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.

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----- 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 (") > UNSW SYDNEY 2052 [EMAIL PROTECTED] > Australia http://parallel.hpc.unsw.edu.au/rks > International prefix +612, Interstate prefix 02 > ---------------------------------------------------------------------------- << 2.dat >> -- ___________________________________________________________ Sign-up for Ads Free at Mail.com http://promo.mail.com/adsfreejump.htm