Dear Bruno, 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. Yours truly, R. Rabbit 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 > problems. > > 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. > > Bruno > > 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 » -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
