On 06 Apr 2017, at 12:02, David Nyman wrote:
On 6 Apr 2017 8:45 a.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 05 Apr 2017, at 22:51, David Nyman wrote:
On 5 Apr 2017 7:46 p.m., "Brent Meeker" <meeke...@verizon.net> wrote:
On 4/5/2017 1:54 AM, Bruno Marchal wrote:
On 04 Apr 2017, at 16:47, David Nyman wrote:
I've been thinking about the Lucas/Penrose view of the purported
limitations of computation as the basis for human thought. I know
that Bruno has given a technical refutation of this position, but
I'm insufficiently competent in the relevant areas for this to be
intuitively convincing for me. So I've been musing on a more
personally intuitive explication, perhaps along the following
lines.
The mis-step on the part of L/P, ISTM, is that they fail to
distinguish between categorically distinct 3p and 1p logics
which, properly understood, should in fact be seen as the stock-
in-trade of computationalism. The limitation they point to is
inherent in incompleteness - i.e. the fact that there are more
(implied) truths than proofs within the scope of any consistent
(1p) formal system of sufficient power. L/P point out that
despite this we humans can 'see' the missing truths, despite the
lack of a formal proof, and hence it must follow that we have
access to some non-algorithmic method inaccessible to
computation. What I think they're missing here - because they're
considering the *extrinsic or external* (3p) logic to be
exclusively definitive of what they mean by computation - is the
significance in this regard of the *intrinsic or internal* (1p)
logic. This is what Bruno summarises as Bp and p, or true,
justified belief, in terms of which perceptual objects are indeed
directly 'seen' or apprehended. Hence a computational subject
will have access not only to formal proof (3p) but also to direct
perceptual apprehension (1p). It is this latter which then
constitutes the 'seeing' of the truth that (literally) transcends
the capabilities of the 3p system considered in isolation.
I don't think so. It is not direct perceptual "seeing the truth";
it is an inference in language and depends on language. The
fallacy of L/P is they assume you can know what machine you are and
therefore you can "see" the truth of your Godel sentence, but in
fact you don't know what algorithmic machine you are.
That's an interesting point also, but I'm not sure you've quite
taken my meaning. I'm specifically making use of Tarski's criterion
of truth as correspondence with the facts. When considering
matters in the first-person, the "facts" in question are in the
first instance perceptual and hence as such directly apprehended.
Hence we have access to a second means of judging truth, in this
specific sense, over and above the restrictions of any purely
algorithmic procedure. In other words, we are able directly to
apprehend or "see" a correspondence *in concrete perceptual terms*
of an assertion with facts to which it purports to refer. And
indeed that's exactly how we are able to make the relevant
distinction: i.e. between working through a formal procedure, which
we are equally able to do, and at the same time grasping a directly
perceptible correspondence that eludes the restrictions of that
procedure. The linguistic part comes later in justifying our
judgement (to another or for that matter to ourselves) post hoc.
Yes, that is what I said, but you put it in a much more better way
than me! Consciousness is in the truth, or in its "direct perception
through sense". Note that happens in dreams too, where the cortex
will build the []p, and the stem is bringing the "p", which
sometimes can be random letting the [] in need of some imagination
(dream weirdness).
Actually it might really have been more accurate to have said that,
rather than it being a second means, our *primary* means of judging
truth is by direct apprehension of perceptual correspondence.
Algorithmic proof is surely secondary to this.
It is secondary, like the brain is secondary to consciousness. This is
a bit like the egg and the chicken. p does precede logically []p (the
representational or algorithmic). Yet the senses are useful only if we
can re-enact the experience. You can see "p" as the fact (like the
true fact that it rains, blurred with some representation of that
fact), and []p as the building of a theory with the axiom "it rains",
which needs to be represented in some way that the entity can re-enact
the experience that it rains when needed, like when looking for an
umbrella in a room without windows (so that you need to remember that
it rains all along).
p comes first, and like Everett you can identify it with the first
perceptual judgment (to be sure that will need more basic "theory"
already in the brain, so we might add nuances on the perceptual p,
(but here the theories are trivial, like accepting that the needle is
on 4 when it is on 4) in between the truth of p and the truth of the
perceptual experience. Then []p is more for a long term memory,
building into the subject his/her conception/theory predicting/
anticipating/extrapolating/explaining the probable neighborhood.
So, as far as reality/truth/the-one is concerned, p is more primary.
But concerning the subject I would say that both p and []p are needed,
and both []p and []p & p are needed to, and collaborate together
though some (arithmetical) corpus callosum. Going from []p & p to p is
quite an out-of-body experience!
It can only be subsequent to apprehension of primary facts (which
exhaust in effect our grasp on concrete inter-subjective reality)
that we are able to deploy algorithmic methods. These latter are
applicable not to the concrete perceptual world directly but rather
to its formally abstracted "view from nowhere" idealisation.
Hmm.. the "[]" is really the body/brain. It is the local
representation of you in the languages of, say, nucleus and
electromagnetic interaction (chemistry). Some would say that it is the
"p" which is in the view of nowhere. It is delicate because it depends
from which mode we tackle the distinction. Eventally we know that G*
knows that there is no difference: all the points of view points on
the same reality (the sigma1 truth), but G* knows that the subject,
and in any of its mode, is unable to grasp the G* truth, making it
trapped in the illusion (of life, physics, ...). That illusion is
"important" to survive on the terrestrial plane. Now in that plane
"important" is a difficult matter by itself (the meaning of life
question).
Hence it is in the last analysis hardly surprising that this
secondary abstraction
It is the little ego. We might need to get rid of it to get
enlightenment, but what is enlightenment for if we cannot come back
and help the others, and this needs the little ego, and its body/brain/
machine so that it can manifest its knowledge/consciousness with
respect to its peers.
