On 01 Nov 2015, at 04:55, Pierz wrote:
OK, a subject title designed to provoke, but here's a thought that
has intrigued me. Computationalism (and let's not worry for the time
being about whether one buys Bruno's UDA) states that consciousness
supervenes on computation. This necesssarily implies (by Church
thesis) that the hardware doesn't matter. This commits us to some
unintuitive scenarios in which thought is instantiated by means of
carrier pigeons delivering letters with symbols written on them, or
dominoes falling or whatever. It's assumed that such a computation
must reach a certain level of complexity in order to become
conscious, though what level of complexity is not specified.
It seems to me that since 2008, I give the precise threshold for both
main "level" of consciousness. I agree that before, I was clear only
on the second one. And I agree that for the first one, I have still
big doubts.
For "just consciousness", it can, and is, somehow there at the level
of Turing universality for its belief system. In that sense I think
that all animals, plants and cells are already conscious, and those
entities can react to sense when they have one. I have not study the
logic of such belief, but they are somehow before the "reasoner of
type 4" in Smullyan's book. Their first person consciousness/knowledge
theory is KT, but is not KT4 (still less KT4L (G)).
Then, there is the level of self-consciousness, which is the preceding
one, + what Smullyan calls "self-awareness", and which makes the
belief system (the "[]") obeying []p -> [][]p.
Basically this comes from "Löbianity", when machine can prove that
they are Turing universal, that is when they can prove, for each
particular sigma_1 sentence that p -> []p. As "[]p" is itself sigma_1,
this entails the self-awareness []p -> [][]p.
So consciousness corresponds to universality, in the sense of Church-
Post-Turing-Kleene-Davis-1956
and self-consciousness corresponds to what I call Löbianity (which is
awareness of one own universality, in some weak technical sense.
In term of provability of arithmetical sentences, it is the difference
between sigma_1 completeness and the so-called provable sigma_1
completeness.
And the usual example are
1) Robinson Arithmetic (RA, sigma-1 complete, p -> []p is true for p
sigma_1): conscious
2) Peano Arithmetic (PA, p -> []p is not only true, but provable by
PA): self-conscious
Now, self-conscious can develop knowledge, but it is not yet clear if
that hides the original consciousness, or if it is only the confusion
between []p and [1]p which hides consciousness. It is related to the
galois connection between theories and models, as consciousness
eventually seems to side on the semantical part of the first person:
you are the infinity of sense you can do with respect to all
computation going through you.
Now, consciousness is more in the formula [1]p -> [1][1] of the KT4
logic, sublogic of S4Grz. It is the 3p "self-awareness" of Smullyan,
after the application of the definition of knowledge of Theaeteus.
It is a good exercise: show that G proves [1]p -> [1][1], using the
Theaetetus definition [1]p = []p & p. I will provide the solution
soon, or later, but that should not be excessively difficult (you
might need that [](p & q) <-> ([]p & []q), which you can see directly
with the Kripke semantics, or you can prove it using necessitation and
classical tautologies like
((A & B) -> B), and (A -> (B -> (A & B))).)
As I try to stay at the propositional level of the logic of
provability/consistency (G), I let harder question necessitating the
full first order provability logic for later.
According to some views (Brent has expressed this position), it is
necessary that the computations reference a "world", though I'll
admit I don"t understand the rationale for that exactly.
I think I do. It is even related to Bruce remark that a digital
machine, which just shuffle symbols can only miss the semantics, and
thus the reference.In the 3p descriptions, all that is correct.
But the 3p only talk on the body, and it is the soul which is the
subject of knowledge/consciousness. The machine cannot define its
soul, but can define it for a simpler machine than itself. We cannot
define the "[1]" in the language of a machine to which it applies. If
Tarski theorem was false, so that we could define the notion of
arithmetical truth by an arithmetical predicate, then the machine
would be able to define consciousness and knowledge, but by Tarski
theorem, no correct or consistent machine can do that. But the Löbian
machine can understand that this is necessarily so, when using
Theaetetus' definition, and that this one makes an operator formalized
by the logic S4Grz, and which makes the tour de force to formalize at
the metalevel, the non formalizable-by-the-machine-itself soul, or
first person.
Socrates rejected this definition, but he missed Church and Gödel.
Important though is that it is neither necessary that the
computations are carried out in some localised "device"/brain nor
that they are carried out by "wetware".
So my thinking is this: isn't evolution precisely such a computation?
The DNA, that is a use of some digitalness, is a strong evidence for
this. The idea of mutation is also quite "digital" in spirit.
Yet, the cell have variate means of regulation, some are quite like
Boolean threshold, but other are quite analogical, complicated non
linear response. Of course this can be imitated by some digital
machine at some level below, but the conscious machine is not the
imitatator: it is the imitated machine.
