On 21 Oct 2012, at 18:42, Jason Resch wrote:
On Sun, Oct 21, 2012 at 8:56 AM, Bruno Marchal <[email protected]>
wrote:
Hi John,
On 20 Oct 2012, at 23:16, John Mikes wrote:
Bruno,
especially in my identification as "responding to relations".
Now the "Self"? IT certainly refers to a more sophisticated level
of thinking, more so than the average (animalic?) mind. - OR: we
have no idea. What WE call 'Self-Ccness' is definitely a human
attribute because WE identify it that way. I never talked to a
cauliflower to clarify whether she feels like having a self? (In
cauliflowerese, of course).
My feeling was first that all homeotherm animals have self-
consciousness, as they have the ability to dream, easily realted to
the ability to build a representation of one self. Then I have
enlarged the spectrum up to some spiders and the octopi, just by
reading a lot about them, looking video.
But this is just a personal appreciation. For the plant, let us say
I know nothing, although I supect possible consciousness, related to
different scalings.
The following theory seems to have consciousness, for different
reason (the main one is that it is Turing Universal):
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
But once you add the very powerful induction axioms: which say that
if a property F is true for zero, and preserved by the successor
operation, then it is true for all natural numbers. That is the
infinity of axioms:
(F(0) & Ax(F(x) -> F(s(x))) -> AxF(x),
with F(x) being any formula in the arithmetical language (and thus
defined with "0, s, +, *),
Then you get Löbianity, and this makes it as much conscious as you
and me. Indeed, they got a rich theology about which they can
develop maximal awareness, and even test it by comparing the physics
retrievable by that theology, and the observation and inference on
their most probable neighborhoods.
Löbianity is the treshold at which any new axiom added will create
and enlarge the machine ignorance. It is the utimate modesty treshold.
Bruno,
Might there be still other axioms (which we are not aware of, or at
least do not use) that could lead to even higher states of
consciousness than we presently have?
Yes, there are interesting transfinities below and beyond omega_1^CK
(the Kleene Church first non constructive ordinal). This has
plausibly, with comp, some relation with possible consciousness states
(but that is not obvious and depends on definitions).
Also, it isn't quite clear to me how something needs to be added to
Turing universality to expand the capabilities of consciousness, if
all consciousness is the result of computation.
Gosh! It is only recent, for me, that I even think that universal
machines are already conscious. I thought Lôbianity was needed. But
then it is basically the same as the consciousness-->self-
consciousness type of consciousness "enrichment/delusion". In a
sense, abstract universality is maximally conscious, maximally
undeluded, or awake, somehow.
But Turing universality is cheap and concerns an ability to imitate
other machine, not to understand them, so for provability and beliefs,
and knowledge there are transfinite improvement and enlargement
possible.
We are not just conscious, we differentiate in developing beliefs, and
get greater and greater view on truth.
It is like you might be near doing a kind of "Searle error" perhaps.
A computation can emulate consciousness, but the computation is not
conscious, only the person emulated by that computations, she can
always progress infinitely (even if "restricted" on the search of
arithmetical truth), develop more and more beliefs and knowledge.
Particular universal machines will develop particular parts (even if
transfinite) of arithmetical truth.
But G and G*, that is the modal logic of the provability of the Löbian
machines, is a treshold. Despite growing transfinitely on her
knowledge(s) of the arithmetical truth, as long as they remain self-
referentially correct, they will obey to G and G*, for their theory of
provability. If consistent, they will for ever been able to prove that
they are consistent, for example, and they can prove that for
themselves. The abstract theology is invariant despite the evolution
of the arithmetical content of the B in Bp. PA and ZF have very
different arithmetical beliefs, but both obeys to G and G*.
Consciousness, from the first person perspective is more related to
"all computations" going through my states, than any particular
computations. The living self is not a computer, it is a believer,
supported by infinities of computer (by UDA).
I am happy you are open to the idea that universal machine are all
conscious, it is then, the state of "you" before developing any more
beliefs than those making you universal. Your first person
indeterminacy, in that state, is all other possible machine/dreams.
The Löbian machine knows that they are universal, and so knows the
price to pay, for "staying consistent", like the possibility of
crashing, in front of the unknown arithmetical truth.
Thanks,
You are welcome.
Bruno
http://iridia.ulb.ac.be/~marchal/
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