On 8/2/2010 12:13 AM, Quentin Anciaux wrote:

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2010/8/2 Brent Meeker <meeke...@dslextreme.com<mailto:meeke...@dslextreme.com>>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 aretotally free of human 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. 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)...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.You did not read entirely... quoting: 'even by following the rulesthat makes 1+1=2 true always'rules == axiomatic systems. So if you use the standard definition ofaddition in base 10.. 1+1=2 always, if it's a human invention, it canbe otherwise somewhere sometimes even if you use the standarddefinition of addition in base 10.

`But that's like saying if you speak according to the rules of English`

`you will utter English sentences. It doesn't make English a fact of nature.`

Mathematical truth are independent of humans, life and the universe and the rest, it's nonsense if it's otherwise.What's "it's" in the above sentence? It's, is the fact that mathematical truths are independent of humans.

Ah. The point in question is asserted. 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.