I would agree with Russell, here. That's what I meant when I said that I didn't 
like Tegmark's mathematical model but I could tolerate it. In the end, it gives 
me what I need in that it supports parallel universes and doesn't threaten E/W, 
etc. At the same time, I don't have a dog in every fight, so until I see 
something about his theory that is simply untenable, I'll let it slide.

----- Original Message ----- 
From: "Russell Standish" 
To: "Patrick Leahy" 
Subject: Re: White Rabbit vs. Tegmark 
Date: Mon, 23 May 2005 09:47:22 +1000 

> On Mon, May 23, 2005 at 12:03:55AM +0100, Patrick Leahy wrote: 
> ... 
> > A very similar argument ("rubbish universes") was put forward 
> > long ago against David Lewis's modal realism, and is discussed in 
> > his "On the plurality of worlds". As I understand it, Lewis's 
> > defence was that there is no "measure" in his concept of 
> > "possible worlds", so it is not meaningful to make statements 
> > about which kinds of universe are "more likely" (given that there 
> > is an infinity of both lawful and law-like worlds). This is not a 
> > defense which Tegmark can make, since he does require a measure 
> > (to give his thesis some anthropic content). 
> > 
> > It seems to me that discussion on this list back in 1999 more or 
> > less concluded that this was a fatal objection to Tegmark's 
> > version of the thesis, although not to some alternatives based 
> > exclusively on UTM programs (e.g. Russell Standish's Occam's 
> > Razor paper). 
> > 
> > Is this a fair summary, or is anyone here prepared to defend 
> > Tegmark's thesis? 
> > 
> > Paddy Leahy 
> > 
> I think most of us concluded that Tegmark's thesis is somewhat 
> ambiguous. One "interpretation" of it that both myself and Bruno tend 
> to make is that it is the set of finite axiomatic systems (finite sets 
> of axioms, and recusively enumerated theorems). Thus, for example, the 
> system where the continuum hypothesis is true is a distinct 
> mathematical system from one where it is false. 
> Such a collection can be shown to be a subset of the set of 
> descriptions (what I call the Schmidhuber ensemble in my paper), and 
> has some fairly natural measures associated with it. As such, the 
> arguments I make in "Why Occam's razor paper" apply just as much to 
> Tegmark's ensemble as Schmidhuber's. 
> Conversely, if you wish to stand on the phrase "all of mathematics 
> exists" then you will have trouble defining exactly what that means, 
> let alone defining a measure. 
> Cheers 
> -- 
> *PS: A number of people ask me about the attachment to my email, which 
> is of type "application/pgp-signature". Don't worry, it is not a 
> virus. It is an electronic signature, that may be used to verify this 
> email came from me if you have PGP or GPG installed. Otherwise, you 
> may safely ignore this attachment. 
> ---------------------------------------------------------------------------- 
> A/Prof Russell Standish Phone 8308 3119 (mobile) 
> Mathematics 0425 253119 (") 
> Australia http://parallel.hpc.unsw.edu.au/rks 
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