On 07 Apr 2017, at 14:21, David Nyman wrote:
On 7 April 2017 at 11:24, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 07 Apr 2017, at 00:11, David Nyman wrote:
On 6 Apr 2017 6:44 p.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
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.
Yes, I think I grasp that subtlety, because of the relation between
the two logics encapsulated in Bp and p. However, I was referring
here in particular to formal analysis as actually performed within
an individual first-person perspective, being inevitability
secondary to primary apprehension within that perspective.
Yes. I ask myself if you are not tempted by founding everything from
the 1p view.
Well, I was certainly much more open to this temptation when we
first began our discussions (was it really 10 years ago?!). But
you have persuaded me - or more accurately helped me to persuade
myself - that this would be merely begging the question for which we
seek an explanation. However, that isn't really what I meant by my
comment. I was simply saying that pragmatically formal analysis is
only ever performed in the framework of some 1p perspective, so it
is secondary in that purely procedural sense.
OK. In fact the first person is "attached" to an infinite of
procedural senses, which differentiates. The "physical" is the
relatively and locally more probable among the one making sense.
However, on the more general point you raise, where comp has been
particularly illuminating for me is the way it can provide a
principled derivation of the logic of self-referential subjectivity
from the basis of a purely objective, abstract ontology. In many
quarters this has been thought impossible. Furthermore, this
subjectivity opens up a logical space in which we can for the first
time make sense of the appearance of "concrete" reality, as distinct
from any of its hypothesised abstract precursors, in terms of direct
perceptual apprehension. This is what permits us to understand
properly a notion of intrinsic or internal, which is otherwise a
genuine mystery on the basis of an entirely extrinsically-
characterised physical mechanism.
OK.
Trouble is, when the latter is accepted more or less uncritically,
as it tends to be, we can all too easily be led into the absurdities
of outright denialism of the subjective on the one hand, or frank
incoherence about the supposedly "intrinsic" panpsychic nature of
primitive matter, on the other. It is difficult to decide which of
these two polarities is the more comprehensively misleading, but
either way they have tended to generate a great deal more heat than
light. In the final analysis it is surely quite useless to think of
"looking inside" physical objects for the locus of consciousness
because matter, as reductively and exhaustively characterised by an
extrinsically-specified mathematical physics, simply *cannot have
any inside*.
Nor genuine outside. They are more like map of the future. Electron
orbital is a map shaping where electron can be found in the
neighborhood of histories.
As I remarked before, it is as if consciousness were concealed from
the outside by a two-part public/private encryption scheme. Whereas
the public part is in principle entirely extrinsically inspectable
the decryption can be completed only in terms of the private
perspective of *the system in question*. This then inevitably
entails that decrypted messages of this kind must be inter-
subjectively incommunicable despite the ultimate irony that they
amount to the entirety of inter-subjectively "shareable" concrete
reality. It is of course in this sense also that the brain is
secondary to consciousness: i.e. that self-referential perceptual
apprehension is the filter through which a concrete reality, with
all its brains and bodies, is enabled in the first place to emerge
(and I do mean emerge in a strong sense). That primary "grasp on
reality" is what enables any subsequent abstract analysis in terms
of a reductive "bottom up" physical mechanism playing the role of a
locally-dominating computational mechanism (or IOW what you have
termed the reversal of physics and machine psychology).
OK. That is it.
It would be truly remarkable if this analysis could be shown to rely
on nothing more than the ontology of 0 and its successors with the
combinatorics of addition and multiplication. But of course this is
strictly implied by computationalism and cannot therefore be
avoided, on pain of abandoning the comp hypothesis.
Yes, and here comes the work of Gödel and followers. The set of
solutions of just one degree 4 diophantine polynomial equation is
already enough for the base level. But any other universal system will
do. By making consciousness invariant for a recursive permutation at
some level of the brain description, we make physics invariant for the
choice of the "first" or "basic" universal system used to describe the
whole things. It is just more natural to believe that 2+2 is 4
independently of us than to believe that (CAR '(A B C)) = A, like in
Lisp, but arithmetic "run" all lisp program like Lisp notion of truth
run all arithmetical computational relations. Then the first person
points of view statistics should be based only on Löbianity, which is
already machine independent.
