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
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