On 18 Jul 2014, at 14:42, Craig Weinberg wrote:
On Friday, July 18, 2014 4:10:47 AM UTC-4, Bruno Marchal wrote:
With the TOE "elementary arithmetic" (predicate logic + RA axioms),
the input are numbers, and they obey the laws of addition and
multiplication. They make more sense according to which universal
numbers they are given to.
But what is an input? What laws indicate that a such thing as an
'input' can exist? What prevents all numbers from being 'put' from
the beginning?
Assume the axioms of RA. use Gödel's technic to define the phi_i in RA
(there are tuns of books which does that in all details). You can
define the enumeration of all the UD computational steps, by the
arithmetical version of the enumeration of the phi_i(j)^n. By
definition the number j are the input, to the program i. the
phi_i(j)^n represent the nth step of the computation of i on j.
nothing prevents all the numbers to be put on the beginning, and that
is why we have a big, yet mathematically soluble, self-indeterminacy
problem in arithmetic. Then we can test the solution, and it fits
already at the propositional level.
Of course if you use the combinators instead of elementary
arithmetic, the inputs are combinators, and the laws are:
Kxy = x
Sxyz = xz(yz)
+ some identity axioms.
Right, but I'm not asking about what kinds of things are inputs, I
am asking what is the ontology of "input" itself and what gives
computationalism the right to assume it?
There is no "ontology" proper. You can choose any first order
specification (definition) a anything capable to imitate any Turing
machine, or computer.
Once, and for all, I have chosen the following theory, which is
accepted by all scientists and most philosophers:
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
+ a bit of "syntactical sugar" (and + predicate logic).
I mention another often, to remind people that it is a key point of
the drivation of physics, that the ontic part has no influence on
physics. Physics is machine independent, like a large part of computer
science is machine-independent, like a large part of geometry and
physics are coordinate independent.
You can't program a device to be programmable if it isn't
already. Overlooking this is part of the gap between mathematics
and reality which is overlooked by all forms of simulation theory
and emergentism.
You are quick. Correct from the 1p machine's view on their own 1p.
You do confuse []p and []p & p.
So you are saying that programmability is universal outside of 1p
views?
At least in the same sense that 23 is prime "outside 1p views".
Then programmability becomes another axiom that computationalism
needs not to require an explanation.
?
A function is programmable if and only if the function is "partial
computable" (this includes the total functions).
I'm not talking about the function of programmability, I'm talking
about the metaphysics of the possibility of programmability.
Sorry, I don't do metaphysics.
The fact that there are tapes for Turing machines, that reading and
writing is even possible.
All that follows from
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
Literally. We know that since Gödel 1931. Turing knew that too.
"Everybody knowing the subjects" knows that.
Like infinite computational resources in a dimensionless pool?
You can see it that way.
Without some initial connection between sensitive agents which
are concretely real and non-theoretical, there can be no storage
or processing of information. Before we can input any definitions
of logical functions, we have to find something which behaves
logically and responds reliably to our manipulations of it.
The implications of binary logic, of making distinctions between
true/go and false/stop are more far reaching than we might
assume. I suggest that if a machine's operations can be boiled
down to true and false bits, then it can have no capacity to
exercise intentionality. It has no freedom of action because
freedom is a creative act, and creativity in turn entails
questioning what is true and what is not. The creative impulse
can drive us to attack the truth until it cracks and reveals how
it is also false. Creativity also entails redeeming what has been
seen as false so that it reveals a new truth. These capabilities
and appreciation of them are well beyond the functional
description of what a machine would do. Machine logic is, by
contrast, the death of choice. To compute is to automate and
reduce sense into an abstract sense-of-motion. Leibniz called his
early computer a "Stepped Reckoner", and that it very apt. The
word reckon derives from etymological roots that are shared with
'reg', as in regal, ruler, and moving straight ahead. It is a
straightener or comb of physically embodied rules. A computer
functionalizes and conditions reality into rules, step by step,
in a mindless imitation of mind. A program or a script is a
frozen record of sense-making in retrospect. It is built of
propositions defined in isolation rather than sensations which
share the common history of all sensation.
