Re: My proposed model - short form

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Tue, 07 Nov 2000 00:18:49 -0800

Dear Bruno:

Thank you for your interest and comments.

I guess I got my model too compressed.

So I will answer some questions and expand things a bit plus cover one
stage at a time.

A) My use of incompleteness is for the most part rather standard I think
[terms defined below]: If a logic system is both complete and consistent
then there exists a Decision Procedure. Thus a consistent logic system
absent a Decision Procedure is incomplete.

B) Consistent: A choice between two meaningful alternates must be inherent
in the logic.

C) Complete: All alternates meaningful to the logic have such an inherent
choice.

D) Decision Procedure: An automatic procedure for listing all alternates
that have an inherent choice. A computer program as per Turing.

What happened historically:

Godel constructed meaningful alternates for which there was no inherent
choice in a particular class of logic - finite, consistent, Formal
Axiomatic Systems [fc-FAS]. That is systems concerned with the structure
of a string of symbols selected from a set of such symbols [an alphabet].

Turing using Cantor's diagonal argument demonstrated the general lack of a
Decision Procedure for consistent FAS up to and including the largest
possible one - one containing a countable infinity of inherent choices.

Chaitin showed that a consistent FAS that actually has a Decision Procedure
and if that procedure is finite then the FAS could not contain a choice
between alternates that were more complex than the Decision Procedure
except for a constant. This shows the existence of all sorts of alternates
for which there is no inherent choice in such FAS. My model focuses on
those that are meaningful in a certain way.

E) In my model "meaningful" requires that extending the FAS to include one
or more of the Chaitin candidate alternates as a new inherent choice aside
from preserving consistency does not alter the previously existing set of
Chaitin inherent choices except in a very specific way. To partially
accomplish this I take the view that it is not necessary to add the new
inherent choices as new axioms. For some FAS I take the view that one can
add additional inherent choices by adding symbols to the alphabet while
retaining the existing set of axioms and set of rules. In other words, the
added inherent choices are new tails of existing running theorem cascades
that - to preserve consistency - preclude any old tails under a mandatory
consistency preserving rule that all theorems must contain all symbols
currently in the alphabet when the cascade reaches them. This does not
intend to introduce "time" but recognizes that cascades are a series of
steps and may be "running" when the incompleteness resolving event takes
place.

On to my model:


BEGINNINGS

My model is a type of zero absolute information approach. However, I
believe it may differ from others in several key ways.

I actually have two initiation paths for this type of universe set. I
think it is necessary to arrive at a position where there are at least two
paths between which one can not make a logical choice. Otherwise it seems
you would put yourself in the position of proving an axiom.

I can think of only one absolutely imperative set of alternates which must
exist and must be or become an inherent choice.

1) Is "nothing" stable with respect to "everything" - Yes or No?

2) Is "everything" stable with respect to "nothing" - Yes or No?

I see the answers as No and Yes respectively. "Nothing" must become
"everything" to answer the question and "everything" will return even if it
should somehow become "nothing". I argued only the first branch in my
compression. Too much compression it seems.

  Well that is my view up to "everything" exists. More later.

Hal
Received on Mon Nov 06 2000 - 21:27:00 PST