Le 03-nov.-05, à 04:23, George Levy a écrit :
From the thread Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet
Theory of Everything
Bruno Marchal wrote:
Le 22-oct.-05, à 04:50, George Levy a écrit :
The 3-plenitude is equivalent with the computationnal states accessed
by the UD. It is also equivalent with the (finite and infinite)
proofs of the Sigma_1 sentences, etc.
The 1-plenitudes are then so big (provably) that they are not
nameable. Approximations can be named though, and their logics can be
assessed, and tested.
Bruno, you are making a distinction between the 1-Plenitude(s) and the
3-Plenitude. This is new to me. I thought that the Plenitude was the
same no matter who the observer is - in a sense, the ultimate
invariant - and also infinite. Could you please elaborate on your
OK. You must keep in mind the methodology I'm following. I do postulate
comp (or its generalisation alpha-comp I mentionned recently).
Comp is really an humility principle, it just means I am a
digitalizable machine. From this all proposition saying that some
particular entity is more complex that myself is undecidable.
Actually the UD, which provably generates many things more complex than
me is itself very plausibly less complex than myself, and the UD is
enough for generating the many interfering dreams from which an
appearance of "physical reality" proceeds from first (plural) peron
points of view.
So with comp, the 3-plenitude can be very simple (near 0 information),
like the UD or any effective part of arithmetical truth in which the UD
can be embedded. I say this in my last paper (see my url) when I say
that with comp AR makes AR+ undecidable (AR = Arithmetical Realism =
arithmetical truth is independent of me; AR+ = Arithmetical Realism AND
NOTHING ELSE = Pythagoreanism= "everything is numbers and their
With OCCAM, comp makes AR+ enough. (But this can be said only after
comp has been shown to imply the physics/psychology reversal).
The situation is quite different for the 1-plenitude, which is
determined in part by all my experiencial accessible states, and which
relies for that reason to the set of all my consistent extensions (this
with respect to any state I am going through). That set is not even a
constructive object. Only the UD can generate those consistent
extensions (like the UD generates all real numbers including the non
algorithmically definable one). The first person point of view relies
on the whole complete UD* (an infinite object) or, more correctly on
non definable subpart of UD*. This follows from the invariance lemma
(see UDA) and mainly on the facts that a first person cannot be aware
of the delays of reconstitution.
Another justification on the "bigness" of the 1-plenitude is that a
first person cannot even give name (description) of itself: the real
"I" is already undefinable. Its extension set cannot be extremely
complex and big. Cf the "Benacerraf principle": if I am a machine I
will never KNOWN which one.
Hope this helps a bit,