On 24 Jan 2015, at 10:30, Quentin Anciaux wrote:
You're twisting words again... you cannot be both agnostic and a
believer... from what you wrote here and the fundamental inability
to doubt god by the way you constantly redifine it to always be the
goal of the theory and true by definition... you are a believer.
At the meta-level, yes; and that would be the case of anyone saying
"yes" to a doctor, or applying any science to some reality. With
Platonism (of Plato, not realism), we are all believers. Either we
believe in a primary physical reality, or we believe in what is at the
origin of the hallucination of that physical universe.
But by Gödel, as I try to explain even being such a believer is a non
trivial happening for machines. If they assume it precisely, they get
inconsistent, but they can, in private, explains why they personally
bet on that or that reality, or put it at the meta-level (a bit like
in second order logic).
You might be confusing levels here, and that is why metamathematics
(the study of those levels) can clarify.
Will say more on this, when I got the time. Perhaps tomorrow.
Bruno
Quentin
Le 24 janv. 2015 09:27, "Bruno Marchal" <[email protected]> a écrit :
On 22 Jan 2015, at 16:45, Quentin Anciaux wrote:
2015-01-22 16:37 GMT+01:00 Bruno Marchal <[email protected]>:
On 21 Jan 2015, at 19:46, Quentin Anciaux wrote:
In the end... if you cannot doubt god because of the way you
define it... then not only you're not atheist (seems obvious)...
but you're not agnostic either, you're what is called a believer...
No problem with this. Actually, it is because I am a believer that
I am not afraid of the use of reason, free speech, critical
thinking, ... in theology, and it is because I am a believer that I
am really shocked by the way the humans misuse the natural animal's
faith in some reality.
Lao-tseu is totally right on this. The wise stay mute. Only the non
believer can asserts answers.
Well, you said before it was the agnostic that were wise... but now
that you're not agnostic... it's the believer... seems more and
more word playing.
It is a subtle point. That is why I use G and G* to make it utterly
clear, even translatable in the arithmetical language, or computer
terms.
In the arithmetical translation "seeing god" is mere consistency
(<>t, ~beweisbar('f')), it is of the type true, but not justifiable
rationally from the (consistent) machine's perspective.
That is why I told you this in "private", and it is just a statement
of hope.
But the theory predict that machine can have "experiential/
historical reason" to bet on <>t, or "see" <>t (according to the
different views). Such machines know that in public talk,
agnosticism is not "true" but polite or scientific, or modest,
or ... all this is equivalent of being Löbian, in the ideal case
(for the mathematical treatment).
So such machines knows that the wise machine (who sees god) are mute
on this, and will submit only questions, that is hypotheses,
theories, etc. those are really only questions.
And believer like non-believer asserts things... and clearly you
cannot doubt god because you want to use the god word, so god ==
anything that will let you use the word... so you're not agnostic
and you assert thing and therefore not wise... there must be a
logical flow in this... (I think it's god...).
No, there is no logical flaw, it is about the truth *about* the
machine, which the machine cannot justify, yet can still have some
knowledge on them (and which indeed can be used to change itself and
accelerate relatively to other machine).
If you don't read the Boolos 1979 or 1993 book, read at least
Smullyan Forever Undecided, which is an introduction to the logic G.
I use (implicitly) Gödel's COMpleteness theorem (not his
incompleteness) theorem, which is in some sense more fundamental. By
that theorem, a theory is consistent (<>t, ~[] f) if an only if the
theory has at least one model.
So consistency is the syntactical way to express the (meta)-
existence of a reality, so that the machine, when justifying
incompleteness: <> t ---> ~[] <> t, can be interpreted, in more
Plotinian-Proclusian terms: if the one exist then I cannot justify
rationally that the one exist.
For a neopythagorian neoplatonist, if you believe in one reality,
you already believe in one god.
No (Löbian) theories can prove the existence of a model of itself,
because that would be equivalent, by Gödel 1930 completness, to
proving their consistency, which they can't (by Gödel 1931
incompleteness).
An that is not entirely unrelated with the christian idea that we
are finite creature, even finite mechanism, for some, by opposition
to God that is infinite (like already with Plotinus).
This remain true for every consistent recursively enumerable
extension of PA.
As a scientist I am agnostic, it is only deep inside that you can
know the fixed point of the doubt. There, thanks to incompleteness
the first person obeys a different logic, and it clarifies the
difficulties that theologian and philosophers have with the notion
of knowledge.
It is counter-intuitive, (but it contains the intuitive part (S4,
actually S4Grz, the logic of the knowable associated with the
machine)). But G and G* are counter-intuitive.
I do think that the hard problem of consciousness is solved by the
non emptiness of most variant X of G, including G, of their X* minus
X logic, and the emptiness of S4Grz* and S4Grz.
All this relies on known relationship between computer science and
mathematical logic.
Gödel, Löb, Solovay, many others.
Do you see the relationship between Gödel's second incompleteness
theorem and the modal formula
<>t -> ~[] <>t ?
(<=>
~[]f -> ~[] ~ [] f,
<==>
[]<>t -> ~<>t,
which shows that in G (and thus for the machine 3p self-reference),
consistency, <>t, is a simple solution to []x -> ~x.
Bruno
The same with machine: the propositional theology is given by G*
minus G. It is the catalog of the solutions of
[]x -> ~x
Those truth which goes without saying, and get awry when said, and
which paves the road to hell with the good intentions.
I am a believer. I would not do research if I was not a believer.
But I am a scientist, and I know I can suggest only public theories
and test them. I can't made public ontological commitment (consider
this post as private!).
