On 03 Jul 2011, at 09:51, selva kumar wrote:
On Sat, Jul 2, 2011 at 4:57 PM, Bruno Marchal <[email protected]>
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 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).
Extrapolating this and working this on human-machine,consider this..
If we firmly believe that all our proofs and instincts on
mathematical 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 are
intelligent,then you become more intelligent (which is in immediate
contracdiction with godel's second incompleteness theorem and your
smallest 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 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.
Why do you always limit the definition of consciousness(atleast
machine 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 you
believe in it)be part (rather than being a consequence or
precondition) of consciousness itself ? In the absence of
consciousness,there is indeed absence of free-will and experiencing
qualia.
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 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/
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