On 8/1/2010 3:42 PM, Quentin Anciaux wrote:

2010/8/2 Brent Meeker <meeke...@dslextreme.com<mailto: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 ofhuman baggageI 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. BrentThe only problem is if numbers were a human invention... other humanscould come with a prime number that is even and not 2... There wouldexists a biggest number, 1+1=2 could be false somewhere sometime (evenby following the rules that makes 1+1=2 true always)...

`They can and do. In modulo two arithmetic 1+1=0. You can invent all`

`kinds of number systems or other logics and axiomatic systems.`

Mathematical truth are independent of humans, life and the universeand the rest, it's nonsense if it's otherwise.

What's "it's" in the above sentence? Brent

Quentinand 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. ------------------------------------------------------------------------ On Jul 29, 2010 2:01 PM, Brian Tenneson <tenn...@gmail.com> <mailto: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 theGoogle Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com <mailto: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 theGoogle Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com <mailto: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 GoogleGroups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com <mailto: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 GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en.

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