Nobody needs a body, but everyone needs a body to manifest itself to
anything else which is not her/him.
Now what I just said, applies to itself. The "[]p" would grasp noting
if it was not accompanied by its semantic p. Somehow, the meaning
would get trivial at the deterministic level. Why did Deep Blue win?
Because of this boolean net configuration and the laws of NAND? Why
did Adolph killed all the kids? Because Adolph got a quantum body
following the quantum laws, etc. That lack of meaning is lifted to all
level of 3p description, but the "truth" of the elementary relation
lift the meaning of the higher level description. For the sigma_1 we
get the "enlightenment: "p <-> []p", a sigma_1 proposition is true
(nobody knows what that really means) if and only if the machine can
prove (syntactical procedure, arithmetical relation). the machine does
not fall in the blaphesm, because despite she knows she is sigma1
complete (Universal, in the sense of Church, Turing), that is: she
knows p -> []p (for p sigma1-arithmetical, shape "it-exists x (s(x) +
s(x) = s(s(x))), she does not know []p -> p, even for p sigma1. Indeed
she does not know that [](0=1) -> (0=1), because that would be knowing
~(0=1), by propositional calculus, and she would proves its own
consistency. That can be shown to be true and knowable, but still not
communicable, because the "[]p" has no name/description for "[]p & p".
It leads to the idea that in the ideally correct machine the corpus
callosum should be a one way road, which I think is not the case, or
some hemisphere lies, leading to self-conspiracy theories ... Well, I
stop here.
fails to bridge the gap to all the truths primarily accessible in
terms of direct perceptual correspondence.
It fails, and the part of us which bridge the gap stay mute, or become
inconsistent.
Scientific theology is the part of science which study the part of
truth which extends science. With computationalism it is computer's
science minus computer's computer science.
From the non experiential to the non memorizable, ... to the not
describable, to the non justifiable, to the infeasible, to the
feasible, eventually to the feasible respecting the deadline.
Even for simple machine, the full theology is quite "out of science",
but there is a non trivial core common to all arithmetically correct
machine.
Propositional theology, or meta-theology, is decidable. It is
platonist only by accepting that a sigma1 sentence is either true, or
false, which is equivalent with saying that a program stop or does not
stop.
The amazing thing with computationalism, and thanks to incompleteness,
is that the proposition that truth extends science is part of that
common core of provable "scientific" statement, in the conditional
form, like <>t -> ~[]<>t. If I am consistent (if that belongs to
truth) then I can't prove/justify/communicate-rationally that I am
consistent. Of course, in the arithmetical interpretation of [], this
is the second incompleteness theorem.
Hoping not boring you too much with the technicalities, but it is the
interest of computationalism that the study is a part of mathematics.
Bruno
David
A remark on entheogen:
I think that with cannabis, you blur the "p" in "[]p & p", and
with salvia you blur the "[]p" in "[]p & p". (with the surprise that
you still remain as a sort of conscious person).
Oops I have to go. Before I fall in the machine's blasphem ... More
on this later most probably.
Bruno
David
Brent
Exact. And going a little further, that is what the Gödel-Löbian
machine already says (or say out of time and space).
If the foregoing makes sense, it may also give a useful clue in
the debate over intuitionism versus Platonism in mathematics.
Indeed, perceptual mathematics (as we might term it) - i.e. the
mathematics we derive from the study of the relations obtaining
between objects in our perceptual reality - may well be
"considered to be purely the result of the constructive mental
activity of humans" (Wikipedia). However, under computationalism,
this very 'perceptual mathematics' can itself be shown to be the
consequence of a deeper, underlying Platonist mathematics (if we
may so term the bare assumption of the sufficiency of arithmetic
for computation and its implications).
Is this intelligible?
I have no critics. Your point is done by the machine through a
theorem of Grzegorczyk on one par: the fact that S4Grz, like S4,
formalises Intutionistic logic, and of Boolos and Goldblatt on
another par: the fact that the formula Grz *has to* be added to S4
to get the arithmetical completeness of the "[]p & p". Note that
this makes the intuitionist into a temporal logic, and attach
duration to consciousness, like with Bergson and Brouwer himself.
Eventually it is amazing and counter-intuitive, because it
ascribes consciousness to all universal numbers, probably the same
before they get the differentiation along the infinitely many
computations supporting them. Needless to say that such
consciousness is in a highly dissociated state at the start, a bit
like after consuming some salvia perhaps (!).
Your analysis can be extended on the intelligible and sensible
(neo)Platonist theory of matter, but with p restricted to the
sigma_1 sentences (which describe in arithmetic the universal
dovetailing), with or without the adding of "<>t", which typically
transform the notion of "belief []p" or "knowledge []p & p" into
notion of "probabilities".
In summary
p (truth, god, the one)
[]p (rational belief)
[]p & p (knowledge, intuitionist subject)
[]p & <>t (probability, quantum logic)
[]p & <>t & p (intuitionist probability, quale logic).
The quanta themselves appear to be qualia. In fact a quanta is a
sharable qualia by two universal number when supported by a same
universal number. That can be used to show that the "many worlds"
of the physicists (Everett theory) confirms Computationalism and
protect it from solipsism. The physical is indeed first person
PLURAL, and its sharableness comes from the linearity of the
tensor product. At each instant we all enter the same replication
machinery. The Z logics justifies the linearity and reversibility,
but not clearly enough to extract the unitarity and use Gleason to
make the measure unique. But this is for the next generation,
hopefully (as many seem to prefer the obscurantist statu quo alas).
Bruno
David
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