On 03 Jul 2011, at 09:51, selva kumar wrote:

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On Sat, Jul 2, 2011 at 4:57 PM, Bruno Marchal <marc...@ulb.ac.be>wrote:On 01 Jul 2011, at 13:23, selva kumar wrote: Is consciousness causally effective ? I found this question in previous threads,but I didn't find a answer.Was it in the FOR list (on the book Fabric of reality by DavidDeutsch) ? I thought I did answer this question, which is a veryimprtant and fundamental question.It is also a tricky question, which is very similar or related tothe question of free-will, and it can lead to vocabulary issue. Ioften defend the idea that consciousness is effective. Indeed therole I usually defend for consciousness is a relative self-speedingup ability. Yet the question is tricky, especially due to thepresence of the "causally", which is harder to grasp or define than"consciousness" itself.Let me try to explain. For this I need some definition, and I hopefor some understanding of the UDA and a bit of AUDA. Ask precisionif needed.The main ingredient for the explanation are three theorems due toGödel:- the Gödel completeness theorem (available for machine talkingfirst order logic or a sufficiently effective higher order logic).The theorem says that a theory or machine is consistent (syntacticalnotion, = ~Bf) iff the theory has a model (a mathematical structurein which it makes sense to say that a proposition is true). I willrephrase this by saying that a machine is consistent if and only ifthe machine's beliefs make sense in some reality.- the Gödel second incompleteness theorem ~Bf -> ~B(~Bf): if themachine is consistent, then this is not provable by the machine. Soif the beliefs are real in some reality, the machine cannot provethe existence of that reality. This is used in some strict way,because we don't assume the machine can prove its completeness(despite this has shown to be the case by Orey). This entails thateventually, the machine can add as new axiom its own consistency,but this leads to a new machine, for which a novel notion ofconsistency appears, and the 'new' machine can still not prove theexistence of a reality "satisfying its beliefs. yet that machine caneasily prove the consistency of the machine she was. This can bereitered as many times as their are (constructive) ordinals, andthis is what I describe as a climbing from G to G*. The modal logicof self-reference remains unchanged, but the arithmeticalinterpretation of it expands. An infinity of previously undecidablepropositions become decidable, and ... another phenomenon occurs:- Gödel length of proof theorem. Once a machine adds an undecidableproposition, like its own consistency, as a new axiom/belief, notonly an infinity of (arithmetical) propositions become decidable,but an infinity of already provable propositions get shorter proofs.Indeed, and amazingly enough, for any number x, we can find aproposition which proofs will be x times shorter than its shorterproof in the beliefs system without the undecidable proposition. Asimilar, but not entirely equivalent theorem is true for universalcomputation ability, showing in particular that there is no bound tothe rapidity of computers, and this just by change of the software(alas, with finite numbers of exceptions in the *effective* self-speeding up: but evolution of species needs not to be effective orprogrammable in advance).Extrapolating this and working this on human-machine,consider this..If we firmly believe that all our proofs and instincts onmathematical truths are correct,will we get shorter proofs ?

`Not really. We will become inconsistent. But actually we can not even`

`define "being correct" as applying to ourselves. But a machine with`

`stronger provability ability can study a the theology of a machine`

`with weaker abilities. And if we lift that theology on ourselves, we`

`transform into another machine (more powerful indeed) or into an`

`inconsistent machine (if we lift the notion of truth itself).`

Now, this turns into a proof for existence of power of belief..(?).

`But belief has power. That is a bit what the Löb formula shows.`

`Sentences or machines asserting their own provability (not`

`consistency!) are true and provable.`

Also,speaking in a strict way,it means If you believe you areintelligent,then you become more intelligent (which is in immediatecontracdiction with godel's second incompleteness theorem and yoursmallest theory on intelligence )

`Indeed. So better not to believe/prove that we are intelligent (in the`

`large sense).`

Now I suggest to (re)define consciousness as a machine (instinctive,preprogrammed) ability to bet on a reality. This is equivalent(stricto sensu: the machine does not need to know this) to anability of betting its own consistency (excluding that very newaxiom to avoid inconsistency). As a universal system, this willspeed-up the machine relatively to the probable local universalsystem(s) and will in that way augment its freedom degree. If twomachines play ping-pong, the machine which is quicker has a greaterrange of possible moves/strategy than its opponent.So the answer to the question "is consciousness effective" would beyes, if you accept such definition.Is that consciousness *causally* effective? That is the tricky partrelated to free will. If you accept the definition of free will thatI often suggested, then the answer is yes. Causality will have itsnormal "physical definition", except that with comp suchphysicalness is given by an arithmetical quantization (based on thematerial hypostase defined by Bp & Dp): p physically causes q, iffsomething like BD(BDp -> BDq). I recall Dp = ~B ~p. But of course,in God eyes, there is only true (and false) number relations. Thelöbian phenomenon then shows that the consciousness self-speeding upis coupled with the building of the reality that the machine bet on.At that level, it is like if consciousness is the main force,perhaps the only original one, in the physical universe! This needsstill more work to make precise enough. There is a complex tradeoffin between the "causally" and the "effective" at play, I think.I hope this was not too technical. The work of Gödel plays afundamental role. This explanation is detailed in "Conscience etMécanisme", and related more precisely to the inference inductiveframe.To sum up: machine consciousness, in the theory, confers self-speeding up abilities to the machine with respect to the mostprobable continuation/universal-machine. It is obviously somethinguseful for self-moving creature: to make them able to anticipate andavoid obstacles, which would explain why the self-moving creatureshave developed self-reflexive brains, and become Löbian (self-conscious). Note that here the role is attributed to self-consciousness, and not really to consciousness. But you needconsciousness to have self-consciousness. Consciousness per se hasno role, like in pure contemplation, but once reflected in theLöbian way, it might be the stronger causally effective forceoperating in the 'arithmetical truth', the very origin of the (self)acceleration/force.Why do you always limit the definition of consciousness(atleastmachine consciousness) to its ability to learn alone ?

`I don't rememeber having done that. For reason of simplicity I study`

`the consciousness of the simple correct self-introspecting machine.`

`That is already very complex and enough to get the qualia and the`

`quanta. A solution of the measure problem should account for the other`

`minds and the gluing of the computations (if not then we get the`

`result that comp is false).`

why shouldn't free-will and sensory experiences(qualia,if youbelieve in it)be part (rather than being a consequence orprecondition) of consciousness itself ? In the absence ofconsciousness,there is indeed absence of free-will and experiencingqualia.In that case,we can't prove that a universal machine is conscious.

`Right. But I took as obvious that nobody can prove than even himself`

`is conscious. We can never proof that anything is conscious.`

Bruno

Note that the Gödel speed-up theorem is not hard to prove. There isa simple proof of it in the excellent book by Torkel Franzen"Gödel's theorem An Incomplete Guide To Its Use and Abuse" which Irecommend the reading (despite it is more on the abuses than theuses). The original paper is in the book by Davis: the undecidable(republished in Dover), and which I consider as a bible for"machine's theology".Bruno 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-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.--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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