Le 27-déc.-05, à 05:43, George Levy a écrit :
Naming this field is difficult. This is why I made several suggestions
none of which I thought were excellent.
I think it is difficult because there is a conflict between pedagogy
and diplomacy there.
Bruno Marchal wrote:
I don't think it is a question of vocabulary,
It is only a question of vocabulary if you intend to communicate with
other people. And this is where the difficulty lies. If you make the
name too esoteric they will not even understand what the field is
about.
OK. But is not "theology" less esoteric than psychomechanics. Everyone
knows what theology is all about: immortalilty/mortality issues, soul's
fate in possible consciousness states, where do we come from,
cosmogony, etc.
"Scientific" theology is of course 100% agnostic on all this; yet it
can provide theories and with comp (or weaker) even testable or
partially testable theories (indeed with comp, physics is an integral
part of theology: physics is given somehow by the mathematical
structure describing the border of the intrinsic ignorance of machines.
and actually I am not sure we are not in, well *perfect* perhaps not,
but at least in an a larger matching area than you think.
Perhaps, like so many, you have not yet really understand the impact
of the discovery by Turing and its relation with Godel's theorem.
When I talk on Platonia, it is really "Platonia" updated by Godel's
and Lob's theorem. I hope you are open to the idea I could perhaps
progress in my way of communicating that. It really concerns machines
and even many non-machines. I think about abandoning comp for ind,
where ind is for indexical, given that G and G* applies to almost
anything self-referentially correct.
I knew this for long, the comp hyp just makes the reasoning and the
verification easier.
I can already say that I disagree the word "quantum" should be in it.
The name should not issue what will or should be derived by the
theory.
I do not fully understand the full ramification of how indexical
relates to this field.
Indexical is used in philosophy to designate term like "now", "here",
"modern", "I", "this" etc. Their meaning change with the situation of
their uses. For example "I" means Bruno for me and George for you.
"here and now" means Brussels and 10h54 am, here and now, but the time
I finish the sentence it already means something else (Brussels and
10h55 am). The approach I follow is based on the logic of
self-reference. "Bp" is really an indexical: it means "I prove p" where
"I" is put for a third person self-reference by the machine M, and
strictly speaking the meaning of "I" is different for each machine (but
by Godel Lob, still obeys similar laws of the self-referentially
correct machine).
However, I think that to use Indexical now is like Heisenberg using
Entanglement instead of Quantum. Nobody would have understood what he
was talking about. It was hard enough already to understand Quantum.
All right, but "quantum" still does not work for this field because it
would give the wrong impression that the quantum hyp. is assumed, where
the UDA shows it must be derived.
the comp hyp is neutral about which type of machine we would be. It
could be a quantum one or not. All what matters is that the machine
should be Turing emulable (or weaker: some Turing oracle can be assumed
without changing the self-reference logics G and G*).
BTW, COMP is not very good, because you have to explain what it is.
Well, that is the name of the hypothesis. The point is to have some
short acronym to put results in short formula like: COMP -> REVERSAL.
But we were discussing the name of the entire field. What *is* G* \ G
from a machine point of view? It is the self-referential truth which we
cannot prove, but which can be hope or fear or just bet upon, like Dt,
DDt, ...
At first glance it appears to be the Mechanist Philosophy and this is
what I originally thought.
Yes. Comp is the DIGITAL or numerical or computational mechanist
hypothesis. The mechanist philosophy is logically weaker due to the
(mathematical at least) existence of non Turing-emulable analogue
machine. The UDA, as it is now, does not work on such analogue machine.
Of course comp is a natural modern sister of the mechanist philosophy.
I think the best approach is to use a compound expression to bridge
the gap between different fields. (i.e., Quantum electro-chromo
dynamics, electro-magnetism, physical chemistry)
There is nothing surprising that quantum physics could be derived
from quantum psycho mechanics.
Of course it is surprising...not to you or me or others on the list
because we have been talking about it for so long... but to the
average scientist in the street... or the university. And these are
the people you intend to communicate with.
I don't follow what you say. Quantum mechanics assumes the quantum hyp
, and some mechanics, by definition. "Quantum X" presupposes the
quantum. But comp should entails the quantum.
Plato is the one who introduced the word "theology" with the meaning
of "Science of Gods", and by extension I take it as the science of
what we can hope or bet upon. It is just the truth *about* machine,
and we can talk and reason about it without ever knowing that truth,
given that no scientist at all can *know* the truth, at least as
knowed.
