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

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 <mailto:her...@acm.org>>
I get my monkeys for nothing and my chimps for free.


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On Jul 29, 2010 2:01 PM, Brian Tenneson <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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