Hi Georges,

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 thought. Thanks.



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 relations). 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,

Bruno



http://iridia.ulb.ac.be/~marchal/


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