I think this science relates primarily to the "self."
Yes. And G and G* are the logic of self-reference. G is really the
machine science of self-reference. It describes what machine can prove
in a third person way on themselves. And G* describes still that same
self. G* is just able to prove more than G: G* proves some true
statement about "I" that "I" cannot prove. G and G* handle the same
type of "I" than the word "me" in the sentence "after my
self-duplication you can find me both at Moscow and Washington". And
then there is a third version of the "I", like in "I will find myself
either at Moscow or at Washington after the self-duplication". This one
is handled neither by G nor by G* but by the Theaetetical variants
which merge in some way the role of G and G*. It will appear that the
lobian first person has no name at all (and I am collecting evidence
that strictly speaking the lobian first person is just
NON-computationalist!).
As I said before, I think that it it the "I" that creates the
(orderliness in the) world.
Ah but this is the main statement in the Platonic theology of Plotinus!
With comp, that statement is made testable: the worlds are creation of
the first person plural "I", probably the one given by the second
theaetetical variant. Their math are entirely defined and thus
comparable with the math of the empirical worlds.
I have promised to Kim to recall the theaetetical variants, and this is
good opportunity.
Let us write B0 for the G or G* modal box. (and D0 for the diamond; in
particular D0p is the same as ~B0~p). B0 captures the (Godel, Lob)
provability predicate when the sentence letter p is a proposition in
arithmetic (or set theory, or more generally any language of a
self-referentially correct machine); and I recall G describes what the
machine can prove about its own provability and consistency; and G*
proves what is true about that. And given that I limit the interview to
sound machine (like PA or plausibly ZF), we know we talk to sound
lobian machine. (A sound machine is a machine which proves only true
statement). So G is included in G*, and all the theatetical variants
applied on G leads to a theatetical variant extended on G*).
The first theaetetical variant consists in defining a new box B1 by B1p
= B0p & p.
Of course, when the lobian machine is simple enough, WE know that B1p
is equivalent with B0p & p, and the machine's G* proves it accordingly,
but the machine's G does not, and the equivalence (B1p <-> B0p & p) is
a member of the machine's G* \ G (it belongs to G* but it does not
belong to G). So the logic of B0 and B1 differs. For example G does not
proves (B0p -> p), but G proves of course (B1p -> p) that is ((B0p &
p) -> p) is a classical tautology (ok?).
The following can be shown:
1) The logic of B1 is given by the modal system S4Grz, typical for a
temporal theory of knowledge à-la Bergson/Brouwer but also Dogen
(japanese "theology").
2) Here, G* does not add anything. S4Grz = S4Grz*. The knower, or the
first person, conflates, from her point of view, truth and provability.
3) the box B1 does not admit a translation in arithmetic (or any
Machine language). You can say the machine "knows" 1+1=2, by saying
that the machine can prove "1+1=2" and "1+1=2" is true. But you cannot
define a truth predicate (by Tarski theorem). So you can just do the
trick of defining Knowing "1+1=2", by saying just: provable("1+1= 2")
& 1+1=2, without using exclusively the godel code of the proposition.
Like truth, the knower is not definissable
in the language of the machine.
The second theatetical variant is B2 with B2p defined by B0p & D0p.
The third theatetical variant is B3 with B3p defined B0p & D0p & p. It
is really a combination of the first two theatetical variant.
Again G* proves that B0 and B1 and B2 and B3 are equivalent. From a
third person perspective they describe machines proving the same third
person propositions. Here too, G does not prove those equivalence, and
indeed G* does prove that their logic are quite different.
More on this latter. You see that it is the gap between truth and
provability, i.e. G and G*, which provides the room necessary for those
nuances. B0 and B1 admit Kripke semantics (multiverses with
accessibility relation). B2 and B3 does not. They get richer semantics
coherent with the continuum present in the unravelling of the Universal
Dovetailer (UD*).
As I said before, I think that it it the "I" that creates the
(orderliness in the) world.
This is not a new idea. Some philosophers have asserted this idea
before. Does this makes "I" a god?
