On 13 Mar 2011, at 18:32, David Nyman wrote:

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On 13 March 2011 17:26, Bruno Marchal <marc...@ulb.ac.be> wrote:But then, consciousness might be the 'mental' state of a universalnumberwhen it believes in a reality. Science might begin when itquestions thatreality, and consciousness might reappear as the unquestionablepart of thatreality. It can be related with a form of ignorance awareness. Itcan get arole of relative self-accelerator.Bruno, I'm not sure I understand what you mean by "relative self-accelerator" in the above.

It is related to two other theorems of Gödel: The completeness theorem and the speed-up theorem.

`The completeness theorem says that a theory is consistent if and only`

`if the theory has a model (a mathematical structure) verifying (making`

`true) its propositions. Like the structure (N, + *) make true the`

`sentence "1+8 = 9". Let us call that a reality.`

`Consistent means that the theory does not prove the falsity. Modally`

`~Bf, or equivalently Dt. You can read Dt, by completeness, as the`

`existence of a reality. (OK, I can add explanations if you ask)`

`I define consciousness by believing in a reality. This is almost like`

`BDt. But by incompleteness BDt -> Bf, and for the correct machine, Bf -`

`> f (damned!).`

`But the machine/theory can also just add the arithmetical form of Dt`

`(consistency) as a new axiom. It is a inferential process, and not`

`only it does not lead to inconsistency, but the speed-up theorem of`

`Gödel (and a similar for universal machine) is that such process can,`

`shorten is some quasi arbitrary way the length of the proofs.`

`Likewise, Blum speed-up theorem shows that universal machine (and`

`weaker interesting sub-universal one) can be sped up arbitrarily,`

`except for finite number of exception (it concerns the computation`

`which are correct above some argument, that is sufficiently big inputs).`

`So, it is suggested that the belief in a reality speed-up your`

`computational power. This I think can be seen by introspection. If you`

`drive a car, the more you take seriously your local reality (the road,`

`the other cars), the more you can actually speed-up. If you don't`

`believe in any reality, you could as well stop your car, even in the`

`middle of the drive-way.`

`Such a theory would endow consciousness (self-consistency inference)`

`to self-moving entity, which will better anticipate the now moving`

`environment (from their perspective) by taking such environment`

`including one self seriously enough.`

`I can speculate that consciousness might be the ultimate accelerator.`

`The reason why bodies move at all. That would make it a sort of`

`fundamental force. By Newton force are accelerator. But this *is*`

`speculation, or analogy.`

. What is "accelerating" what?

`A universal machine M accelerates (= diminishes the length of personal`

`computations) a universal machine M (itself) relatively to arithmetic,`

`or to some other universal machine U computing M. In that case the`

`machine M transforms itself into a new machine "M+consistent(M)", and`

`the process can continue in the constructive transfinite (and are`

`known as autonomous progressions).`

`They cannot reach arithmetical truth, but they can approach it, and in`

`the long term it is, from their points of view, self-accelerating.`

`The logic of the 8 hypostases remains invariant, despite their`

`arithmetical interpretation (the arithmetical B and thus D) evolves.`

`The length of proof theorem of Gödel paper is in the book "The`

`undecidable" edited by Martin Davis (the comp bible!)`

`Torkel Franzen wrote a little chef d'oeuvre on the autonomous`

`progressions: "Inexhaustibility, A Non exhaustive treatment".`

Bruno

On 12 Mar 2011, at 18:18, Ismail Atalay wrote: [in the FOR list]So we should not be in a position to say "for the essence ofconsciousnessto exist, this type of physical/mathematical features should bepresent inthis universe". Physical/mathematical features are required for its manifestation, implementation and realization.You might conceive that the manifestation, implementation andrealizationare concept definable relatively to universal numbers which arenumberscoding universal partial computable function relatively to elementaryarithmetic. So a minimal amount of arithmetic is required indeed.Universalnumbers exists, and their many interactions are already emulated,atemporally, by the laws of addition and multiplication of nonnegativeintegers. This makes things complex because Universal numbersreflect eachother including themselves.But then, consciousness might be the 'mental' state of a universalnumberwhen it believes in a reality. Science might begin when itquestions thatreality, and consciousness might reappear as the unquestionablepart of thatreality. It can be related with a form of ignorance awareness. Itcan get arole of relative self-accelerator.I agree with you that free will is not an illusion, because thatignoranceis real, and *that* awareness is correct (trivially so for theideal simplemachine I study). Choice is not an alternative. There is anentertainingnovel by Smullyan illustrating this in the book Mind's I. (*)*A* non compatibilist notion of free will is correct, but it is theonewhere non compatibilism is relative to the personal point of viewof theuniversal number, which cannot, indeed, entirely determinateitself, andyet, in the usual computations, has to decide of some action,relatively tosome other universal numbers in its neighborhood.Universal numbers are driven by self-satisfaction, I think, but ineachuniversal numbers there are conflicts between lower self and higherselfsatisfaction.Higher self satisfaction is better in the long run, but opposesitself withshort term lower self satisfaction, and free will comes from thefact thatwe can chose in between. Perhaps. I mean it is hard not to talk undertorture, a situation which usually maximizes the conflict betweenthe shortand long term satisfactions. Bruno Marchal (*) (edited by Dennet and Hofstadter, which is, BTW, an excellentintroduction to Digital Mechanism. Dennett come close to the firstpersonindeterminacy indeed) http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups"Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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