Re: Consistency? + Programs for G, G*, ...

From: George Levy <GLevy.domain.name.hidden>
Date: Wed, 15 Aug 2001 11:38:18 -0700

Hal, thanks for restarting our discussion. After my last inane post of July 12th on
adding the singunal/plenal concept to language to deal with I-plural, I thought I
had killed the group.

Hal Ruhl wrote:

> Dear George:
>
> Just a quick comment since I happened to read the end first.
>
> At 6/3/01, you wrote:
>
> >hmmmm... I thought that was a trick question. An axiomatic system cannot
> >be both
> >complete and consistent. Therefore there can't be a program for it. We go
> >back on how
> >you implement both G and G*.....
> >
> >
> >George(s)
>
> As far as I know that is not true. I understand it to be that some
> axiomatic systems are both complete and consistent.
>
> Godel deals with systems at the complexity of arithmetic and above.
>

OK. I was thinking of systems with a complexity of arithmetic and above. I'll
explain the reason below.

>
> Chaitin puts an upper limit on the complexity of a proof in any axiomatic
> system.
>
> IMO the everything is sufficiently low in complexity - no information at
> all - that it is both
> complete and consistent, thus it can not answer any question including that
> of its own stability. So also with its [in my model] oscillatory alter ego
> - The Nothing.
>
> Since at its heart I feel that Bruno's approach and mine are linked -
> though at the moment I can not follow the majority of his explanation -
> There is only one axiom => Nothing.

The Nothing is the converse of the Everything (Plenitude). Nothing is like a black
screen. Everything is like a white screen. What they have in common is zero
information. I prefer to think in terms of the Everything axiom than in terms of
the Nothing axiom. The reason is that other conditions you may decide to bring in,
act as constraints that restrict the range of the universe you live in and it's
easier to restrict the Everything than to build on the Nothing. This approach is in
fact partially validated in quantum physics in which any phenomenon which is not
expressly forbidden is compulsory.

Now this being said, starting with the Everything axiom (or Plenitude axiom) is OK
but not sufficient. You are ignoring the anthropic constraint. If you factor in
this constraint you'll find that the only systems which are acceptable are those
with a complexity equal or greater than arithmetic. Otherwise, conscious thought is
not possible.

>
> While this must lead to an all universes concurrently system - again no
> information - there can be no answer as to why we find ourselves in this
> one based on a distribution of types because there can be no such distribution.
>

I am puzzled by the whole concept of distribution when the number of items is
infinite. As Jacques Mallah has pointed out that the methods of limits should take
care of that. I am still not satisfied. IMO, when the number of items is infinite,
their ordering seems to be an important issue in defining the distribution. Yet how
is this ordering defined without resorting to distribution?

George

PS. I am still waiting for Bruno's explanation of G*.
Received on Wed Aug 15 2001 - 11:41:48 PDT