Re: Flying rabbits and dragons

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Sat, 6 Nov 1999 12:39:41 -0000

----- Original Message -----
From: Russell Standish <R.Standish.domain.name.hidden>
> I agree, that if you restrict your attention to wffs only, then there
> is no problem. It is also no surprise. However, I don't believe one
> can solve the White Rabbit problem by defining it away.

It is most certainly NOT just being 'defined away'.

The whole point is that we are confining ourselves to *logically consistent*
universes (and perhaps other entities), that is, universes with some kind of
logical structure. The only assumption in my analysis is that these must be
definable with some kind of formal system (I don't even assume that it would
be contained within fig 1 of Tegmark's table). A non-wff is just a
meaningless string of symbols - we can't even *consider* any logically
consistent universe without at least a wff-string. Once we have the
wff-string, then we can start to build towards defining logically consistent
universes (via axiom sets, *consistent* theories, metric spaces (probably),
and so on). It is *then* that the analysis of axioms comes into play (see my
original post), and flying rabbits are banished to a very small minority of
universes.

There is no 'defining away' of the white rabbit problem. It sounds to me as
if you are confusing white rabbit universes with logically inconsistent
universes (the latter should not be able to exist in anyone's book). Perhaps
if I add some comments to an earlier post of yours, it may help to clarify
the wider issue, but remember that what follows below is mainly based on our
earlier scheme and not the same as one described at the start of this
thread.

> I don't think anyone said they don't exist. Its the measure of the
> worlds that contain that is interesting. There are two possibilities:
>
> a) The dragon universe is the outcome of a mathematical
> description. In the sense we use dragon here of being non-lawlike, we
> may suppose that they are the outcome of a very complex mathematical
> description. As we well know, the measure of such universes is much
> smaller than the very lawlike universe we inhabit.

We don't know this unless we can find a proof. In fact the analysis that we
developed earlier can provide a strong indication of the small measure of
dragon universes. (See my web pages.)

> b) The dragon universe corresponds to one of the "nonsense
> bitstrings", which we know to vastly outnumber the lawlike ones. In
> this case, we must apply the argument I worked out with Alistair
> Malcolm to show that indeed these dragon universes are of small
> measure compared with lawlike universes, and that the remaining
> "nonsense" universes are like noise - unobservable.

If the bits are interpretable as anything, they would normally be
interpretable mathematically (or at least as part of some formal system,
otherwise we would be ranging beyond the formality of information theory
itself), in which case what they represent will be coherent, but not in
general visible to us (usually because what is represented will be in
another universe) - again the general argument we derived holds as required
for their small measure. For totally nonsense bitstings, or for any parts of
bitstrings which are non-interpretable - these are ontologically
problematical (as are non-wffs); I think that we have to remember that we
are just trying to find generic schemes that can subsume all logically
possible universes - the particular set of building blocks used to ground
each scheme ought not to affect the relative measures of various types of
universes. Neither non-wffs nor non-interpretable bits can represent
anything, and to include them in any analysis is giving them unwarranted
ontological credibility. Fortunately neither are required to ascribe low
measure to dragon universes.

Alastair
Received on Sat Nov 06 1999 - 04:43:11 PST