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 <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? > > > 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-dem...@googlegroups.com Public archive: http://groups.google.com/group/abram-demski Private address: abramdem...@gmail.com --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---