Does evolution makes machine imitating conscious machine, at higher
levels: no doubt. But it is an open problem to attribute personhood,
if the entities are not named. is a tree conscious, or only a forest?
Or a Forest + a mushroom linking all trees, etc.
It is undoubtedly an extremely complex calculation (more so than any
human thought has ever been),
and it undoubtedly "references a world". Bruno mentions "Loebianity"
in this context as well, or the capacity for self-reference.
RA has already a capacity of self-reference, but it lacks the ability
described by the ability of proving
[]p -> [][]p, despite it is true for RA. If RA proves []p, for some p,
soon or later RA will prove [][]p, but RA is not able to prove "[]p ->
[][]p' for all p. PA can do that, and it is about the jump from the
worms to the jumping spider, or octopus.
But keep in mind that both the theory and salvia invites me to
consider seriously the possibility that PA has already sinned, and
might be less conscious than PA. In that case, the more neurons, the
less you can be conscious, like if the building of the self eventually
hides more deep knowledge than it produces.
I don't know. Big brain can be much more deluded much than small
brains, somehow.
I'm not so sure about this in relation to an evolutionary
computation. Certainly it is a highly recursive procedure with a
continual self-environment feedback loop. I don't understand
Loebianity sufficiently to say whether genes , or the gene-
environment system, might possess it.
I doubt bacteria have it. A long time ago, my criterion was homeotherm
animals, as it was believed that was needed for dreams, but I use now
the criterion of showing you have induce a reality, and the video here
makes me believe that a jumping spider has belief about a reality.
With consciousness you are God and live the life you live. With self-
consciousness you begin to believe in God, and the blaspheme, and all
the catastrophes, is on the horizon.
However I'm also not sure if it's required for consciousness, or
merely self- consciousness.
I was quite undecided up to 2008. The reason was that I was agreeing
with Brouwer that consciousness needs time, and this appears with soul
"S4Grz". Once we accept that a non Löbian machine can be consciouss,
then consciousness can be dissociate from brouwer subjective time,
which I thought to be non sense. But Salvia makes me doubt on this,
and so confirms a possibility that there is a consciousness state
which is ... well, let us say perpendicular to time.
I don't see that the possession of qualia demands the possession of
self-awareness,
Nor do I. Worms can suffer, even plants I think, but God knows on
which scale(s).
though I can also see that it is at least conceivable that an
evolutionary feedback system might possess a kind of self-reference.
I completely agree. The problem with computationalism, is that you can
understand completely a level, and understand nothing at the next
higher level. Reductionism fails at all levels. Now, again, if there
is something Löbian, you have to name it: evolution is not enough, as
it is very low level, but some procedure evolution used on large scale
might be conscious: we just have no evidence yet.
Anyway it seems that if we're committed to computationalism plus
Church thesis,
Comp -> CT (you need CT to just explain properly what is a
computation). And to explain CT, you need some minimal amount of
realism in arithmetic (technically, the excluded middle must be
accepted for the sigma_1 and thus Pi_1 formula, to show the closure of
the partial computable function, or the sem-decidable (RE) sets, for
the diagonalization procedure (Gödel's "miracle").
then we have to consider the possibility that evolution may be a
conscious process
yes, but a bit like RA, or the universal dovetailer. And it is the
universal machine behind, and it could be dissociate of what it is
doing in time. If not, you subsume a self, and you have to name it in
a way we can address the question.
Would you say that your left hand is conscious? It can feels things,
or it is only you?
- indeed the onus should be on us to say why it wouldn't be
conscious. Which does not mean I am suggesting some mystical
additional ingredient. Evolution would still be described
objectively in terms of random mutation plus environmental
selection, but this process may have an interior component, its own
"1P".
Thoughts?
"evolution" is a process. It might involve conscious subroutines, and
large + long scale dialog, but to find them can be a terribly complex
task for us.
My current feeling is that there is only one 1p. The universal person,
and only one consciousness, the first person of that universal person,
then Löbianity makes possible more fun and difference in experience,
but also the possibility of losing oneself in exploding many selves,
and yes, probably much more than what is apparent.
Even our own brain might contain conscious high level subroutines we
are not aware of. Such person can fuse and differentiate, without ever
being aware of each others. When the corpus callosum is sleepy, we can
do two dreams simultaneously, according to L. Jouvet (the discoverer
of the REM dream); and the split brain people are said sometimes to
implement two persons, but of course, all this is just very difficult,
and Löbian machines warn us, if we are correct machine, we don't know
which machine we are (even after surviving (apparently) a
teleportation).
The Löbian machine has an anwer for the "Who am I" question of Ramana
Maharsi. The answer is "we don't know". the precise answer, we can't
know that in any public communicable way. That might be part of the
reason why, according to Lao Tseu, the wise stays mute.
Bruno
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