----- Forwarded message from Russell Standish <hpcoder.domain.name.hidden> -----
Date: Wed, 23 May 2007 07:39:58 +1000
From: Russell Standish <hpcoder.domain.name.hidden>
To: Ricardo Aler <aler.domain.name.hidden>
Subject: Re: Theory of Nothing
In-Reply-To: <43ed4f2b0705230130l55f740d1sfb0f29c081529168.domain.name.hidden>
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 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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----- End forwarded message -----
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Wed May 23 2007 - 06:48:39 PDT