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.



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