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.


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?

Brent


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 <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
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