The computing machine itself does not exist in the natural world,
but rather is distilled from the world's most mechanistic
tendencies. All that does not fit into true or false is
discarded. Although Gödel is famous for discovering the
incompleteness of formal systems, that discovery itself exists
within a formal context. The ideal machine, for example, which
cannot prove anything that is false, subscribes to the view that
truth and falsehood are categories which are true rather than
truth and falsehood being possible qualities within a continuum
of sense making. There is a Platonic metaphysics at work here,
which conjures a block universe of forms which are eternally true
and good. In fact, a casual inspection of our own experience
reveals no such clear-cut categories, and the goodness and truth
of the situations we encounter are often inseparable from their
opposite. We seek sensory experiences for the sake of
appreciating them directly, rather than only for their truth or
functional benefits. Truth is only one of the qualities of sense
which matters.
The way that a computer processes information is fundamentally
different than the way that conscious thought works. Where a
consistent machine cannot give a formal proof of its own
consistency, a person can be certain of their own certainty
without proof. That doesn't always mean that the person's feeling
turns out to match what they or others will understand to be true
later on, but unlike a computer, we have available to us an
experience of a sense of certainty (especially a 'common sense')
that is an informal feeling rather than a formal logical proof. A
computer has neither certainty nor uncertainty, so it makes no
difference to it whether a proof exists or not. The calculation
procedure is run and the output is generated. It can be compared
against the results of other calculators or to employ more
calculations itself to assess a probability, but it has no sense
of whether the results are certain or not. Our common sense is a
feeling which can be proved wrong, but can also be proved right
informally by other people. We can come to a consensus beyond
rationality with trust and intuition, which is grounded the
possibility of the real rather than the realization of the
hypothetical. When we use computation and logic, we are extending
our sense of certainty by consulting a neutral third party, but
what Gödel shows is that there is a problem with measurement
itself. It is not just the ruler that is incomplete, or the book
of rules, but the expectation of regularity which is
intrinsically unexpected.
One of the trickiest problems with the gap between the
theoretical and the concrete us that the gap itself is real
rather than theoretical. There can be no theory of why reality is
not just information, since theory itself cannot access reality
directly. Reality is not only formal. Formality is not real.
There is a bias within formal logic which favors certainty. This
is at the heart of the utility of logic. In mathematician Bruno
Marshall's
Marchal, actually.
Gack! Sorry about that. :( I changed in the blog post. My wife
babysits a by called Marshall so he might have gotten in there.
Thanks, no real problem.
book "The Amoeba's Secret", his view on dreams hints at what is
beneath the surface of the psychology of mathematics. He writes
"What struck me was the asymmetry existing between the states of
dreaming and of being awake: when you are awake, you can never be
truly sure that you are. By contrast, when dreaming, you can
sometimes perceive it as such."
Surely most of us have no meaningful doubt that we are awake when
we are awake.
That ambiguous. I agree we felt like that. but we felt like that
in contra-lucid dreams. In those dreams, we dream that we have no
no meaningful doubt that we are awake.
But in all cases any doubt or doubt of doubt could be right or
wrong in the same way. The awakeness we feel in our doubt of a
lucid dream is no more than the awakeness if waking life, so if we
can trust the lucidity of a dream we can surely trust the lucidity
of actually being awake.
Not really. It is the same for correctness. You can know that you
have been wrong, because you can see the error,
No, you can be wrong about the error also. You might think that you
were wrong, but then find out that you weren't. There could always
be some time in the far future where every error you think you made
would be vindicated.
I assumed a case where you are correct of course---in the eyes of God.
Does correctness depend on the eyes of God?
