Brian, nothing could be more remote for me than to argue 'math' (number's application and theories) with you. I thinkyou mix up* 'counting'* for the stuff that serves it. As I usually do, I looked up Google for the Peano axioms and found nothing in them that pertains to the origination of numbers. They USE them and EXPLAIN sich usage. Use what???? I wonder if you have an example where application of numbers is extractable from ANY quantity the numbers refer to? <Three plus four> is not different from <blue plus loud>, <sound plus speed>, *whatever*, meaningless words bound together. UNless - of course - you as a human, with human logic and complexity, UNDERSTAND the amount * three* added to a *comparable* amount of *four *and RESULT in *sevenpertaining to the same kind of amount. * ** *Axioms* however sounds to my vocabulary like inventions helping to justify our theories. Sometimes quite weird. And *Brent* was so right: *"...I don't think the existence of some number of distinct things is the same as the "existence" of numbers...."* - Tegmark's quoted "accounted for..." is not "consists of". *To 'explain' *something by a conceptualization does not substitute for the existence and justification of such conceptualization.

Does it make sense that 'numbers existed' when nobody was around to *K N O W or U S E??* Especially when they did not* C O U N T* anything? BTW: what are those abstract symbols you refer to as numbers? (and this question is understood for times way before humans and human thinking). Sorry I asked John M On 8/1/10, Brian Tenneson <tenn...@gmail.com> 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 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<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.