---------------------------------------- > Date: Fri, 30 Nov 2007 09:00:17 +0100 > From: [EMAIL PROTECTED] > To: [EMAIL PROTECTED] > Subject: Re: Theory of Everything based on E8 by Garrett Lisi > > > Jesse Mazer skrev: >> >> >> >>> Date: Thu, 29 Nov 2007 19:55:20 +0100 >>> From: [EMAIL PROTECTED] >>> >>> >>> 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. > > What do you mean by a "well-defined criterion"? Is this a well-defined > criterion? : > > The set R is defined by: > > (x belongs to R) if and only if (x does not belong to x). > > If it fits the criterion (x does not belong to x), then it's a member of > the set R. > > Then we ask the question: "Is R a member of the set R?". How shall we > use the criterion to answer that question? > > If we substitute R for x in the criterion, we will get: > > (R belongs to R) if and only if (R does not belong to R)... > > What is wrong with this? My instinct would be to say that a "well-defined" criterion is one that, given any mathematical object, will give you a clear answer as to whether the object fits the criterion or not. And obviously this one doesn't, because it's impossible to decide where R fits it or not! But I'm not sure if this is the right answer, since my notion of "well-defined criteria" is just supposed to be an alternate way of conceptualizing the notion of a set, and I don't actually know why "the set of all sets that are not members of themselves" is not considered to be a valid set in ZFC set theory. Jesse --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---

- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- Re: Theory of Everything based on E8 by Garrett Lisi Quentin Anciaux
- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- Re: Theory of Everything based on E8 by Garrett Lisi Quentin Anciaux
- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- Re: Theory of Everything based on E8 by Garrett Lisi Quentin Anciaux
- RE: Theory of Everything based on E8 by Garrett Lisi Jesse Mazer
- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- RE: Theory of Everything based on E8 by Garrett Lisi Jesse Mazer
- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- RE: Theory of Everything based on E8 by Garrett Lisi Jesse Mazer
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- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
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- Re: Theory of Everything based on E8 by Garrett Lisi Bruno Marchal
- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
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- Re: Theory of Everything based on E8 by Garrett Lisi Torgny Tholerus
- Re: Theory of Everything based on E8 by Garrett Lisi Bruno Marchal
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