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

From: Jesse Mazer <lasermazer.domain.name.hidden>
Date: Thu, 29 Nov 2007 14:14:45 -0500

----------------------------------------
> Date: Thu, 29 Nov 2007 19:55:20 +0100
> From: torgny.domain.name.hidden
> To: everything-list.domain.name.hidden
> Subject: Re: Theory of Everything based on E8 by Garrett Lisi
>
>
> Jesse Mazer skrev:
>>
>>
>>> From: torgny.domain.name.hidden
>>>
>>>
>>> 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...)

Why can't you say "If it can be generated by the production rule/fits the criterion, then it's a member of the set"? I haven't used the word "all" there, and I don't see any circularity either.

>
>> 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?)

I would just define the criterion recursively by saying "1 is a natural number, and given a natural number n, n+1 is also a natural number".

Jesse
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Received on Thu Nov 29 2007 - 14:38:29 PST

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