Bruno, you navigate into perillous waters. Your statements are extremely smart and applicable - to a certain limit, at which they vanish into undecidedness. You chose arithmetic thinking as your anchor to firmness - it is your choice and it works for you. It does not work for me: I am still in the undecidedness and whatever I want to grab dissipates upon touching. I do not state to be an atheist, for - as you correctly pointed out - it would necessitate a 'god' to deny and I do not get to such definition. I claim to be a "scientific" agnostic, questioning whatever traceable to a human 'mind's' (?) understanding and its limitations (including numbers - cf: David Bohm). In my approach we are limited and can extend our thinking only within our limits. I try to do my best - knowing that it is not enough.

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The developing human 'mind' (= mental capabilities altogether) went through stepwise enwidenment including the religious faith and your extension into a universalized 'god' idea etc. This is why I cringe when accepting ancient ideas - definitely in an earlier stage of our development - *to be applied*to our 'later stage' (I almost wrote: more advanced - assuming we IMPROVE). I climb on the shoulders of giant oldies - not to see exactly as far as they do, but further. What do I see? something unexplainable - beyond my limitations. And definitely beyond the horizon of those whose shoulders I climbed onto. What does not mean that I am smarter. I just have a vision I don't understand. I enjoyed your post - thank you - and warn you: going all the way may lead you into deep agnosticism and you may lose the grip on the assumed 'reality' that you are holding on today. I can afford it at my age, but you have work to do in a world that does not appreciate in science the "I DON'T KNOW" position. Best regards John Mikes On Fri, Nov 13, 2009 at 12:44 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: > Hi Kim, > > Thank you very luch for the link to Carolyn Porco's presentation. Very nice > talk. I appreciate a lot. > > She is correct (even comp-correct) on the main thing: Science is > agnostic. > > "I believe in God" (Bg) is a religious statement. (B = I believe, g = > 'God' exists", "~" = negation) > But B~g, the athesist statement, is a religious statement too. Atheism is a > religion. (and doubly so for the materialist atheists). > > Crazily enough, I note she shows this in the exact manner of the > introductory chapter of "Conscience et Mécanisme"). So honest atheists > exists. > > Not so sure why she said she believes (religiously) in the non existence of > God, without saying what she means by the word, especially that later she > talk of science as the "quest for the truth", but with comp the mathematical > notion of truth (relative to a machine and relative to the possible machine > views) obeys literally to the notion of "God" in the Greek Theology of Plato > (according to my own understanding of Plato, but confirmed by Plotinus and > Hirschberger). > > Mainly 'God' = the transcendent human-ineffable truth we are invited to > search/explore/contemplate. > > Making "Science", the quest of the truth, like Carrolyn Porko did (two > times, at the two third of that video), is the basic axiom of Plato's > theology. It makes science and reason (and mathematics, and music, ...) the > most basic tools in the search of the admittedly religious (by science > modesty!) truth. > > * * * > > Let me give you 3, (3! yes there is one more!) basic reasons to consider > "Digital Mechanism" as a theology (actually a framework for variate > theologies (Mechanism will not stop all possible religious conflicts, on the > contrary given the existence of very different possible practices, like > overlapping or not with the duplicate ... ). > > - 1) To say "yes" to the doctor, even if some oracle guaranties the > competence of the doctor and the accuracy of the comp substitution level, > etc, is an irreductible act of faith in the possibility of a (relative) > digital reincarnation. > > - 2) It is a "scientific theology" in the following precise sense: To each > machine, or machine's state, (or machine relative description) we associate > the set of true arithmetical sentences concerning that machine (described in > arithmetic, say). Roughly speaking: > > Science = provability > Religion = truth (in the spirit, I am humble and modest, and I search) > > Then, not only a universal machine can introspect itself and discover the > gap between truth and provability. It can not only discover the > unnameability of its own truth notion, but a very rich (in term of > provability power) machine (like ZF) can study a big (not all) part of the > theology of a more simpler Löbian machine, like Peano-Arithmetic. So > although a machine cannot know that she is correct, she can lift the > "invariant" theology of simpler lobian machine. Of course she cannot assert > she has proved those statement, but she can assert that those are probably > true as far as she is "correct", and comp is correct. > > But there is a third reason. > > -3) Church thesis. Also called Church Turing Thesis, and which I call > sometimes Post law, or Gödel Miracle, or Post, Church, Turing, Markov > thesis. Its truth entails the truth of the weaker thesis according to which > there exists a universal machine. But do we know that? can we know that? > > Do we know if there is a universal language, or a universal machine? > > No one can prove that, of course. So here too you need to do a bet: an > axiom, a thesis, an hypothesis. The miracle (Gödel) is that the set of > partial computable functions is closed for the diagonalization, it cannot be > transcended. As Gödel said, for the first time we get a mathematical > definition of an epistemological concept. Gödel did hope that a similar > thesis could exists for the notion of provability, but its own theorem, > together with Church thesis prevents this (I think). > And then all attempts to define the computable