Hi Abram:

I have interlaced responses with --------- symbols.

----Original Message-----
From: everything-l...@googlegroups.com
[mailto:everything-l...@googlegroups.com] On Behalf Of Abram Demski
Sent: Sunday, December 28, 2008 3:10 PM
To: everything-l...@googlegroups.com
Subject: Re: Revisions to my approach. Is it a UD?


Is there a pattern to how the system responds to its own
incompleteness? You say that there is not a pattern to the traces, but
what do you mean by that?


That is not what I actually said.  I indicated that there were no
restrictions on the copy process.  There would be a pattern to some of the
traces.  The incompleteness of the Nothings causes them individually to
eventually become a more distinction encompassing Something.  This is a
little like cold booting a computer that has a large [infinite] hard drive
containing the All.  [a Nothing -> a Something] -> The BIOS chip loads the
startup program and some data into the dynamic memory and the computer
boots.  The program/data would be the first Something in a trace.  From this
point on there is no fixed nature to traces.  The program could at one
extreme generate the entire remaining trace [a series of Somethings] from
just the data already present in the computer - without reading in more from
the All - outputting each resulting computer state to the All on the hard
drive.  The All already contains these states many times over so this is
just a copy process.  At the other extreme the program could just generate
random output which states are also in the All - another copy process. There
would be all nature of traces between these two extremes. 

The incompleteness I cite is just the instability question.  There may be
others.  [A trace would end if the output went into a continuous repeat of a
particular state.]

Other incompleteness issues of a particular Something seem like they should
also prevent a trace from stopping.     


It sounds to me like what you are describing is some version of an
inconsistent set theory that is somehow trying to repair itself.


In other postings I have said that the All, being absolutely complete, is
therefore inconsistent since it contains all answers to all questions [all
possible distinctions and therefore no distinction]. 


(Except rather then sets, which are 2-fold distinctions because a
thing can either be a member or not, you are admitting arbitrary
N-fold distinctions, including 1-fold distinctions that fail to
distinguish anything... conceptually interesting, I must admit.)


I am not well versed in set theory or logic but I believe I understand what
you are saying.  I see this as the All contains an N-fold distinction -


So the question is, what is the process by which the system attempts
to repair itself?


The individual traces so far are attempts by a Nothing to repair its
incompleteness.  The terminus of some traces would be the All - an
absolutely complete, and thus inconsistent divisor.

You seem to be adding traces based on inconsistency which seems reasonable -
see my responses below.


Here is one option:

The system starts with all its axioms (a possibly infinite set). It
starts making inferences (possibly with infinitistic methods),
splitting when it runs into an inconsistency; the (possibly infinite)
split rejects facts that could have led to the inconsistency.

So, the process makes increasingly consistent versions of the set
theory. Some will end up consistent eventually, and so will stop
splitting. These may be boring (having rejected most of the axioms) or
interesting. Some of the interesting ones will be UDs.


So far I have not tried to identify a second source of the dynamic.  I see
the Nothings as consistent because they can produce no answers but therefore
incomplete since they need to answer at least one.  Some traces starting
here evolve towards completeness. The All contains at least one inconsistent
divisor - itself.  It is interesting to consider if traces could originate
at inconsistent divisors and evolve towards consistency.    


The entire process may or may not amount to more than a UD, depending
on whether we use infinities in the basic setup. You did in your post,
and it seems likely, since set theory is not finitely axiomizable and
your system is an extension of set theory. On the other hand, there
would be some fairly satisfying axiomizations, in particular those
based on naive set theory. This does have an infinite number of
axioms, but in the form of an axiom schema, which can be characterized
easily by finite deduction rules. So, your system could easily be
crafted to be either a UD or more-than-UD, depending on personal
preference. (That is, if my interpretation has not strayed too far
from your intention.)



So far I think the inconsistency driven traces you describe may be a
possible addition to the dynamic - Thank you.  



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