Yes, given that in comp Arithmetical Truth is a good candidate for
God, as machine will not been able to distinguish them (as truth is
already too much dazzling or glaring, so that to distinguish truth
from God is already a super 1014 mistake on the par of the machine: no
doubt we can add nuance somedays).
Is God the source of correctness?
The source or the garant.
Is there no hope of a scientific explanation?
?
Scientific explanation provides the only public sharable hope.
But reality is bigger than that, as you can understand by looking
inward. (I know you do).
but you cannot know that you are correct, because "not seeing an
error" is not a valid argument that there are none.
That correctness of that statement would be subject to the same
logic - so not seeing an error in it is not a valid argument that
there is none.
See above. You are right, but it is not relevant for what I say. We
of course never know that we know for sure as such.
Given that we can never know for sure, the question becomes what it
is we are expecting from the universe to even use the language of
'sure'. If there can be no sure knowledge, then maybe we should not
assume that sure knowledge means something more than what is
possible. Maybe sure knowledge by definition means 'as sure as
possible within a given context'.
You forget that I did mention one sure knowledge, and it as a pivotal
role in the arithmetical dream glueing. Consciousness.
Altered state of consciousness can probably provide some others
"knowledge *sure* fixed points", but I am far for being able to really
interview the machine on that (unless salvia dissociation can be
explain in term of cut of []p & p & <>p into []p & p. But I speculate
here.
In fact, I see an error in it, since knowledge of correctness is
not necessarily an ontological fact.
Yes, it is. That's the key point. Knowing A is believing A *and* A.
That is the key point that I am disagreeing with.
That's hardly original. The point was even considered as refuted since
Socrates. Again, my point here is that machines, all by themselves can
refute Socrates.
I am saying that there can never be any such thing as knowledge or
propositions in reality. They are linguistic artifacts which
represent the intellects inflated opinion of its own views and
methods. A is made up. A is a truncated stereotype of
abcdefghijklmnopqrstuvwxyz. Blue is not simply blue, but the
opposite of yellow and red, the brother of green, the precursor to
violet, etc. Knowing blue has nothing to do with belief or a
hypothetical object of belief, it is a direct visual-emotional
acquaintance. Blue is a sensory experience, not a sensory experience
*of* something else, but of visual sense itself.
I have no problem with that. Yet, that is still a knowledge of the
visual sense itself through some consciousness.
But only God or the ontology is responsible for A. Knowing is
partially epistemological, and partially ontological.
I think that knowing is nothing but a sense of intellectual security
that arises out of coincidence across multiple frames of sensation.
The ontology of knowing is the ontology of feelings associated with
problem solving, not with any ontology beyond experience (there is
none).
That is solipsism.
There may be no such thing as knowledge or correctness in absolute
terms. Not seeing an error may be the extent of the reality of
correctness.
It is not symmetrical.
It is when you use the same standards.
Not at all. I do refer to the fact that we assume A, at the meta-
level, to provide that definition.
You use a separate standard for the dreamer when he is asleep
compared to when he is awake and not dreaming. When the dreamer
awakens in a dream and knows it, you applaud.
Yes, because it is fun. The dreamer can exploit the fact and fly among
galaxies or realize any sexual fantasies legally!. Usually the dreamer
applaud itself, in some sense.
When the dreamer awakens in reality and knows it, you add an
academic sophism of doubt.
Because he has no evidence other than an experience which can be
imitate in contra-lucid dream, and implicitly in all non lucid dreams.
In fact dreaming is absolute, and awaken is relative. Then in
theoretical context physics is defined by the awaken state, somehow.
But only God knows if you are at the base physical level. I grant you
that I tend to believe that you and me are at that level. It motivates
me to answer you!
It is bit like true ExP(x), with P decidable, is decidable, and is
more easy than its negation, which can be true and undecidable.
It is like finding an error shows the wrongness, but not finding an
error does not show the correctness.
