On 20 Dec 2010, at 17:15, Jason Resch wrote:

On Mon, Dec 20, 2010 at 6:07 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:On 20 Dec 2010, at 03:15, Jason Resch wrote:On Wed, Dec 15, 2010 at 4:39 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:But then a digital machine cannot see the difference between itsbrain emulated by a physical device, of by the true existence ofthe proof of the Sigma_1 relation which exists independently of usin arithmetic. Some will argue that a physical universe is needed,but either they add a magic, non comp-emulable, relation betweenmind and matter, or if that relation is emulable, they just pick upa special universal number (the physical universe) or introduce anad hoc physical supervenience thesis.I think multiple realizability applies to mathematical objects aswell. Arithmetic may be simple enough to support minds and explainwhat we see, but should we discount the possibility that morecomplex mathematical objects exist, or that they are validsubstrates for consciousness? I think a computer existing in amathematical universe performing computations is ultimately stillrepresenting mathematical relations. If this is true, does itmakes the UDA less testable or formally definable?Once a computer exists in any mathematical structure, it will existin the UD* (the UD deployment). But only the UD deployment can bedefined in a way which does not depend on any choice of mathematicaltheory to describe it. Now, the measure of consciousness will dependon all mathematical structure, even if the measure bears only on theUD*, given that the measure pertains of first person experienceswhich are necessarily non computational. That is why the distinctionbetween 3-ontology is 1-epistemology is very important.The true metamathematics of numbers is beyond numbers. The truetheology of persons is beyond persons.But doesn't this change the relative proportions that exist forprograms contributing to a mind, and therefore change the likelihoodof what one might experience? For example, do you see any reasonfor a civilization to upload their minds onto computers? Would thisnot increase the likelihood that their future experiences extendinto this new reality of their choosing? Why should we bother to doanything at all if our actions don't change the relative measures ofdifferent conscious experiences?

`Our actions change our relative computations measure, yes. I don't see`

`the link with the fact that computers can be said to exist in model of`

`theories having large cardinals. My point was that those computer's`

`state are still generated by the UD, and if the measure depends of`

`those high cardinal, that is what we have to justified from comp, once`

`we assume that comp is true.`

I agree. But the consequence seems to be a big leap for many."Seems" because the results are more ignored than criticized.The problem (for many) is that mechanism is used by materialists,but in fine mechanism is not compatible with materialism. Mechanismmakes matter an emerging pattern from the elementary arithmeticaltruth seen from inside. That makes mechanism a testable hypothesis,and that can already explain many qualitative features of theobservable worlds, like indeterminacy, non-locality, non-clonability of matter, and some more quantitative quantumtautologies.I thought non-locality is solved with Everett's interpretation, ordo you mean the appearance of non-locality?*Quantum* non locality is solved in Everett, and made into anappearance, indeed. But here I was saying that such an appearance ofnon-locality is already a theorem of (classical) digital mechanism.I think I see what you are saying now. Consciousness can leapthrough space or time when instantiated elsewhere.

`Yes. Notably through UD-times, and UD-spaces, or UD-memory`

`(technically any 'Blum complexity', that is, decidable relations`

`pertaining on the 3-description of the computations).`

Also, I am curious how mechanism accounts for the non-clonabilityof matter.By UDA, any piece of observable matter is determined in totalityonly by an infinity of computations. That is why the physicalreality is NOT Turing emulable, and not describable by anythingfinite. To copy exactly any piece of matter, you would need to copythe results of the entire running of the UD (and extract the firstperson plural perception from it). Only your first person experiencecan interact with such piece of matter, but your digital mind alwaysmakes a digital truncation of that reality. That truncation leads tocopiable things, but there are always approximation of the "realphysical reality", which is really an infinite sum of computations.That's the rough idea.Russell is correct, it is better to attach the mind to all theinstantiation in the UD, and then consciousness is a differentiatingflux emerging from the number relations. Observation = selection ofinfinities of universes/computations among an infinity of universes/computations.Okay. I had thought you meant conservation of mass/energy, ratherthan the infinite complexity of matter.A key idea not well understood is the difference between proof/belief and computation/emulation. I will send a post on this.I look forward to this post.Searle can emulate (compute) the brain of a chinese. But Searle willnot understand and live the conscious experience of that chinese(Searle category error, already well analysed by Dennett andHofstadter in Mind's I).I think Searle's mistake (perhaps among many) is that he substituteshimself in the place of the computer's processor, but this is likesaying the physics understands Chinese (because the laws of physicsare processing all the interactions in the Chinese speaker's brain).

