# Re: numbers?

```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

>
>
> 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.

Quentin

>
> 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>
>> I get my monkeys for nothing and my chimps for free.
>>
>>
>>  ------------------------------
>> On Jul 29, 2010 2:01 PM, Brian Tenneson
>> <tenn...@gmail.com><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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>
>
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