It is useless to seek to found comp on a primitive physical ontology
because such an ontology need result in neither subjectivity itself
nor a fortiori the entire hypothesis of a concrete "physical"
reality, which can (or should) be understood to be an inter-
subjective perceptual projection. It is difficult to say the least
to see how either consciousness or its concomitant perceptual
accompaniments might be relevant to the continuing evolution of the
wave-function, or for that matter any alternative hypothetical
characterisation of a fully-reducible "bottom up all the way down"
primitive physics.
We need math to compute the limit, or limits, and test the hypothesis.
If it miss key physical apparent features, it will be tempting to add
oracles, or to believe we are failed by daemons (or malevolent
descendant). It is about the same if we find serious
discrepancies, ... all this can help to measure a sort of degree of
non-computationalism, like if the divine could invite itself to the
lower plane after all. But there is no sign of this, except for the
random oracle, and that is a good sign, as it makes us more free, I
think. But strictly speaking, the limit can reserve surprises,
especially near death, or just in sleep. We know few things. Science
has not yet reawaken. Taboos persist.
Bruno
David
Note that this can be done, but is technically much more difficult.
You would need to formalize "provability" in something like Heyting
Arithmetic (PA without excluded middle). Albert Visser has studied
this, but it is more difficult (no truth table in intuitionist
logic, so the propositional basic logic is already more complex).
You will need some formula like
([](~~[]A -> []A) -> [][]A). in Intuitionist logic ~~A does not
imply A.
An interesting question would be in this context: can we get all
this from S4Grz. I think we should, but that is an open problem,
like the intuitionist Church thesis, or close constructive principle.
I understand your motivation for this. I prefer to stay in the
classical framework mainly for pedagogical reason: the basic logics
are better known.
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)
In that case, perhaps p is the view from everywhere.
p is the view from all points of view, but that is seen only from
the "divine intellect" view. I would say here that it is the view
from everywhere, when see from the view of nowhere. But I guess we
get closer and closer to "1004". Of course, subtle philosophy
requires eventually to add nuances in the formal apparatus.
But again, my reference was to the actual practice of algorithmic
reasoning which I'm contending leads to the L/P mis-step because of
the implicit assumption that its application is entirely restricted
to the 3p view from nowhere.
... up to invoking their feeling that they know their own
correctness, or that mechanism asks for knowing which machine we
are. But this cannot be known by machine. Of course would Penrose be
able to prove that he is a correct entity, then his proof on non-
mechanism would be correct. But he has not done that, and indeed, it
is hard to imagine how that would be possible. self-correctness
requires some faith in a reality. His proof relies on an intuition.
But his idea that machine cannot have a similar intuition relies on
the fact that for simple machine like PA we can be confident that
[]p = []p & p. PA cannot know this, but no machine can know this
about themselves. Charitably, Penrose proves in this case, that he
is not PA. But of course we knew that beforehand.
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.
No indeed, I appreciate the rigour that you add. I always read with
interest and do my best to understand.
Thanks for telling me.
It's just that I have insufficient command of the technicalities to
satisfy my intuition purely by this means.
It is useful when we are on the highly counter-intuitive fringe of
computationalism. To develop an intuition there is like to develop a
taste for the bizarre. The best introduction is probably "Alice in
Wonderland". As Liz said: we must train ourself to believe at least
five impossible things before breakfast!
Hence my "grandmother" versions. Thank you as ever for your
helpful responses.
You are welcome. I thank you for giving me the opportunity to try to
handle interesting subtle points in the available formalism.
Computationalism is the diplomate which invites the mystics and the
rationalists at the same table. Not always easy those days. But when
we look at the antic greeks, we can see that it all started by that
form of open-mindness, in between the 1p mysticism/experience and
the 3p-description-reasoning/sharing-understanding.
Bruno
David
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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