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
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