Quentin Anciaux wrote:
> 2009/6/6 Torgny Tholerus <tor...@dsv.su.se>:
>   
>> Jesse Mazer skrev:
>>     
>>>       
>>>> Date: Sat, 6 Jun 2009 16:48:21 +0200
>>>> From: tor...@dsv.su.se
>>>> To: everything-list@googlegroups.com
>>>> Subject: Re: The seven step-Mathematical preliminaries
>>>>
>>>> Jesse Mazer skrev:
>>>>         
>>>>> Here you're just contradicting yourself. If you say BIGGEST+1 "is then
>>>>> a natural number", that just proves that the set N was not in fact the
>>>>> set "of all natural numbers". The alternative would be to say
>>>>> BIGGEST+1 is *not* a natural number, but then you need to provide a
>>>>> definition of "natural number" that would explain why this is the case.
>>>>>           
>>>> It depends upon how you define "natural number". If you define it by: n
>>>> is a natural number if and only if n belongs to N, the set of all
>>>> natural numbers, then of course BIGGEST+1 is *not* a natural number. In
>>>> that case you have to call BIGGEST+1 something else, maybe "unnatural
>>>> number".
>>>>         
>>> OK, but then you need to define what you mean by "N, the set of all
>>> natural numbers". Specifically you need to say what number is
>>> "BIGGEST". Is it arbitrary? Can I set BIGGEST = 3, for example? Or do
>>> you have some philosophical ideas related to what BIGGEST is, like the
>>> number of particles in the universe or the largest number any human
>>> can conceptualize?
>>>       
>> It is rather the last, the largest number any human can conceptualize.
>> More natural numbers are not needed.
>>     
>
> What is the last number human can invent ? Your theory can't explain
> why addition works... If N is limited, then addition can and will (in
> human lifetime) create "number" which are still finite and not in N.
>   

It is very unlikely that anyone will get to the number 10^10^100 by 
addition.  :-)

Would agree that a any given time there is a largest number which has 
been conceived by a human being?

> N can be defined solelly as the successor function, you don't need
> anything else. You just have to assert that the function is true
> always.
>
>   
>>> Also, any comment on my point about there being an infinite number of
>>> possible propositions about even a finite set,
>>>       
>> There is not an infinite number of possible proposition.
>>     
>
> Prove it please.
>   

That would seem to turn on the meaning of "possible".  Many (dare I say 
"infinitely many") things are logically possible which are not 
nomologically possible (although the posters on this list seem to doubt 
that).

Brent

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