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".
Bruno
http://iridia.ulb.ac.be/~marchal/