Let us be very careful here. G is the *provable* part of the logic of
provability/consistency of a self-referentially correct machine. It can
be shown that G itself inheritates that self-referential correctness:
that is G is a (mini, non Turing-universal) lobian machine. I.e. G is
self-refrentially correct. That is the technical reaéson why Raymond
Smullyan can explain the logic G just true visists to the Knight-Knaves
Island (cf Forver Undecided). Now, G* is the *true* part of the logic
of provability/consistency of a self-referentially correct machine. If
you really want to introduce a Machine's God at this stage, G* could be
a candidate, although I would prefer to consider G* as a machine
theology, not as a God, you know I call it frequently a machine's
guardian angel. The point is that G* is NOT self-referentially correct,
it is just referentially correct whenthe reference is tmade toward the
machine (or G) about which he is talking. For example G* does prove D0t
meaning that the machine he talks about is consistent. G* proves B0p ->
p, meaning that he knows the machine is sound. But G* does not prove
B(Bp -> p) nor BDt. On the contrary G* proves ~BDt. If G* was talking
about itself the proves of Dt and of ~BDt would make him unsound (but
still consistent!).
By this, deriving that "I" is a God because "I" plays a so fundamental
role in the building of the (physical) reality, would be a confusion
between proof and truth, like if the G* \ G gap was empty.
Well, we know the gap *is* empty for the 1-person (S4Grz = S4Grz*), and
so there is a sense to say "I" is a God, for the first person. OK, but
then, like the notion of Truth and Knowledge,
for the first person "God" is just utterly not definissable, not
nameable, not this, not that,... etc, etc.
Somehow here the machines I am considering, which I recall believe in
Plato-Aristotle excluded middle law, are making the move from Plotinus
to Proclos, that is a move from a fuzzy "I" who build reality to a
purely negation-based notion of God. Proclos is the one who argued that
a scientific theology can only approximate God by negations: God is not
finite, God has no description, etc. Actually lobian machine's
ignorance behaves like that to if you "modelize" ignorance by some
1-person view of incompleteness.
Not in the traditional sense of "Theology" which carries too much
baggage.
OK, but note that the term "mathematics" carries also much negative
connotation baggage, especially for those working in the human
sciences. I am not sure that is a reason for not using a term. Perhaps
the contrary. perhaps we should use the term "theology" just for
helping people to forget the term has got negative baggage due to its
historical institutionalisation by the (Roman) Church.
This is my own emphasis which may not be shared by everyone on this
list.
I am aware of the popular meaning of "psycho" = crazy as John
mentioned. We could draw from other language than the Greek (auto,
psyche) or Latin (anima, spiritus) but we lose the ability to be
widely understood: Hebrew: nefesh, neshamah Japanese: tamashii.
Neshamah Mechanics is not going to fly. Tamashii Mechanics sounds like
sushi to the average westerner.
To talk on immortality issues (cf: quantum immortality or
comp-immortality) without accepting we are doing theology is perhaps
a form of lack of modesty. Nobody would dare to try to help me making
a case for the use of the word "theology"?
Of course we are doing theology but don't say it too loud or you'll
get involved in a religious war.
A war? Why not. A war is better than an hidden conflict. Well I'm not
sure. Science has always been in conflict with institutionalised dogma
(being it dialectical materialism or christianism: science is deeply
anti-dogmatic because science is above all modesty and doubts).
I think theology has too much baggage and is populated by people with
faith - a virtue for them, a vice for us. :-)
No, no; here I disagree. Comp needs an act of faith too. A "doctor" who
would say that science has proved that we survive an artificial digital
brain graft surgery is lying. Comp has this in common with the
Pythagorean, and perhaps with the neoplatonist (but unlike the muslim
neoplatonist) which is that they believe (hope for) a form of soul
transmigration possibility. This follows from the "yes doctor", and
that explains why I recall you the comp hyp. all the times. It is an
hypothesis which justifies by itself its necessarily *hypothetical
character". This is subtle and eventually clear through the G G* gap.
The whole of G* \ G can be considered as a collection of possible act
of faith. Note that given the fact that comp is necessarily
hypothetical and needs in practice some act of faith, a
computationalist is bound up to tolerate non-comp people. The funny
thing is that the comp 1-person is already non-computationalist
(probably: I mean it is still an open problem). It will be probably as
hard for machines than for us-human to believe they are machines, and
if they want to practice comp explicitly (by managing their own backup
for example) they will need an act of faith too.
Bruno
http://iridia.ulb.ac.be/~marchal/