That applies a different level of sophistication for the two. The
lucid dreamer is allowed his naive realism of knowing that he is
awake within a dream but to the same person, actually waking up is
subject to a further epistemological doubt. It's a fallacy.
You don't need naive realism to know that you are wrong, or in a fake
environment. You know that when you play a video game (unless you are
addicted to them up to the point of losing your lucidity, 'course).
Neither can be more correct than the other because they both have a
sense of being-more-awake-than-they-were which is not subject to
doubt. There is no proof that being awake is anything more than a
particular context of participation - we don't have to imagine that
it is ontologically pristine and all that is not awake is a
deviation from God's correctness. To me, that's not been true since
Godel, Einstein, and Heisenberg. Truth is sense, but sense is much
more than truth.
?
Of course there are intermediate. In dream I was flying, so I
conclude first that I was dreaming. But then I was not flying so
well and I eventually concluded that I was awake, as in dreams, I
fly much better than that!
But we can be wrong about thinking that we are dreaming. We could
be dead instead and living in an afterlife. We could have false
memories implanted which convince us that there is another world in
which dreams exist, but that in reality that world was the dream.
Exactly. That is why we cannot know that we are NOT dreaming.
No, that is why we cannot know that we ARE dreaming also. As I just
said - we could THINK that we ARE dreaming, but find out later that
we are dead, or that there is no such thing as dreaming and our
expectations of dreams are implanted.
But we can know that we are dreaming-or-wrong,
No, we cannot know that any more than we can know that we are
dreaming or wrong. The epistemology is precisely symmetric because
in order to know that we are wrong, we have to assume that there is
away to know that we can be right. If we can't know that we are
right, then have nothing against which to be wrong about.
when we find the "mistake", assuming it is indeed a mistake. That is
what is convey in the []p & p. The "p" is for "God knows p".
Yes, I understand, but that is what I am proposing. The entire model
is false. There is no p at all. There is no God knowing p, there are
only histories of experiences within a context of experience beyond
history. It all makes sense because it is sense - we/it shares a
common semantic gravitation which is inescapable but is not based
only on truths and beliefs. It's flavors and colors, faces, music,
etc.
of course nobody can know that, but we can reason in hypothetical
context where p is supposed to be true. The math of the reversa,
including the current argument,l is based by construction to ideally
correct machine.
I'm not talking about machines, I'm talking about the nature of
nature itself - of consciousness.
No problem with consciousness being the nature of nature, but that
does not make invalid that consciousness is a semantical fixed point
from the 1p of the machine's too, and that's what happen when the most
known definition of knowledge (and the most criticize) is applied in
arithmetic.
The addition of the qualification of being "truly sure" that we
are awake seems to assume that there is a deeper epistemology
which is possible - as if being awake required a true certainty
on top of the mere fact of being awake. To set the feeling of
certainty above the content of experience itself is an inversion;
a mistake of privileging the expectations of the intellect over
the very ground of being from which those expectations arise.
p was before []p, and even p & []p happens before (in machine's
self development) []p.
There is no p at all. p is formatting of an input.
p is put for some true arithmetical statement.
I am saying that does not exist fundamentally. There are no
statements, no truths, no arithmetic, only experiences about which
we can make arithmetic insights.
That makes sense assuming non-comp. It is not my theory. If you
believe that comp is contradictory, you have to to give an argument
which does not assume non-comp, of course. We already know that we
work in different theory.
I understand that comp is based on bad assumptions and is therefore
false.
I don't do any philosophy. I *never* argue for the truth of falsity of
any proposition. It is not my job.
My arguments are to point to all of the experiences which cannot
realistically be supported within comp. I do not subscribe to the
belief that comp can only be invalidated using arguments which
assume comp - that is ridiculous. That's like the church telling
Copernicus that if he believes that geocentricism is contradictory,
has to give an argument which does not assume heliocentricism.
