2010/8/2 Brent Meeker <meeke...@dslextreme.com>

>  On 8/2/2010 12:13 AM, Quentin Anciaux wrote:
>
>
>
> 2010/8/2 Brent Meeker <meeke...@dslextreme.com>
>
>>  On 8/1/2010 3:42 PM, Quentin Anciaux wrote:
>>
>>
>>
>> 2010/8/2 Brent Meeker <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.
>
>
Meaning of words can change and do change. Meaning of english words are
dependant of humans. Meaning of mathematical thruths aren't.


>
>
>
>>
>>
>> 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
>

No, it's about the meaning. If mathematical truth are dependant on humans
they mean utlimately nothing at all. So it's nonsensical.

Quentin

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