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 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".



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