On 04 Feb 2011, at 17:28, Johnathan Corgan wrote:

On Fri, Feb 4, 2011 at 7:20 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

IF comp is correct, the SWE has to be deduced from comp, and not to be

How do you think this might be approached?

You have demonstrated a chain of reasoning (MGA+AUDA)

I guess you UDA+MGA

that starts with
the assumption of "yes doctor" and concludes that the subjective
appearance (both 1st and 3rd person perspective) of physical matter
must be explained by extracting digital physics from modal logic.
(Forgive the perhaps oversimplified summary.)

Let's assume, for the purposes of furthering the argument, that the
above is all sound and reasonable.

So what's next?


The Arithmetical version of the UDA.
Let us ask the self-referentially correct machine. What does she think?

Now a correct machine cannot prove the existence of any consistent extension of itself, still less of a universe. That would be a proof of their own consistency and contradict incompleteness(*). So the machine cannot know that the provability of p entails the consistency of p (although that is true); G does not prove Bp -> Dp; but G* does prove Bp -> Dp. So, to transform provability into a measure one indeterminacy, from the machine points of view, you have to define a new connector by adding explicitly Dp to Bp: Bp & Dp. To model comp and the UD itself in the language of the machine, you have to restrict the arithmetical interpretation of p by the sigma_1 sentence. Then you can verify that the logic of Bp & Dp obeys a quantum logic, so that you can define a quantization (BDp, in the new logic). If from that quantization you can implement a quantum computer (say) then you know that a quantum computing dovetailing wins the measure battle in the limit, and that the SWE is a law of observation for almost all (correct) machine (all except those rare unlucky one living in white rabbits realities).

The SWE is exceptionally well supported empirically, so having it
"fall out" of your reasoning rather than being postulated would be a
very convincing argument in your favor.

You mean a very convincing argument for *comp*, (assuming the UDA+MGA is a valid reasoning). I agree. Finding an explicit equation of physics contradicting the quantum would refute comp.

My paper on plotinus summarizes AUDA. It is also the part II of sane04, where AUDA is called "the interview of the Löbian machine".


(*) I assume here that the machine talks in first order predicate logic (like PA, ZF). It is then a consequence of Gödel's completeness (not incompleteness) theorem. But I don't need that really. It just simplifies the exposition. I identify Dp with the existence of a continuation where p is true (not necessarily with the existence of a model (in the logician's sense) satisfying p. That is equivalent for the machine talking first order language (Gödel's completeness theorem, 1930).


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