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).
Bruno