Likewise, to say that we can sometimes perceive our dreaming in a
lucid dream is to hold the dream state to a different
epistemological standard than we do of being awake. If we could
be awake and not really be sure that we are, then certainly we
could think that we are having a lucid dream,
No. In the lucid dream, you know that you are dreaming.
You know that you are in a dream, but the part that knows that is
not completely dreaming and is more awake than usual during dreams.
OK. Some would say that for all dreams. It is an awaken
hallucinated and paralysed state. Just that in a lucid dream we
know that we are dreaming, that we know that we are "awaken", but
in the hallucinated state. But some use "awake" as contrary to be
be "asleep".
Using awake as contrary to be asleep is fine for informal use, but
to really get into consciousness and human psychology, I don't see
any grounds for asserting that the epistemology of dreaming is more
reliable than the epistemology of being awake.
I don't say that it is more reliable, except when the dreamer find
that he is dreaming, in the case he *is* dreaming.
But you are making a mistake here. The moment that the dreamer finds
that he is dreaming, he is no longer completely dreaming. He is only
able to suspect that he is in a dream because he has a degree of
certainty that he will be waking up. That degree of certainty is
validated when he does in fact wake up. When he does in fact wake
up, it is a different experience than a false awakening within a
nested dream, and he knows it. Whether there are further levels of
being awake is no more or less likely than there being further
levels of being asleep. I understand why you are seeing an
asymmetry, but I am saying that it is because you are injecting a
bias that assumes a higher epistemological standard for discerning
awake from 'really' awake than awake for 'really' dreaming.
If he concludes that he is dreaming, when awake, that it is case of
error when he is awake!
He doesn't conclude that though. Unless he is delirious, in which
case he is not 'awake'.
Example. I do believe that human cannot fly by hands. I fly by
hands. I conclude that I am dreaming.
False. You can fly by hands and fail to conclude that you are
dreaming. Before you can even notice that flying by hands is
unusual, you have to already raised your consciousness to the level
of lucidity.
I wake up, and yes, I was dreaming. That dream was (by definition) a
lucid dream.
You might not wake up. You might think that you are dreaming, but in
reality there is no such thing as dreams and you are flying around
in the real world of the afterlife.
I don't see that they are asymmetric unless we inject a double
standard which is biased toward confirmation of the negative rather
than confirmation of the positive.
That is frequent, and useful.
It's useful for some things, but not for the hard problem of
consciousness. We have no choice in consciousness but to assume the
positive.
In order to doubt the dream, we must affirm the non-dream. We
cannot doubt the dream unless there is an assumption that the non-
dream is first undoubtedly confirm-able by us.
I don't see that.
I know. That's the problem.
Nor the brain which reacts often, when we train in lucid dreaming,
by creating a false awakening. We are lucid, and wake up from the
dream ... in another dream. Bertrand Russell claimed having live a
succession of hundred false awakenings. I got once a succession of 4
or 5 awakenings. It is a common type of experience, especially when
we concentrate for having a lucid dream.
I have had 4 or 5 false awakenings too (not an especially pleasant
experience really, not very restful). Just because we wake up into
another dream though doesn't mean that we can't know when we do in
fact wake up.
OK. But in thats sense, your argument above stop to be relevant as a
critics of comp.
It might be tempting to test your reality when you do finally wake
up from such a succession of false awakenings, but it is more
playful than epistemological. In a matter of seconds the realization
of reality evaporates any doubt - not because our doubt is fragile,
but because the magnitude of sensory realism is overwhelming. It is
not a matter of knowing that we no longer can fly by hand, it is a
stark, direct revelation of the human life that we are living.
Lucky you. If comp is true, and if my last theory of salvia is
correct, I can predict what you would probably feel smoking salvia. I
would like so much make the test.
When you are awake, well ypou might discover later that you were
not, but the fact that you don't know does not entail that you
know you are dreaming a priori.
If you really are awake, you will not discover later that you were
not. Knowing isn't relevant, because knowledge is not applicable
to states of awareness. Our dreaming state of awareness can think
that it is not dreaming, but that does not mean that the fully
awake state can be fooled - even if it can be fooled under rare
circumstances.
