On 06 May 2017, at 11:21, Telmo Menezes wrote:
On Wed, May 3, 2017 at 4:51 PM, Bruno Marchal <[email protected]>
wrote:
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.
Ok, I have no problem with any of this.
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.
But our belief in numbers is pretty mysterious, no?
Yes. Total mystery akin to the problem of consciousness. But unlile
consciousness, this one is completely solved: we can derive the
natural numbers from anything simpler (failure of logicism).
Consciousness, on the contrary, is derivable from that "number
mystery", except for a tiny part of it, which, like the number, needs
to exist for us not falling into insanity/inconsistency.
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).
Ok.
The salient thing for me here is that you tend to place consciousness
and knowledge as very close concepts. While I agree that consciousness
is a form of knowledge, for me the big mystery is closer to asking
"who knows?" or "what knows?".
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.
Ok.
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.
Is it fair to call comp a theory? Do you think it can be falsified?
yes, it is the whole point of my work. If someone set up an experiment
showing that the logic of the observable violate the material
hypostases, then we get a string clue that computationalism is false---
or that we are in a second order malevolent simulation.
Computationalism makes the whole physics derivable from arithmetical
self-reference, so it is hard to imagine a theory more easily
refutable, and indeed, I predicted that it would be refuted quickly.
I believe we talked about this before, sorry in that case.
No problem. The subject is difficult. It is normal to make a lot of
passes.
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.
Ok, nice.
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.
Ok, then I agree.
OK.
So it looks like you agree with the following axiomatic for
consciousness:
true and undoubtable
true and unjustifiable.
Then we solve the "consciousness problem" by finding something
verifying that axiomatic for all (Löbian) machines.
The solution, of course, is partial, as it leads to the matter
problem, where we can no more use the ostensive definition of matter.
In fact, we can no more invoke matter to justify the stability of our
consciousness. We must justify the appearance of matter by the
statistics on all sigma_1 sentence, and we get indeed types of quantum
logics for each of them, making digital mechanism, or classical
digital mechanism, quite plausible ... up to now.
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.
Yes, this is more or less what happens in Blade Runner, except that
they shoot the machines.
Shooting is pehaps more "human" than "burning alive". We progress,
perhaps! (in movies!).
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.
The only thing that confuses me here is the direct use of t.
I can follow:
<>p -> ~[]<>p
Intuitively this makes sense if I say, for example, that p means "I
am sane".
I understand things like t -> f in the context of reductio ad
absurdum, but the direct use of t in the expression above still
baffles me.
I am not sure why. <>t is simply ~[]f. Consistent ~('0 = 0') =
~beweisbar('~(0=0)'). OK?
To prove "~p" is the same as proving 'p -> f", and is not a reduction
ad absurdum, it is just a proof of a negation. A reduction of
absurdum, of the type disliked (and rejected) by the intuitionists is
proving p by proving (~p -> f). An intuitionist would say that we
have proven only ~~p, which he believes is weaker than p (indeed, ~~p
is not *constructively" equivalent to p, only classically equivalent).
Bruno
Telmo.
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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