Hal,
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?
--Abram
On Sun, Dec 28, 2008 at 7:19 PM, Hal Ruhl <HalRuhl.domain.name.hidden> wrote:
>
> Hi Abram:
>
> I have interlaced responses with --------- symbols.
>
> ----Original Message-----
> From: everything-list.domain.name.hidden
> [mailto:everything-list.domain.name.hidden] On Behalf Of Abram Demski
> Sent: Sunday, December 28, 2008 3:10 PM
> To: everything-list.domain.name.hidden
> Subject: Re: Revisions to my approach. Is it a UD?
>
>
> Hal,
>
> 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 -
> itself.
>
> -----------
>
> 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.)
>
>
> --Abram
>
> -----------------
>
> So far I think the inconsistency driven traces you describe may be a
> possible addition to the dynamic - Thank you.
>
> Yours
>
> Hal
>
>
>
>
> >
>
--
Abram Demski
Public address: abram-demski.domain.name.hidden
Public archive: http://groups.google.com/group/abram-demski
Private address: abramdemski.domain.name.hidden
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Received on Mon Dec 29 2008 - 01:59:00 PST