>
> ----- Original Message -----
> From: Russell Standish <R.Standish.domain.name.hidden>
> > Why it fails is that you assume that all universes are wffs. The
> > underlying challenge of white rabbits and dragons is that the number
> > of non-wffs vastly outnumber the number of wffs. The assumption is
> > that that each non-wff corresponds to to a white rabbit universe. As
> > we discussed, and you have explained fairly clearly on your web page,
> > most non-wff universes are in fact indistinguishable from a wff
> > universe sufficiently close to it, so may be identified with it. In
> > that case, the number of non-wff universes corresponding to white
> > rabbits or dragons (ie actually recognisable paranormal phenomena) is
> > a vanishingly small proportion of the total.
>
> No! I am very sorry, but I have to correct this - every sentence above is
> false!!! (Though stemming from one underlying misunderstanding, I think.)
>
> One of the main reasons to use the formal systems approach is that it solves
> the principal interpretation problem - some symbol strings build wff's, some
> wff's are axiom sets, some axiom sets build theories, some theories specify
> universes. In my first post to this thread (my web pages don't mention
> wff's - yet), wff's rather than non-wff's are selected - wff's are a
> precondition for the specification of *any* universe (with or without
> dragons/white rabbits); a non-wff is like a nonsense bitstring - totally
> irrelevant (except conceivably for some measure purposes).
We're obviously running up against a misunderstanding here, which I
believe we should be able to resolve. Surely dragon universes are
nonsense bitstrings (the non wffs mentioned above), just ones that
happen to be close to a mathematical system, but not so close to be
indistinguishable. I thought the whole point of our argument was that
while most bitstrings are non-wff, the vast majority of them are
completely uninterpretable, and hence irrelevant. Of the ones that
are interpretable, the vast majority will be indistinguishable from a
mathematical system. (Sorry, I realise the last sentence of the above
paragraph that you objected to is a little misleading) This then
justifies the Tegmark position of adopting the "all mathematical
systems" plenitude from the more basic "all bitstrings" plenitude.
>
> The only way that a universe couldn't be specified by a wff is if it is not
> mathematically modellable (*and* certain other conditions pertain), since
> mathematics is grounded in formal systems (see fig 1 in Tegmark's paper) and
> formal systems are derivable from axiom sets (a subset of all wffs).
>
> > I am currently writing a paper as I mentioned outlining this argument
> > (amongst others). Currently, it is in draft hand-writing form, so I
> > can't send it to you yet. I hope to type it up in the next week or
> > so. It would be useful getting feedback - maybe we could even
> > co-author it.
>
> I think it would be a good idea if some people on the list look over
> drafts/pre-drafts of papers (I don't mind volunteering in this case, though
> I'm afraid I've too much on my plate to co-author at the moment - thanks for
> the offer anyway), but potential commenters should stick to making factual
> points (otherwise interminable discussions could ensue), and authors should
> try to be fair to alternative all-universe hypotheses.
>
> May be one day we'll all agree on one theory?
>
> Alastair
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Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Sun Oct 24 1999 - 17:17:07 PDT