`Yes. It is typical level confusion. In the quotation below it would be`

`the same as saying that RA to the thinking of ZF when RA emulates ZF.`

`But of course it is ZF which thinks, not RA.`

Likewise, PA cannot prove (believe) in its own consistency, but PAcan emulate/compute completely the proof by ZF that PA isconsistent. There is just no reason that PA begin to believe in theaxiom of ZF. PA can emulate ZF, like Searle can emulate the chineseguy, but they keep different beliefs.Here RA = Robinson Arithmetic, PA = Peano Arithmetic, ZF = Zermelo-Fraenkel set theory, ZFC = ZF + axiom of choice, ZF+K = ZF + theaxiom of existence of inaccessible cardinals.Emulation/computation is a universal notion, independent of anyformal apparatus needed to describe those computations. But belief/proof is highly dependent of the system used. It is not because Ican emulate Einstein's brain that "I" will have Einstein's beliefs.But I will have Einstein computability power. And also, by emulatingEinstein's brain, I can have a genuine conversation with Einstein(not with myself).Once universal, all machine can emulate any other universal machine,yet they will have different and non equivalent provabilityabilities, and believability abilities.It is useful to compare (<) theories in term of the portion ofarithmetical truth that they can prove.RA < PA < ZF = ZFC < ZF+KNote that ZF and ZFC have different beliefs on sets, but the samebeliefs on numbers!ZF+K knows much more about numbers than all the other theories.RA is the only one not rich enough (in provability) to be Löbian,but PA, ZF, ZFC, ZF+K, are Lobian numbers, and RA can emulate all ofthem. The key point is that RA cannot believe in general what theysay. RA cannot prove its own consistency, but PA can already provethat RA is consistent, and RA *can* prove that PA can prove that RAis consistent. But that does not help RA, except if it feels aloneand want to talk with someone richer than itself.Only computation has such a remarkable invariance for change ofsystems, and that is a consequence of Church thesis. There is nosuch invariance for provability power. All theories (Löbian numbers)grasp only a tiny part of the Arithmetical truth, and all grasp adifferent parts (except ZF and ZFC). But they all compute the samecomputable functions.It's not clear to me the role provability plays. Is the simpleaccess to information within the state of a mind not sufficient?

