----- Forwarded message from Russell Standish <[EMAIL PROTECTED]> -----
Date: Wed, 23 May 2007 07:39:58 +1000 From: Russell Standish <[EMAIL PROTECTED]> To: Ricardo Aler <[EMAIL PROTECTED]> Subject: Re: Theory of Nothing In-Reply-To: <[EMAIL PROTECTED]> User-Agent: Mutt/1.4.2.1i On Wed, May 23, 2007 at 10:30:44AM +0200, Ricardo Aler wrote: > > With respect to set theory, there is something else that came to mind > when I read your book, although it's probably more connected to > Tegmark's approach. In your case, your "everything" is the set of > infinite binary strings (or the set of histories of MWI?). In any > case, it's a well defined "everything", with the cardinality of the > real numbers. In Tegmark's case, if I remember well (I read his paper > long time ago), his Plenitude is made of all possible consistent > mathematical objects. All of them exist simultaneously, sort of. > However, in set theory (or its philosophy anyway), the "absolute > infinite everything" (Cantor's set of all sets) cannot exist, or > cannot be considered to exist, or at least it's not a set. Otherwise, > you can always construct a higher cardinality "everything". Likewise > with the set of all ordinal numbers (Burali-Forti paradox). I'm not > quite sure that the Tegmark's set of all mathematical objects is > riddled with the difficulties of the set of all sets, but I wonder if > this has been considered?. Bruno Marchal has most strongly leveled this criticism against Tegmark's approach. Tegmark has not, to my knowledge, responded to this, although he has written a "sequel" to his 1996 paper, which I haven't got around to reading yet. I get around this issue in my paper (and also book - see page 52) by interpreting Tegmark's ensemble as being the set of all finite axiomatic systems. This then doesn't have the problem you raised. -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- ----- End forwarded message ----- -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
