# Re: Theory of Everything based on E8 by Garrett Lisi

```Jesse Mazer skrev:
>
>
>> From: [EMAIL PROTECTED]
>>
>>
>> As soon as you talk about "the set N", then you are making a "closure"
>> and making that set finite.
>>
>
>
> Why is that? How do you define the word "set"?
>
>
>   The only possible way to talk about
>
>> something without limit, such as natural numbers, is to give a
>> "production rule", so that you can produce as many of that type of
>> objects as you want.  If you have a natural number n, then you can
>> "produce" a new number n+1, that is the successor of n.
>>
>
>
> Why can't I say "the set of all numbers which can be generated by that
> production ruler"?```
```
As soon as you say "the set of ALL numbers", then you are forced to
define the word ALL here.  And for every definition, you are forced to
introduce a "limit".  It is not possible to define the word ALL without
introducing a limit.  (Or making an illegal circular definition...)

>  It almost makes sense to say a set is *nothing more* than a criterion for
> deciding whether something is a member of not, although you would need to
> refine this definition to deal with problems like Russell's "set of all sets
> that are not members of themselves" (which could be translated as the
> criterion, 'any criterion which does not match its own criterion'--I suppose
> the problem is that this criterion is not sufficiently well-defined to decide
> whether it matches its own criterion or not).
>

A "well-defined criterion" is the same as what I call a "production
rule".  So you can use that, as long as the criterion is well-defined.

(What does the criterion, that decides if an object n is a natural
number, look like?)

>
>>
>> It is not possible for "a set" to have no limit.  As soon as you
>> construct "a set", then that set will always have a limit.
>>
>
>
> Is there something intrinsic to your concept of the word "set" that makes
> this true? Is your concept of a set fundamentally different than my concept
> of well-defined criteria for deciding if any given object is a member or not?
>

Yes, the definition of the word "all" is intrinsic in the concept of the
word "set".

--
Torgny

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