I am learning something very valuable from this experience. I think
that, coming from different backgrounds, if we want to have an
exchange of ideas we need to create a common language.
My lack of a common language with you prevents me to follow you
through your argumentations. I sense that what you say is important
and interesting, but we seem to speak in different languages.
A way to move forward could be not to take for granted that the other
is familiar with our concepts. If you explain a concept at a time it
would be also very helpful for me.
On Jun 19, 9:26 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 18 Jun 2010, at 17:03, Rabbi Rabbit wrote:
> > Dear George,
> > Thank you for your beautiful interpretation of B'reshit (Book of
> > Genesis).
> > By your description, I have the feeling that you think about Sefirotic
> > Kabbalah. Briefly, Sefirotic Kabbalah believes that God emanated in 10
> > Sefirot (the meaning of the word is unclear, the root "Seper" is
> > related to the words "letter", "number" and "speech"). This 10 Sefirot
> > are attributes of the divine that need to be in a harmonious
> > relationship with each other in order to pour the divine influx over
> > the world. This school of kabbalists believed that they could
> > influence the Sefirot and in this way exert changes in the divine and
> > human realms, basically making sure that the divine influx continued
> > pouring and sustaining the world. For this reason Sefirotic Kabbalah
> > is also described as Theurgical Kabbalah.
> > The kabbalist I have been talking about, Abraham Abulafia, created a
> > different school. Deeply influenced by Maimonides philosophy (who, in
> > turn, adapted Jewish beliefs to harmonize with Aristotelian
> > philosophy) Abulafia practiced a form of Kabbalah aimed at the union
> > with the divine intellect. To put it in radical terms, his Kabbalah
> > was not about influencing God's divine emanations but to become (part
> > of) God.
> > I think your insight into consciousness is very thought-provoking.
> > From the whole Creation, nothing makes me feel greater wonder than
> > consciousness. The union with the divine intellect (prophecy) could be
> > probably described as a higher state of consciousness. What is
> > surprising about Abulafia is that he did not reach this state by
> > suppressing his conscious mind, as most mystics do by repetition of a
> > single formula/mantra, but by overstimulating it with letter
> > combinations accompanied by body motions.
> > I haven't thought enough how the technique of letter combinations
> > could be related to consciousness. Any ideas?
> Well that is exactly what the digital, or numerical, mechanist
> hypothesis provide.
> The choice between letter or number is not relevant. You can choose
> for the ontology the formal existential quantifier on any term taken
> from a first order specification of a universal, in Post,
> Church,Turing sense, system.
> It happens that any system with terms for numbers, that is 0 and its
> successors, together with the addition law and the multiplication law,
> provides a universal system, so I use it to fix the things.
> In that system I can enumerate all partial computable functions:
> phi_0, phi_1, phi_2, phi_3, ...
> A number u can be said universal if phi_u(<x,y>) = phi_x(y).
> This u is like the Golem. You write x on its forehead, and it compute
> phi_x on some input y. <x,y> is some number describing the "program",
> x, and the data, y.
> This defined, or show to exist, sequence of "causal relation" like
> sequences, with fixed x and y, of terms:
> phi_x(y)_1, phi phi_x(y)_2, phi_x(y)_3, phi_x(y)_4, describing
> faithfully computations. Faithfully means that there are implemented
> in some genuine intensional sense, relatively to u.
> A tiny, yet universal, part of arithmetical truth describes
> (faithfully) all possible computational relations.
> Such universal machine cannot distinguish the infinitely many
> computations going through its computational states, so that its
> consciousness is distributed on the projection of infinitely many
> computations, and that ... leads to awfully complex mathematical
> Yet, ideally correct machine (number) can reflect (proves, relatively
> asserts) that problem relatively to themselves, and extract the logic
> obeyed by such projection.
> Let us write Bp for the machine proves (asserts and justified if
> asked) p.
> Obviously Bp -> p. Because we restrict ourself to correct machine.
> But the machine cannot always prove Bp -> p. It would prove Bf -> f (f
> = the constant false of propositional logic, or "0 = 1" from
> elementary arithmetic). But (elementary classical logic: Bf -> f is
> equivalent with ~Bf, (~ = NOT), which asserts self-consistency, and
> correct classical machines can't do that (Gödel's second
> incompleteness theorem).
> Now machine can reflect that: they can prove their own "second
> incompleteness theorem" for example. They can prove:
> ~Bf -> ~B(~Bf) = As far as I will never say bulshit, I will never say
> that I will never say bulshit. Roughly speaking, with f = false =
> bulshit. Its contrapositive: If I say that I will never say something
> false, I am saying something false, or more shortly: if I say that am
> sane, I am insane.
