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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

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

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