`I am not sure I grasp what you mean by 'simple access to information'.`

`The only simple thing is your consciousness, and this is "just" a`

`simple but no that simple, natural bet of all Löbian machine or`

`numbers that there is a reality. That bet is natural in the sense that`

`it occurs for all such machine/numbers due to the G/G* splitting (or`

`simply: incompleteness). I write it often "Dt?", which can be`

`justified by Gödel's completeness theorem which shows that to believe`

`in your own consistency (Dt, or ~Bf) is the same as to believe that`

`your belief are satisfied (true) in some world. You can prove such`

`completeness for first order theory/machine or sufficiently effective`

`higher order logic/machine/theory/believer.`

`Now, when you look at the moon, the "seeing the moon" and the`

`"interpreting that seeing as an evidence for the moon" need the`

`collaboration and 'voting' of millions of neurons, and they manage to`

`integrate their works in such a way that you don't have to think`

`consciously that your body/neurons are doing a very hard work (but`

`well elaborated by millions years of evolution/deep-computational-`

`history).`

`The role of provability consists in defining a very simple notion of`

`believers. RA believes that 0+1 = 1+0, but RA has not the cognitive`

`ability to believe that for any x and y x + y = y + x. PA has it, and`

`thus are more beliefs on numbers, and ZF still more.`

`Of course we (humans) are full of circumstantial belief axioms, like`

`water is good, fire is bad, etc. Then I limit myself on perfect ideal`

`believers like PA and ZF, ... because they have already a very rich`

`theology, and we can understand why they have a soul, why they`

`confused it with the 3-describable believer, why the soul falls and`

`generate the material view, etc.`

`The key is that computation does not need any special formal system,`

`but belief and provability does. I identify a believer with a set of`

`axioms (his body), close or not (depending of what I want to explain)`

`for the deduction rules (= life, local relative dynamics).`

`Of course all the dynamics are emulated statically by the computation`

`done by RA. There is an implicit use of the notion of (arithmetical)`

`truth to distinguish an emulation of a computation from a mere`

`description of a computation (that is a tricky point needed for the`

`notion of computational supervenience).`

`Computation can be seen as a particular form of provability: indeed`

`the Sigma_1 provability (that is: the proof of sentences having the`

`shape ExP(x) with P decidable). RA is Turing universal = Sigma_1`

`complete. But Löbian believers like PA, ZF, ZF+kappa are not just`

`Sigma_1-complete, they belief (correctly) that they are universal.`

`This gives them the needed cognition ability to let the 'universal`

`consciousness of the abstract Löbian numbers' differentiates through`

`them, and select their consistent histories.`

Just remember that PA cannot prove its own consistency ZF can prove the consistency of PA

`and PA can prove that ZF can prove the consistency of PA, but cannot`

`deduce from this that she is consistent.`

`That is: emulating a machine having some belief or knowledge (of the`

`chinese language for example) does not make the emulator to have such`

`beliefs. To confuse computability with provability is a form of`

`Searle's error. As you say, it would give all beliefs to the physical`

`laws, or to arithmetic. Arithmetic emulate all believers, but does not`

`have all the beliefs or all the believers (actually it would make it`

`directly inconsistent).`

Bruno

That is why, also, ontologically, it is absolutely undecidable ifthere is anything more than sigma_1 (turing accessible) arithmeticaltruth. All the other arithmetical truth can be believed or not bysuch or such reasoner. The UD emulate (like RA proves) all the(conscious) beliefs of all machines, including ZF, ZF+K, etc.Consciousness is related to those computation/emulation of beliefs,not to the computations themselves. In a sense, a machine or a brainis never conscious: a relative machine, or a relative brain, justcorrelate consciousness experience relatively to plausiblecomputation.> No. The running of a program does NOT create a mind. It justmakes it possible for a mind to manifest itself relatively to you.> The mind is already related to the platonic relations between thenumbers which exist in an infinity of exemplars in Platonia.If a single program does not create a mind, how does an infinitenumber of programs in the UDA create one? Perhaps I am unclearwhat you mean by mind.Russell has given the correct answer. Here by mind I mean theconscious first person mind. By UDA-8 (MGA), consciousness is notattached to the physical running of a computer, but is attached tothe logical number-theoretical relations describing thatcomputation ... and all similar (with respect to the relevantlevels) computations which exist in Sigma_1 (computational)arithmetical truth (and which might bear on beliefs and proofs whichextends far beyond the computable).Of course this is a delicate point. The notion of "a single program"is ambiguous. If it is a concrete physical instantiation of aprogram, then with digital mechanism, but also already quantummechanism, it is already unclear if we speak about real infinitiesof indistinguishable histories/computations or of something unique(by taking some quotient of some equivalence relation).Consciousness is never created. Consciousness comes from the factthat universal numbers can develop true (relative) beliefs, and thatsuch true beliefs appears to be stable with respect of infinities ofshared computational histories. From our point of view thisconsciousness *seems* to be related to our bodies, but this is adeformation-from-inside. Programs only makes possible for some*content* of consciousness to be correlated with those histories,and with the content of consciousness as lived by entities withwhich we share computational histories. It is, and has to be,counterintuitive. From "outside arithmetical truth" physicalrealities are "just" the intersubjective correlation of infinitiesof universal numbers beliefs. That is why I can understand very wellRex's first person feeling that consciousness is fundamental orbasic. But numbers explains that feeling can be justified by thenumbers relations, and have to, if we accept the existence of thesubstitution level.Hope this helps. Bruno http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-l...@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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