Re: Flying rabbits and dragons

From: Russell Standish <>
Date: Mon, 25 Oct 1999 10:17:52 +1000 (EST)

> ----- Original Message -----
> From: Russell Standish <>
> > 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

Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Room 2075, Red Centre
Received on Sun Oct 24 1999 - 17:17:07 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:06 PST