> So the machine can know (know p = Bp & p) that, as far as she is
> correct, she will not confuse Bp and B'p = Bp & p. For the first one
> Bf -> f is hopefully true but never provable, and for the second B'f -
> > f is trivially provable ((B'f & f) -> f) is an elementary truth of
> propositional logic.
> Incompleteness forces in the same way the machine to distinguish the
> logic obeying by p, Bp, Bp & p, Bp & ~B~p, Bp & p & ~B~p, and some
> other variants. And the machine can know that those five "hypostases/
> perspective on arithmetical truth" have their logics split into two
> parts: a terrestrial (provable) part, and a divine (true but
> unprovable) part, giving mainly ten hypostases.
> Well two of them don't split: the knower (Bp & p) does not split for
> example (this is not trivial to prove, but "well known" by
> mathematical logicians: see Boolos books if and when enough curious).
> This gives 8 hypostases.
> The diamond "~B~" plays the role of Plotinus "privation" or Aristotle
> "indetermination", and it is the conceptual and logical (and
> arithmetical) bloc of the material hypostases. Matter is a deep
> invariant of all (arithmetical) contingencies.
> There is a big price for having consistent continuations:. the (first
> person) knower can access to God (truth), but it cannot communicate it
> nor justify it. The intellect can share its knowledge, but it cannot
> prove it as such. The observer is necessary, by the impossibility of
> the terrestrial intellect (its logic obeys to G) to make union with
> the divine intellect (G*). Even one word is too much, there.
> So, well he will need faith to believe in any reality. That faith can
> develop only from the knower experience. But this leads to a
> "catastrophe", the expansion of the knower in richer and richer
> differentiating deep computations/history (the origin of consciousness
> differentiation, time and eventually the analytical and physical
> realm(s)). That corresponds somehow to the "fall of the soul", or to
> "God getting lost in its own creation". I think it begin to explains
> why "matter" can "truly" hurt, even if this corresponds to a (true,
> yet relative) ignorance.
> PS I add what I have send to the FOR-LIST (a forum based on David
> Deutsch' book on "The fabric of reality". It explains a bit more on
> the relation of consciousness with the numbers. Apology for a long
> post which will be partially redundant in case you follow both lists.
> On 17 Jun 2010, at 18:11, yanniru wrote:
> > --- In fabric-of-real...@yahoogroups.com, Bruno Marchal
> > <marc...@...> wrote:
> > > On 16 Jun 2010, at 19:55, Ismail Atalay wrote:
> > > > Do we have any reflexive emergent property being implemented on a
> > > > computational system?
> > > Not only that. We have discover that elementary arithmetic has
> > natural
> > > emergent reflexive property. And when the usual induction axioms are
> > > explicitly added, those reflexive emergent property can be show to
> > be
> > > maximal. The logic of that reflexive property will be inherited by
> > all
> > > sound (arithmetically correct) effective theory/machine.
> > > Elementary arithmetic is already conscious, and the content of that
> > > consciousness, which is a first person notion, is already not
> > > computable by being related to a non computable (by elementary
> > > arithmetic) space of its consistent extensions. This consciousness
> > is
> > > not even definable. Consciousness is a non effective (computable)
> > > property, like (Arithmetical)Truth.
> > > Computable things have a lot of non computable features.
> > Bruno,
> > Could you please elaborate on how elementary arithmetic can be
> > consciousness?
> I am assuming that we are digital or just digitalizable machine (DM).
> In that case, your consciousness "here and now" can be justified by
> the (mathematical) existence of a computational state, and your
> consciousness "soon and there" is related to the existence of a
> neighborhood of other computational states and to all proofs relating
> those computational states. (*All* proofs, even the many identical one
> (fungible one) reappearing as lemma of other proofs).
> Now the computational states and the relations between those
> computational states don't depend on *which* universal machine you
> choose to describe them (this can be explained precisely in computer
> science terms). In particular you can choose elementary arithmetic.
> The natural numbers, together with addition and multiplication, give a
> full universal programming language.
> The block "universe" of computer science is the same as the block
> universe of elementary arithmetic. It contains all the machine's or
> number's "dreams".
> But now, you consciousness cannot be attached to only one number/
> state, only to all number/state relative to all universal number
> accessing those state. From you own first personal subjective view,
> your current state is undetermined below your mechanist substitution
> level, so this entails that what we take as appearance of matter and
> physical reality is really a probabilistic or credibilistic sum on the
> works of an (enumerable) infinity of universal machines/numbers. And
> the entire work is not enumerable. This can already explain
> qualitatively many physical features (role of real numbers,
> indeterminacy, non locality, presence of invariant and symmetries,
> read more »
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