Hello Günther,
>> I have already presented an argument (an easy consequence of the
>> Universal Dovetailer Argument, which is less easy probably) showing that:
>>
>> - CRH implies COMP
>> - COMP implies the negation of CRH
>> - Thus, with or without COMP (and with or without the MUH) the CRH does
>> not hold.
>
>
>
>Regarding:
>
>COMP implies the negation of CRH
>
>Is this also in your Sane 2004 paper? (then I missed that point) - if
>not, where did you argue this?
It is not in the Sane 2004 paper. I have argue that COMP imples NOT-CRH online, in reply to Schmidhuber or someone defending the idea that the universe could be the product of a computer program.
Universality, Sigma_1 completeness, m-completness, creativity (in Post sense), all those equivalent notion makes sense only through complementary notion which are strictly sepaking more complex (non RE, productive, ...). The self-introspecting universal machine can hardly miss the inference of such "realities", and once she distinguishes the 1, 1-plural, 3-person points of view, she has to bet on the role of the non computable realities (even too much getting not just randomness, like QM, but an hard to compute set of anomalous stories (white rabbits, coherent but inconsistent dreams).
It's a bit like "understanding" (putting in a RE set) the (code of) the total computable functions, forces us to accept the existence of only partially computable functions, which sometimes (most of the time, see the thesis by Terwijn) have a non recursive domain.
OK, the ontic part of a comp TOE can be no *more* than Sigma_1 complete, but a non self-computable part of Arithmetical truth and analytical truth, is needed to get the *internal* measure, we can't even give a name to our first person plenitude and things like that.
The quantified "angel guardian" of a simple Lobian machine like PA, that is qG*, is itself Pi_1 in the Arithmetical Truth (see Boolos 1993 book). The "God" of PA (already unameable by PA) is already NOT omniscient about PA's intelligible reality, if you follow the arithmetical interpretation of Plotinus I did propose.
Perhaps this is why the Intelligible has been discovered (Plato) before the "ONE" (Plotin). It is far bigger. With comp you can restrict the ontic to the Universal Machine (the baby ONE), but its intelligible realm is well beyond its grasp.
All this is related to the fact, already understood by Judson Webb, that comp is truly a vaccine against reductionist theories of the mind.
Have a good day,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu May 01 2008 - 15:11:15 PDT