Most strong-atheists are believers too, as most believe in things
like Big-Bang, Energy, Wave, and they "blasphem" in the greek-
machine theological sense (equivalent with asserting a proposition
from G* minus G) when they invoke those beliefs' contents as beyond
doubt, that is as "non hypotheses" or "obvious".
With the general sense of God, we are all believers. It is quasi-
trivial for the humans, ("quasi", it still involves consciousness
and some reality), but it is not completely trivial to prove this
for all ideally correct machines. You need incompleteness and the
fact that (löbian) machines can justified their own incompleteness
in the conditional way.
I would like to add an explanation here, which is that the general
theology is a science, not the application of a theology to
oneself. To each machine M, ideally arithmetically sound, you can
associate its proper theology
G*(M) minus G(M)
where G*(M) and G(M) is the interpretation of the logic G*, and G,
in the machine turing-universal language.
In particular, []A is interpreted by "the machine M asserts A", in
his own language, for A some specific proposition.
Then if the machine asserts any proposition of G*(M) minus G(M),
the machine get inconsistent and can assert anything.
But Löbian machine knows this, and actually, can justify why it
needs to be like that in case they are correct. Their own theology
is not speakable, but they can deduce the truth of them, and their
mathematics, from assumption of self-correctness, keeping the
interrogation mark and explaining that they do not pretend to prove
or justify those beliefs, which are more like hope.
So theology, among the sciences, has a special status: it *cannot*
be applied normatively. Like a sacred text should be (!). It can
inspire us, and it is hard (for me) to not find that discourse (G*
minus G) tremendously interesting. It shows that the introspective
machine find a transcendental reality in her head, but has to stay
mute about it, or talk on it in a derived way, and insist that it
is conditional, like insisting we make the computationalist
hypothesis, and that it requires an authentic act of faith (the
"yes" doctor).
And this is valid for the other "proper" true but unprovable part
of the hypostases, with the corresponding nuances (X1* minus X1,
Z1* minus Z). Note that S4Grz1* = S4Grz1. The first person
knowledge do confuse proof and truth, in her perspective. That
knowledge implies a self which has no name/description: we don't
know who we are, and we can know that if we introspect oneself deep
enough. It might explain the distinction between the "little ego"
and the "higher self" made by the mystics.
Bruno
Quentin
2015-01-21 19:30 GMT+01:00 Bruno Marchal <[email protected]>:
On 21 Jan 2015, at 01:40, meekerdb wrote:
On 1/20/2015 10:17 AM, Bruno Marchal wrote:
The more I think about it, the more I doubt that these subjects
were simply "abandoned" in an innocent fashion. The problem is
that beliefs about fundamental reality are at the foundations of
political power, and the powerful know this, even if only
intuitively.
Read Craig A. James little book, "The Religion Virus" for a
history of religion from that standpoint.
The term religion is too large for such analogy.
In a recent article of the french journal "La Recherche" there is
a paper which shows that historians debunk Ernst Mach idea that
science progressed *against* christianity, and that on the
contrary, the root of modern science might relied in the idea that
nature was a mechanism made by God. I already knew the more
obvious relation between computationalism and christian's self-
finiteness belief.
With the greek One, religion is what science is for. The goal is
going near truth, the tool is science. The goal evolves as much as
the tool in the process.
Yes, since always. That is why we are mucky to be in a place where
scientists have regained some freedom in some domain, but clearly
not in all (theology and human science are still not done with the
scientific attitude).
We're in a mucky place because a lot of theologians promote mucky
religions. :-)
And you can expect this will continue if we don't let theology
going back to academy.
When atheist politicians say that we must respect the Vatican,
they are agreeing on some border of power. They are saying, ok we
can't have absolute power but we can negotiate peace with the
Vatican.
Vatican and bishops love atheism, because atheists are their
allies in preventing seriousness in theological matter.
Incidentally, I went to a lecture by a theologian last night. He
gave a definition of theism, the same as mine: Belief in a
supernaturally powerful person who cares about human behavior and
wants to be worshipped. And he went on to say that all serious
theology is a-theistic.
No problem with that. Science by itself is agnostic, but as much
about primary matter than any reality, we can only try religion,
and change of religion, or change religion. A religion is a
conception of reality, and it is based on the belief that there is
a reality, that we can share some aspect of it, and discuss about
the way to unify all the views and reflexion we can have on it.
Now, you frighten me a bit about which theologian you are
listening too, and I give you a tip, go back to the time theology
was a science, that is before +523 in occident (and of course, if
you study the theologians since, you will see many "saying
sentences like above, but only in context of being able to develop
other interesting ideas: that is, not all modern theologian
believe in such naive theist god). But officially: the field is
sick (authorianistist) since +523 in Occident, and about the
eleventh century in Middle-East.
Strong-atheism is a religion, and is dishonest when not saying so,
as it is the belief in a primary physical universe or matter,
object of the laws described in the book of physics.
That might be true. We don't know. But we can know that this view
is problematical if we assume there is no magic in the brain or in
matter.
It is nice because it illustrates the existence of a realm, a
simple one conceptually (a tiny part of arithmetic), where the
laws of physics originate.
The difficulty to accept this is similar with the difficulty some
accepted evolution. Perhaps.
Read history of science. Humans pervert science all the time, for
short run purpose, or for power purpose. For all of them we must
distinguish the object of study from the humans theories which can
always be wrong, if not escape the well guided practice (laic
academy, laic school, agnostic presentations, encouragement of
doubting, even mocking, *all* authorities, etc.).
Bruno
Brent
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