dslextreme.com> > On 8/1/2010 3:24 PM, Brian Tenneson wrote: > > I quite agree that counting and the existence of numbers are different. > > The Peano axioms for numbers makes it seem like numbers are not dependent > on us humans to exist which entails that there are infinite sets by assuming > an induction property held by (sets of) numbers. > > So while counting may not have been around forever, numbers have, > independent of us humans. The Peano axioms are totally free of human > baggage > > > I don't think so. Where's the natural instance of "successor". "This is a > successor of that" seems to me a human conceptualization based on the mental > equivalent of moving pebbles into a group. That it can be done indefinitely > is merely a convenient assumption. > > Brent > > The only problem is if numbers were a human invention... other humans could come with a prime number that is even and not 2... There would exists a biggest number, 1+1=2 could be false somewhere sometime (even by following the rules that makes 1+1=2 true always)...

Mathematical truth are independent of humans, life and the universe and the rest, it's nonsense if it's otherwise. Quentin > > and did not need Peano to utter them in order for numbers to exist. > Consequently, I believe most if not all of math is discovered. > > The formalism for counting as describing a one-to-one correspondence to a > (formally defined) finite set of numbers also exists independent of humans > in the same way that the unit circle exists. The formalism for counting is > of course not how biological machines such as we count; the formalism is > just meant to intuitively express what we actually do when we count. > > Brent Meeker wrote: > > On 7/29/2010 3:28 PM, Mark Buda wrote: > > Quantum mechanics suggests maybe not. If there were no conscious observers > to collapse the wave function of the universe after the big bang, then what, > pray tell, would constitute an atom that might be counted? > > This assumes that conscious observers are necessary to collapse the wave > function, of course. > -- > Mark Buda <her...@acm.org> > I get my monkeys for nothing and my chimps for free. > > > ------------------------------ > On Jul 29, 2010 2:01 PM, Brian Tenneson > <tenn...@gmail.com><tenn...@gmail.com>wrote: > > Numbers existed before people on this rock began to understand them. If > not number of atoms in the universe, then the number of cells in organisms > one day prior to 10,000 years ago. or anything really, that had the > potential to be counted, one day prior to 10,000 years ago. > > > I don't think the existence of some number of distinct things is the same > as the "existence" of numbers. Numbers are defined by order and successor - > neither of which are present or implicit in a mere collection of atoms or > anything else. > > Brent > -- > 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. > > > -- > 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. > > > -- > 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. > -- All those moments will be lost in time, like tears in rain. -- 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.