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
>
>
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