On 01 Jul 2011, at 13:23, selva kumar wrote:

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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 David`

`Deutsch) ? I thought I did answer this question, which is a very`

`imprtant and fundamental question.`

`It is also a tricky question, which is very similar or related to the`

`question of free-will, and it can lead to vocabulary issue. I often`

`defend the idea that consciousness is effective. Indeed the role I`

`usually defend for consciousness is a relative self-speeding up`

`ability. Yet the question is tricky, especially due to the presence 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 hope for`

`some understanding of the UDA and a bit of AUDA. Ask precision if`

`needed.`

The main ingredient for the explanation are three theorems due to Gödel:

`- the Gödel completeness theorem (available for machine talking first`

`order logic or a sufficiently effective higher order logic). The`

`theorem says that a theory or machine is consistent (syntactical`

`notion, = ~Bf) iff the theory has a model (a mathematical structure in`

`which it makes sense to say that a proposition is true). I will`

`rephrase this by saying that a machine is consistent if and only if`

`the machine's beliefs make sense in some reality.`

`- the Gödel second incompleteness theorem ~Bf -> ~B(~Bf): if the`

`machine is consistent, then this is not provable by the machine. So if`

`the beliefs are real in some reality, the machine cannot prove the`

`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 that eventually, the`

`machine can add as new axiom its own consistency, but this leads to a`

`new machine, for which a novel notion of consistency appears, and the`

`'new' machine can still not prove the existence of a reality`

`"satisfying its beliefs. yet that machine can easily prove the`

`consistency of the machine she was. This can be reitered as many times`

`as their are (constructive) ordinals, and this is what I describe as a`

`climbing from G to G*. The modal logic of self-reference remains`

`unchanged, but the arithmetical interpretation of it expands. An`

`infinity of previously undecidable propositions become decidable,`

`and ... another phenomenon occurs:`

`- Gödel length of proof theorem. Once a machine adds an undecidable`

`proposition, like its own consistency, as a new axiom/belief, not only`

`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 a proposition`

`which proofs will be x times shorter than its shorter proof in the`

`beliefs system without the undecidable proposition. A similar, but not`

`entirely equivalent theorem is true for universal computation ability,`

`showing in particular that there is no bound to the 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 or programmable in`

`advance).`

`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 an ability`

`of betting its own consistency (excluding that very new axiom to avoid`

`inconsistency). As a universal system, this will speed-up the machine`

`relatively to the probable local universal system(s) and will in that`

`way augment its freedom degree. If two machines play ping-pong, the`

`machine which is quicker has a greater range of possible moves/`

`strategy than its opponent.`

`So the answer to the question "is consciousness effective" would be`

`yes, if you accept such definition.`

`Is that consciousness *causally* effective? That is the tricky part`

`related to free will. If you accept the definition of free will that I`

`often suggested, then the answer is yes. Causality will have its`

`normal "physical definition", except that with comp such physicalness`

`is given by an arithmetical quantization (based on the material`

`hypostase defined by Bp & Dp): p physically causes q, iff something`

`like BD(BDp -> BDq). I recall Dp = ~B ~p. But of course, in God eyes,`

`there is only true (and false) number relations. The löbian phenomenon`

`then shows that the consciousness self-speeding up is 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 needs still more work to make`

`precise enough. There is a complex tradeoff in between the "causally"`

`and the "effective" at play, I think.`

`I hope this was not too technical. The work of Gödel plays a`

`fundamental role. This explanation is detailed in "Conscience et`

`Mécanisme", and related more precisely to the inference inductive frame.`

`To sum up: machine consciousness, in the theory, confers self-speeding`

`up abilities to the machine with respect to the most probable`

`continuation/universal-machine. It is obviously something useful for`

`self-moving creature: to make them able to anticipate and avoid`

`obstacles, which would explain why the self-moving creatures have`

`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 need consciousness to have self-`

`consciousness. Consciousness per se has no role, like in pure`

`contemplation, but once reflected in the Löbian way, it might be the`

`stronger causally effective force operating in the 'arithmetical`

`truth', the very origin of the (self) acceleration/force.`

`Note that the Gödel speed-up theorem is not hard to prove. There is a`

`simple proof of it in the excellent book by Torkel Franzen "Gödel's`

`theorem An Incomplete Guide To Its Use and Abuse" which I recommend`

`the reading (despite it is more on the abuses than the uses). 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 Google Groups "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.