I do not understand why the Nothings are fundamentally incomplete. I
interpreted this as inconsistency, partly due to the following line:
"5) At least one divisor type - the Nothings or N(k)- encompass no
distinction but must encompass this one. This is a type of incompleteness."
If they encompass no distinctions yet encompass one, they are
apparently inconsistent. So what do you mean when you instead assert
them to be incomplete?
On Sun, Dec 28, 2008 at 7:19 PM, Hal Ruhl <halr...@alum.syracuse.edu> wrote:
> 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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