# Re: The seven step-Mathematical preliminaries

```Quentin Anciaux wrote:
> 2009/6/9 Torgny Tholerus <tor...@dsv.su.se>:
>
>> Jesse Mazer skrev:
>>
>>>
>>>> Date: Sat, 6 Jun 2009 21:17:03 +0200
>>>> From: tor...@dsv.su.se
>>>> Subject: Re: The seven step-Mathematical preliminaries
>>>>
>>>> My philosophical argument is about the mening of the word "all". To be
>>>> able to use that word, you must associate it with a value set.
>>>>
>>> What's a "value set"? And why do you say we "must" associate it in
>>> this way? Do you have a philosophical argument for this "must", or is
>>> it just an edict that reflects your personal aesthetic preferences?
>>>
>>>
>>>> Mostly that set is "all objects in the universe", and if you stay
>>>>
>>> inside the
>>>
>>>> universe, there is no problems.
>>>>
>>> *I* certainly don't define numbers in terms of any specific mapping
>>> between numbers and objects in the universe, it seems like a rather
>>> strange notion--shall we have arguments over whether the number 113485
>>> should be associated with this specific shoelace or this specific
>>> kangaroo?
>>>
>> When I talk about "universe" here, I do not mean our physical universe.
>> What I mean is something that can be called "everything".  It includes
>> all objects in our physical universe, as well as all symbols and all
>> words and all numbers and all sets and all other universes.  It includes
>> everything you can use the word "all" about.
>>
>
> It includes all set, but no all set as it N includes all natural
> number but not all natural number... excuse-me but this is non-sense.
> Either N exists and has an infinite number of member and is
> incompatible with an ultrafinitist view or N does not exists because
> obviously N cannot be defined in an ultra-finitist way, ```
```
That's not obvious to me.  You're assuming that N exists apart from
whatever definition of it is given and that it is the infinite set
described by the Peano axioms or equivalent.  But that's begging the
question of whether a finite set of numbers that we would call "natural
numbers" can be defined.  To avoid begging the question we need some
definition of "natural" that doesn't a priori assume the set is finite
or infinite; something like, "A set of numbers adequate to do all
arithmetic we'll ever need" (unfortunately not very definite).  The
problem is the successor axiom, if we modify it to S{n}=n+1 for n e N
except for the case n=N where S{N}=0 and choose sufficiently large N it
might satisfy the "natural" criteria.

Brent

> any set that
> contains a finite number of natural number (and still you haven't
> defined what it is in an ultrafinitist way) are not the set N.
>
> Also any operation involving two number (addition/multiplication) can
> yield as result a number which has the same property as the departing
> number (being a natural number) but is not natural number... Also
> induction and inference cannot work in such a context.
>
>
>> For you to be able to use the word "all", you must define the "domain"
>> of that word.  If you do not define the domain, then it will be
>> impossible for me and all other humans to understand what you are
>>
>
> Well you are the first and only human I know who don't understand
> "all" as everybody else does.
>
> Quentin Anciaux
>
>
>> --
>> Torgny Tholerus
>>
>>
>
>
>
>

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