On 03 May 2017, at 15:21, Telmo Menezes wrote:
I think that mechanism gives the most of what we can hope for an
explanation
of what consciousness is.
A number e can refer to itself and develop true belief about
itself,
including some guess in its relative consistency.
I can understand self-referentiality, and at the same time that
there
is "something" to it that is profound but not fully graspable -- as
Hofstadter talks about with his "strange loops".
Then the theory explains
why any Gödel-Löbian machine can access to the truth that such
belief can
be
correctly (but that is not seen by the machine, only by god/truth)
related
to the truth, but only in a non communicable way. So the machine
knows
truth, that she is unable to justify, and can only seem mysterious.
I am ok with this.
Then, it is weirder for me why you are not convinced by the machine's
explanation of consciousness.
But you conclude yourself, that the machine knows truth, that is
unable to justify, and can only seem mysterious. The fact that I find
consciousness mysterious isn't exactly what you would expect?
Yes. But now we are in the Gödelian trap. Interpret (momentarily)
"consciousness" by "consistency" (<>t), and justify x by "prove
x" ([]x).
We seem to agree with ~[]<>t (we cannot justify/explain/rationally-
believe-in consciousness, so there is a mystery)
Then the machine explanation comes: <>t -> ~[]<>t (the machine proves
that if she is consistent then she cannot prove it), and similarly, my
explanation of the "mystery" is that if we are conscious we can
understand that we cannot justify it.
So there is a mystery (a non justifiable truth), but in the cadre of
the mechanist hypothesis, we can explain why there is necessarily a
mystery. The mystery remains "lived" from the first person
perspective, but we can understand, even in the 3p view, that if
mechanism is true then it is expected that we feel it as mysterious.
Eventually, it is no more mysterious than our belief in numbers.
That does not explains the whole of consciousness, but that
reduce its
mystery to the mystery of our belief in anything Turing
universal, like
the
numbers.
But then again, the numbers explains, by themselves, why if you
belief in
anything less than them, you cannot get them, and so justify their
mysterious character. We don't know, and it is the fate of any
machine to
not know that.
Don't mind to much. I am not sure if what you miss is a part of
mathematical
logic, or something about consciousness.
Again, I am convinced by your explanation of why the mystery exists.
The mystery is our understanding or belief (in apparently a finite
time) of
elementary arithmetic.
For me, the hard problem remains: you talk about mathematical
constructs.
Only half of the time, unless you put mathematical truth in the
mathematical
construct, something typically impossible to do, except for some
approximation, for theories much simpler than ourself. I guess you
know the
difference between the true fact that 2+2=4, and the much weaker
fact that
some machine or theory believes or prove that 2+2=4. In fact the word
"mathematical construct" is a bit ambiguous. The semantic in
general is not
a construct, when we do mathematics, but partial semantic can be
associated
to mathematical construct, when we do metamathematics (mathematical
logic),
but this is due to the fact that we approximate meaning by
"mathematical
construct" (which are most often infinite and non computable
mathematical
object).
Physicalists talk about emergence from complex
interactions of matter. I remain baffled and ask you the same
question
that I ask physicalists: what is the first principle from where
consciousness arises?
Truth. That cannot be a mathematical construct (provably so if
computationalism is true). It is not 3p definable.
Aren't you just renaming the mystery?
Truth is much more general than consciousness. All logicians and
mathematicians believe in (arithmetical) truth, but few would even
dare to use a term like consciousness. Truth has been very well
treated by Tarski, and I use that (sometimes implicitly, sometimes
more explicitly). It is a key notion, which is on the side of
semantic, or model theory, unlike provable and consistency, which
admit arithmetical definition. Arithmetical truth can still be treated
mathematically, at the meta-level, using set theory or second-order
logic. Consciousness/knowledge remain more problematical, and mix
syntax and semantics, like with the Theaetetus' definition []p & p. We
cannot define this in arithmetic. We would need []p & true(p), but if
true p was definable, we would be able to get a sentence k provably
equivalent with its falsity (PA would prove p <-> ~true(p), leading to
inconsistency).
The whole key is in the theorem that ([]p & p) does not admit a
predicate
definable to any machine from which "[]p & p" is (meta)defined.
I understood this as a key to understanding why certain things cannot
be known, but not to knowing them...
Well, "[]p & p" obeys to the logic of knowledge. So PA knows all its
theorem, for example. The difficulty with consciousness, is that it is
close to consistency (<>t) in the 3p view, and close to the
triviality (<>t v t) in the 1p view. That makes consciousness
"obvious" for the machine, and unprovable, once the machine
approximates it by any third person notion.
I confess I have a hard time formulating the question correctly. I
feel that what I am trying to ask is so fundamentally simple that it
becomes hard to write the real question.
That is common when we dig on notion like truth and consciousness.
Those
notion are too much obvious from the 1p view, and almost non
intelligible in
the 3p view, which explains why materialist want to eliminate them.
Ok.
