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
>
> --
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>
> ----------------------------------------------------------------------------
> A/Prof Russell Standish Phone 8308 3119 (mobile)
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Received on Sun May 22 2005 - 20:38:21 PDT