Bruno Marchal 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 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!". 
(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). 


I used to tell people who asked that I was an agnostic.  But the trouble with that was that they supposed I was uncertain about the existence of *their* god: a supernatural immortal agent would loved us but had an obsessive interest in our sex lives.  So now I generally tell people I'm an atheist, unless I think they are interested in a philosophical answer, because I don't believe what theists believe.  So atheism is not a religion, it is a failure to believe in the theist gods - those gods that are agents, omnipotent, omniscient, and ominibenevolent.  Thinking that such a god is does not exist is a scientific theory, i.e. one supported by the evidence and not contradicted by any credible evidence.  I know you adopt a very abstract and mathematical meaning for "theism", but we don't get to define the meaning of words any more than I got to define "agnostic".

You say you are agnostic on (primitive) matter; but you usually claim to have proven that matter doesn't exist, because to assume it does leads to contradiction.


On 13 Nov 2009, at 12:17, Kim Jones wrote:

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


Kim Jones


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