Yes, I came across this over and over. Materalists want to eliminate
the question because they can sense that it is subversive to their
belief system.
Plausibly so.
The core of the explanation is in
the G/G* separation, and its inheritance by the intelligible and
sensible
matter. We might come back at this some day or another. I am of
course
very
interested in trying to see what you miss here. The explanation
is like
the
cow koan: the head of the cow go through the window, like the
legs and
the
truncs, but not the tail. That will play a role also in the fact
that
computationalism is a theology: the soul of the machine cannot
understand
rationally that she will be resurrect. That is the fun of it:
the soul
of
the machine says "no" to the doctor, until some leap of faith in
some
situation.
This is harder for me to follow, but I think I follow you on the
"barriers to knowledge".
I definitely don't understand the cow koan!
The idea is that about truth and consciousness we can explain
everything,
except for a tiny detail. But with computationalism, we can explain
why they
should remain a tiny detail which has to be NOT explainable from the
machine's pov.
Ok, thanks! It's a nice koan :)
Maybe I will just ask you this. 1) Do you agree that
consciousness is a
form
of knowledge?
I'm not sure. I think that I know that I am consciousness, but that
consciousness itself is unlike anything else that I can talk about.
I am inclined to think that consciousness = existence. Perhaps it's
such a simple and fundamental thing that it becomes almost
impossible
to talk about it.
Consciousness is the 1p feeling that there is something real. I am
not sure
why consciousness would be existence. There are things which exists
and are
not conscious.
What I mean is more along the lines of: are there things that exist
outside of the content of someone's consciousness?
Call it collective solipsism, maybe...
With mechanism, we need to believe that phi_i(j) is defined or is not
defined independently of us, for any choice of an acceptable
enumeration of the partial recursive function. We need to be platonist/
realist on the sigma_1 (and pi_1, the negation of sigma_1)
propositions. We need to believe in the consequence of Robinson
Arithmetic (at least).
But the reason why I wrote it has to do with the radical simplicity
that I attribute to consciousness. It exists, and I don't know what
else I can say about it (from my 1p experience).
Yes, here you talk like the subject described by S4Grz. It is
basically <>t v t. It is "there is a reality of (0 = 0)". But the
machine cannot equate that consciousness with this, unless she buy
mechanism (against its first person instinct) and try to make a
theory. In that case you add something highly non trivial to your
consciousness, which is the bet that it is sustained by some relative
digital processing, and maintained through the doctor's brain
transplant.
Consciousness is more what we need to give meaning to word like
"meaning".
It is on the semantical side, like truth.
Do you agree that consciousness is undoubtable and unjustifiable. I
cannot
doubt consciousness because doubt requires consciousness, and I
cannot
justify consciousness (cf the conceptual existence of philosophical
zombie).
I agree that it is undoubtable. In fact, I think that it is the only
thing I can think of that is undoubtable.
That is very nice, as it would make its undoubtability useful for an
axiomatic definition of consciousness. It would be define by what is
true and undoubtable.
I don't know if I agree that it is unjustifiable. I feel you are using
"unjustifiable" as a technical term that perhaps I don't fully
understand.
I mean that you cannot rationally convince another conscious entity
that you are conscious. You will need poetry, music, art, etc. There
are no 3p discourse, nor 3p test which would prove that some entity
are conscious. Of course, we can add evidence for betting that some
entity is conscious, and we have some instinctive empathy, it seems,
for our human fellows.
2) that knowable obeys the S4 axioms?
S4 =
[](A->B) -> ([]A -> []B) K
[]A->A T
[]A -> [][]A 4
Then incompleteness explains why this works with "[]" payed by
provability,
I don't understand this sentence, what do you mean by "payed by
provability"?
I meant "played by provability". Sorry for the typo. It means that
"[]" is
for Gödel's provability predicate. It is Gödel's incompleteness
which makes
the box behaving like a belief, and unlike a knowledge.
Ok.
Imagine that incompleteness would have been false. Then we would
have "[]p
<-> []p & p" not only true, but provable by the machine, and the
logic of
the 3p self would have been the same as the logic of the 1p-self,
making
impossible to associate to a machine a different notion for its 1p
and 3p
points of view.
Ok.
It is because []p -> p is NOT provable by the machine, that the
logics of
[]p and []p & p differs. Without incompleteness the 8 hypostases
would
collapse.
Ok.
and gives a temporal non nameable subject, which cannot identify
itself
with
any third person notion. Looks like my poor soul to me :)
I agree that what I call "consciousness" is something that cannot
identify itself with third person notions. This is what leads me to
suspect that it is not something that can be studied scientifically.
When doing science, we cannot invoke first person notion (or god,
or truth),
but there is no reason why we cannot make a 3p theory *on* those
notion, and
do the 3p reasoning and the 3p experimental verification for the 3p-
sharable
part of the theory.
That is exactly the case with computationalism. We cannot define
consciousness, but we know pretty well what it means for each of
us, and can
make hypothesis on it (like "yes doctor"), and study the consequence.