functions leaded to the same > class of partial computable functions. We get all the (total) computable > functions, but they have to be situated in a non computable sequences among > all the partial functions, as shown by Kleene's diagonalization (as shown in > the last "seventh step serie thread", but I guess I have to come back on > this). I recall that a total function is a partial function with subdomain > equal to the whole N (N is included in N). > > So comp, by Church thesis, is also a positive belief in a *universal > machine*, despite the lack of proof of existence). > Of course Turing *did* prove its famous theorem saying that A Universal > Turing machine exists. It is a theorem (even of arithmetic) that universal > TURING machine exists, and that universal CHURCH lambda expression exists, > and that universal SHOENFINKEL-CURRY combinators exists, etc. > For each universal language it can be shown a universal finite entity > exists. But this does not prove that there is a universal machine for all > computable functions, only that all those class have a relative universal > entity. I mean Turing's theorem is not Turing's thesis. But Turing (Church)' > thesis makes its universal machine "really" universal (with respect to > digital computability). > What can arithmetic still prove is that TURING system, and CHURCH, one, and > algol, fortran, lisp, etc. are all equivalent, making the universal TURING > (or Church, ...) machine universal for all of CHURCH lambda expression, etc. > They are all provably equivalent. > > Now to prevent any misinterpretation, let us address the question: > > Is the universal machine God? > > I would say no. Sometimes I like to call it the baby god, though. In the > arithmetical interpretation of the hypostasis the universal machine, once > she knows that she is universal, (in a weak technical sense) can play the > role of Plotinus' man, or discursive terrestrial intellect. It is man, not > God. man means humans. > > Universal machine are always finite entities, and exists always relatively > to many other Universal machines (even if you can define the whole set of > relations into arithmetic, or combinators, quantum topologies, ...). > > I may refresh the arithmetical hypostases (cf AUDA). I limit myself to > correct machines (they prove only correct arithmetical sentences, by > definition). So when the machine says "p", it means that "p" is true. By > Tarski theorem, it is the only way to say that "p is true". She just say p. > So by "p" below, I mean the assertative proposition by the (correct) > machine. > > Plotinus one = arithmetical truth = p. > Plotinus divine Intellect (or intelligible) = Bp (Gödel's arithmetical > "BEWEISBAR" provability predicate). But by incompleteness that INTELLECT > admit an effective part borrowed by the machine: it is Plotinus' man. > That is, here, the INTELLECT splits into the true Intellect and the > provable intellect. By Solovay theorem those two logics are axiomatised (at > the propositional level) completely by G for the provable (by the machine) > part, and by G* for the true but unprovable (by the machine) part. For > exemple ~Bf (I will not assert a falsity) belongs to G* \ G. It is true, but > not provable, by the correct machine. > > Plotinus "universal soul" is the Theaetetical first person. It is the logic > of the knower "inside the machine". It is given by the logic of the > conjunction of Bp and p: Bp & p. It obeys, and is characterized by the modal > logic S4Grz. Amazingly, it is not splitted by the incompleteness phenomenon= > S4Grz = S4Grz*. > > Then intelligible matter and sensible matter logics are given by the logic > Bp & Dt, and Bp & p & Dt. respectfully. They both split by the Solovay "*" > incompleteness results. > > Plotinus admit at least this very precise arithmetical interpretation, and > shows how incompleteness and insolubility structures the ignorance space of > the (universal) machine. > > Seen from inside, that space is *very* big, but incredibly richly > structured, and the physical world, if the neoplatonist are correct, or if > comp is correct, is given by the "mathematical bord of that ignorance space. > > This is a verifiable (refutable) statement, making machine's theologies > testable. Note that all correct Lobian machine (or even non machine, but > still self-referentially correct entity) have the same abstract > propositional theology (given by G and G* and their intensional variant). > > *** > > Kim, thanks. I think I will send your Carolyn Porco's link to the salvia > forum where discussion on atheism appears a lot. I was just abou trying > to,explain the problem with *some* atheists. > Probably in the thread "Atheists, be nice!". > http://www.entheogen.com/forum/showthread.php?t=25489 > (my username is "salvialover24", well sorry for that ...) > > It will help me to explain that there is no problem with atheists, only > with dishonest atheists (saying that atheism is not a religion, that science > is on their side, etc.). > > Of course, as a scientist, I am agnostic on ALL the Aristotelian Gods. > This includes Matter (primitive matter). > > > Bruno > > > > > > > On 13 Nov 2009, at 12:17, Kim Jones wrote: > > > http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov > > > Carolyn Porco - the genius behind the Cassini mission. My favourite > female on the planet. > > If you ever read Carl Sagan's only novel "Contact" (or saw the movie) > - this is the person on whom Sagan modelled Ellie Arroway (Jodie > Foster in the film) > > Introduction by Richard Dawkins > > cheers, > > Kim Jones > > > -- > > 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<everything-list%2bunsubscr...@googlegroups.com> > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=. > > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > 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<everything-list%2bunsubscr...@googlegroups.com> > . > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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