2009/6/6 Torgny Tholerus <torgny.domain.name.hidden>:
>
> Jesse Mazer skrev:
>>
>>
>> > Date: Sat, 6 Jun 2009 16:48:21 +0200
>> > From: torgny.domain.name.hidden
>> > To: everything-list.domain.name.hidden
>> > 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.
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.
> You can only
> create a finite number of proposition with finite length during your
> lifetime.
What is a lifetime . What is truth ? Either you ****CAN*** define a
limit or you ***CAN'T***.
> Just like the number of natural numbers are unlimited but
> finite, so are the possible propositions unlimited but finte.
****EVERY*** ***MEMBER*** of the set ***N*** is
****************************FINITE*********************************
>> or about my question about whether you have any philosophical/logical
>> argument for saying all sets must be finite,
>
> 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. Mostly
> that set is "all objects in the universe", and if you stay inside the
> universe, there is no problems. But as soon you go outside universe,
> you must be carefull with what substitutions you do. If you have "all"
> quantified with all object inside the universe, you can not substitute
> it with an object outside the universe, because that object was not
> included in the original statement.
>
>> as opposed to it just being a sort of aesthetic preference on your
>> part? Do you think there is anything illogical or incoherent about
>> defining a set in terms of a rule that takes any input and decides
>> whether it's a member of the set or not, such that there may be no
>> upper limit on the number of possible inputs that the rule would
>> define as being members? (such as would be the case for the rule 'n is
>> a natural number if n=1 or if n is equal to some other natural number+1')
>
> In the last sentence you have an implicite "all": The full sentence
> would be: For all n in the universe hold that n is a natural number if
> n=1 or if n is equal to some other natural number+1. And you may now be
> able to understand, that if the number of objects in the universe is
> finite, then this sentence will just define a finite set.
>
> --
> Torgny Tholerus
>
> >
>
I will read the rest (and others) email later unfortunatelly.
--
All those moments will be lost in time, like tears in rain.
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Received on Sun Jun 07 2009 - 00:36:40 PDT