[time 644] Re: [time 636] Worlds as Lexicon -> Possible Worlds of Kripke structure?

Stephen P. King (stephenk1@home.com)
Mon, 30 Aug 1999 09:12:17 -0400

Dear Bill,

        I have been thinking hard about your ideas! It occurred to me that you
may be really on to something. I am sorry to hear of Paul's plight. :-(
I do not earn a living from my philosophizing so I can risk being a
heretic, but we must remember Bruno!

WDEshleman@aol.com wrote:
> In a message dated 8/25/99 8:01:08 PM Eastern Daylight Time,
> stephenk1@home.com writes:
> > Are "close copies" a minority or majority? Well, there measure
> > theoretic properties of real valued labeled worlds is "measure one", in
> > other words it is certain that if we picked a pair of worlds out of an
> > urn that they would look almost alike! The article by F.W. Meyerstein
> > (http://www.cs.auckland.ac.nz/CDMTCS//researchreports/089walter.pdf) is
> > a good discussion of this!
> >
> Stephen,
> I have read the paper now; I sure like short papers. At first, one may
> think that infinite sums are Lexicons, then it becomes apparent that
> infinite sums of infinite sums are really the Lexicons; that is if each
> inner sum represents the same information as the outer sum.

        I like them little papers too, short and to the point...

        We could discover if this were true if we could compare the two sums to
each other, but simple isomorphism would not work since it is blind to
ordering. Umm, this looks like it requires cohomorphism testing, which
tests the topology to see if it is simply or multiply connected. The
former shows that the space of points (= sums) is commutative and has
"no holes" and the latter is non-commutative, as if the space has knots
or wormholes in it. (Oh, BTW, Pratt has something about that in his
        Since I am trying to advance the idea that our individual realities
(read space-times) are constructions, it follow that the topology of
such follows from some aspect of the process. More on this later. For a
preview read:


> This is where infinite products surface (sums of sums are products).
> I had not thought of a product as a Lexicon, but it makes sense if
> a Lexicon must have near copies of itself coded into its parts.
> The infinite products of my study have parts (factors) that differ
> from the the total product only by very small amounts of information.

        Have you thought about how the concept of neighborhood could be defined
using infinite products? Since I see everything visually, this
immediately popped up. :-) I noticed that the notion that "infinite
products of my study have parts (factors) that differ from the the total
product only by very small amounts of information" would imply that
there is some variational principle derivable from the way that the
products differ in their information content. (I am seeing your ideas in
light of Pratt's!) Can we think of a metric (or ultrametric!) to measure
how far apart a pair of factors are?
> I am interested to read some of your ideas on this Lexicon topic.
> To understand my approach to infinite products, all you need to
> know is some algebra, and simple rules of logarithms. What may
> appear as complex at first, is really quite simple in concept
> accessible (probably) to philosophers and high school kids too. :-)

        I am thinking of how the lexicons relate to states of Mind qua
information structures and how causality is defined in a "branching
time" or "lazy binding" way. This is important as it allows for
observers to "chance their mind", which I will argue is necessary and
sufficient to allow free will.
        Pratt says in ratmech.ps pg.9 paragraph 8: "...we find that two events
or two states ... communicate with each other by interrogating all
entities [read worlds!] of the opposite type. Thus event a deduces that
it precedes event b not by broaching the matter with b directly, but
instead by consulting the record of every state to see if there is any
state volunteering a counterexample [a contrafactual of "has this been
experienced before"?]. When none is found, the precedence is
established. Conversely, when a Chu space is in state x and desires to
pass to state y, it inquires as to whether this would undo any event
that has already occurred. If not then the transition is allowed."

        Note the phrase "communicate with each other by interrogating all
entities of the opposite type". I added the "[other worlds]" since I am
trying to point out how causality is an active process and it is
necessary to consider all possible variations when considering even the
simple process of motion! In your thinking, Bill, what do you see as the
role or purpose of the infinite products?
        You make a good point about "keep it simple!" :-)



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