# Re: numbers?

```Bruno wrote:

* ( - "...are true independently of you, matter, universe, bibles, etc.
*- )
*       No theorem of math, even of intuitionist math makes any sense,
without such belief*..."
*
*WHO'S BELIEF?* or rather: *WHAT"S BELIEF*? does a snail believe  that
2+13=15, or a rock?
I bet for the answer it is:  *h u m a n s .  -  or - maybe: super-human
intelligence. *
So it is US, humans, (at least) who ought to believe the numbers. Most of us
do. It's OK.```
```
John

On 7/26/10, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>
> On 26 Jul 2010, at 18:22, Brent Meeker wrote:
>
> On 7/26/2010 6:24 AM, Brian Tenneson wrote:
>>
>>>
>>> Does this mean that sets of numbers are inventions or just particular
>>> numbers are inventions?
>>> If the latter, then there must be a largest number which is, to me,
>>> counterintuitive.
>>>
>>> Numbers existed before 10,000 years ago when they were first understood
>>> by humans to some extent.  There was a specific number of atoms in the
>>> universe one day before any numbers were understood by humans, for example.
>>>
>>
>> But there weren't an infinite number of atoms (or anything else).
>>
>
>
> But arithmetical realism does not ask for an infinite number. All finite
> numbers is quite enough. You need only to believe that statement like
>
> s(s(0)) + s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) =
> s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))      (commonly written 2 + 13 =
> 15)
>
> are true independently of you, matter, universe, bibles, etc.
>
> No theorem of math, even of intuitionist math makes any sense, without such
> belief. You can threw Pythagorus theorem in the trash.
>
> Only ultrafinitists are not arithmetical realist. But it is impossible for
> them to say so, because the cognitive abilities you need to say that you do
> NOT believe in arithmetical realism needs arithmetical realism.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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