On 8/2/2010 12:13 AM, Quentin Anciaux wrote:
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 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)...
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 rules
that makes 1+1=2 true always'
rules == axiomatic systems. So if you use the standard definition of
addition in base 10.. 1+1=2 always, if it's a human invention, it can
be otherwise somewhere sometimes even if you use the standard
definition 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
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