Ok, this is how you convinced me that computationalism and physicalism
are incompatible.
OK.
Similarly, Pean arithmetic cannot define arithmetical truth, and
cannot
define knowledge, but can simulate truth by the assertative p, and
conjunct
it, for each arithmetical sentence to its boxed presentation, and
so even PA
can see that it obey S4, which is usually a good axiomatics for
knowledge.
And that explains why, if the machine tries the Maharshi koan "Who
am I",
she might get the ineffable point. In fact, if she succeeds to
remain
correct all along the introspection, she cannot avoid the "ineffable
answer".
I have to think about this, but I believe I see your point.
Brent argues that AI will dissolve the hard question. I think that
people know intuitively that it will not. This is what pop-culture
works such as "Blade Runner" are about.
Like Minski, or McCarthy, I think that not only the problem will not
dissolve, but the machines will work on it, and have hard time with
it. Of course, we can dissolve the problem by burning the machine
alive when they contradict the government theory, which is the usual
human method.
I think that what you need to keep in mind, and understand, is that
despite
its simple 3p meta-aspect, "[]p & p" refers to something which does
not
admit any 3p explicit definition. That is also the reason why I
insist so
much that "[]p & p" is a theological notion, and why saying "yes"
to a
doctor is a theological act of faith. The machine is simply unable
to prove
for each p that []p and []p & p are equivalent. Only its own G*
knows that.
I feel that, in the end, this is all I was saying. That you don't have
a 3p definition of consciousness, although you might be able to show
why such a definition is not possible.
OK. Then the point is in the consequence of what I call the third
theorem of Gödel, which is that PA (or Gödel's Principia Mathematica)
can prove its own second-incompleteness theorem. Gödel announced it in
his 1931 paper, but it was proved by Hilbert and Bernays later, and
embellished and generalized by Löb.
It might be useful to have in mind the four theorems of Gödel
0) 1930: the completeness theorem for predicate calculus. A first
order theory is consistent iff it has a model (equivalently if a first
order theory proves some formula A, then A is true in all models of
that theory).
1) 1931: first incompleteness theorem: If T is a "rich enough" theory
there will be an undecidable sentence (yet true in the standard model
of the theory)
2) 1931: second incompleteness theorem if T is rich enough and
consistent T cannot prove that (personal) consistency.
3) The Gödel-Hilbert-Bernays-Löb theorem: if T is rich enough, T
proves <>t -> ~[]<>t (the formalisation of the second theorem made by
or in T).
The "machine theory on machine consciousness" uses them all, and
others, but the most important one is the "3)". It can be used quickly
to refute Luca/Penrose type of argument based on Gödel's
incompleteness against Mechanism. It shows that the machine PA found
Gödel's incompleteness before Gödel, so to speak.
Bruno
Telmo.
Bruno
Telmo.
Bruno
What I don't like about your position is this: just because
science
cannot address (or as not so far been able to address) a mystery,
doesn't mean that this mystery becomes irrelevant or that we can
pretend it doesn't exist -- or worse, that we should pretend
that we
have a viable theory when we don't. This is essentially what
makes me
agnostic instead of an atheist: I recognise that the big mystery
is
there. Labelling people that recognise that the mystery is there
as
lunatics does not serve intellectual rigor.
Then we can talk about evidence.
Second. An argument from authority is not necessarily a
reason to
reject
that argument. Because life is short and we cannot be experts
in
absolutely
everything, we frequently have to rely on authorities --
people who
are
recognized experts in the relevant field. I am confident that
when I
drive
across this bridge it will not collapse under the weight of
my car
because I
trust the expertise of the engineers who designed and
constructed the
bridge. In other words, I rely on the relevant authorities
for my
conclusion that this bridge is safe. An argument from
authority is
unsound
only if the quoted authorities are themselves not reliable --
they
are
not
experts in the relevant field, and/or their supposed
qualifications
are
bogus. There are many examples of this -- like relying on
President
Trump's
assessment of anthropogenic global warming, etc, etc.
I agree that arguments from authority are necessary to save
time, but
in the context of a debate about a mystery of nature for which
no
strong and widely-accepted scientific theories exist, it is
nonsensical to invoke authority.
Also, this is not a place where people come to have their car
repaired, or their doctor appointment. This is a discussion
forum
about the unsolved deep mysteries of reality.
Which is exactly the point. Because their mechanic can repair
their
car
they suppose we have explained cars - but we have only found the
Lagrangian
that described them. When we can write the programs that produce
"conscious" behavior of whatever kind we choose, cheerful,
autistic,
morose,
lustful, humorous,..., then most people will think we have
explained
consciousness. Mystics will still claim there's a "hard
problem".
This feels like thought policing. Of course the mystery is still
there, and it's huge! Why am I conscious? I can't think of a more
compelling mystery. Why is it so hard to say: "I don't know"?
Congrats on your daughter's wedding!
Telmo.
Brent
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