One is enough.
I don't think that it is. If your consciousness is compromised - by
grief, drugs, lack of sleep, stroke, etc, the fact that levels of
awareness can be confused is a special case against the majority of
consciousness which is not confused about its own status.
But one contralucid dream is enough to loss any metaphysical
certainty of being awake.
No, I think that is an intellectual, logical assumption, but it is
not true. There is no metaphysical certainty of being awake.
That is what I say.
If there is any uncertainty - true uncertainty, then you are not
truly awake.
You confuse "awake" and "enlighten" I think.
You can make your mind uncertain, but if you act on that
uncertainty, then your mental health has been compromised and you
cannot be considered competent to judge metaphysics.
It is unclear. As far as I get the point, I believe the contrary.
Public certainty is madness.
Of course in practice, we don't care, but we are discussing theory
here.
That's a problem too. Theory cannot address consciousness, just as
it cannot address color or flavor.
If you take that decision, you just say "don't even try to
understand". That is not good mysticism, that's dogmatic pseudo-
mysticism. Sad that you use this to assert machines are condemned to
dumbness.
Our theory of consciousness must place itself within consciousness,
not the other way around.
but could be similarly misinformed. We could be dead and living
in an afterlife from which we will never return or some such
goofy possibility. Mathematical views of reality seem to welcome
a kind of escapist sophism which gives too much credence to
rabbit holes and not enough to the whole rabbit.
That we sometimes tell when we are dreaming means only that we
are more awake within our dream than usual - not that our usual
awareness is any more true or sure than it ever is. If we are
uncertain in waking life and certain in dreams, it is because our
capacity to tell the difference is real and not a dream or
theory. There is no way to prove that we are awake, but neither
is there any need to prove it since it is self-evident.
So here the brain teaches to the soul that sometimes self-evidence
can be false. A lesson in (Löbian) modesty.
I think that the brain has nothing to do with it. It shows that
consciousness is primary,
Because you assume this at the start.
It has to be assumed in order to be considered fairly.
The concept of truth, or God, is simpler and enough for this task.
Truth and God both can be denied in consciousness, but consciousness
cannot be denied without overlooking the circularity of using
consciousness to deny itself. This to me makes consciousness simpler
than truth or God. Consciousness is simpler than simplicity itself.
All this is correct from the machine's 1p, so it provides a counter-
example to your statement.
and proof is an comparative function within consciousness which
does not itself have any proof of its own validity.
I am OK with this, though.
ok
Any proof that we could have could theoretically be duplicated in
a dream also, but that does not mean that there is no difference
between dream and reality.
Absolutely. Indeed there is a special level with stable
observable. We cant know it for sure, but we can be correct in
some bets or act of faith (like in front of the doctor).
What can know for sure?
Consciousness.
Is it really any more than tautology to say that though?
It is indeed obvious for the knower, but not even assertable.
Usually tautology are assertable and justifiable. Consciousness is
not.
Consciousness makes assertion and justification possible. Any idea
that thinigs can exist outside of consciousness is formed within
consciousness, and therefore is contingent upon it's justifiability.
If consciousness cannot be asserted, then nothing can be.
?
What does knowing consciousness for sure give us which simply being
conscious would not? It's redundant, like LET X = instead of just X
=. If you have consciousness, knowing it for sure is irrelevant.
It needs self-consciousness. It differentiates between the raw
consciousness of Turing universal RA, and the consciousness of the
Löbian PA. I speculate, for example, that such a distinction occurs
in between the worms and the octopus or cuttlefish.
Self-conscious or no, what difference does 'knowing it for sure' make?
The first obeys knowledge theories, the second obeys more statistics
type of theories. This plays some technical/conceptual role in the
matter matter.
Bruno
http://iridia.ulb.ac.be/~marchal/
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