On 12/20/2010 3:07 AM, Bruno Marchal wrote:

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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<mailto:marc...@ulb.ac.be>> wrote:But then a digital machine cannot see the difference between its brain emulated by a physical device, of by the true existence of the proof of the Sigma_1 relation which exists independently of us in arithmetic. Some will argue that a physical universe is needed, but either they add a magic, non comp-emulable, relation between mind and matter, or if that relation is emulable, they just pick up a special universal number (the physical universe) or introduce an ad 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 more complexmathematical objects exist, or that they are valid substrates forconsciousness? I think a computer existing in a mathematicaluniverse performing computations is ultimately still representingmathematical relations. If this is true, does it makes the UDA lesstestable or formally definable?Once a computer exists in any mathematical structure, it will exist inthe UD* (the UD deployment). But only the UD deployment can be definedin a way which does not depend on any choice of mathematical theory todescribe it. Now, the measure of consciousness will depend on allmathematical structure, even if the measure bears only on the UD*,given that the measure pertains of first person experiences which arenecessarily non computational. That is why the distinction between3-ontology is 1-epistemology is very important.The true metamathematics of numbers is beyond numbers. The truetheology of persons is beyond persons.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. Mechanism makes matter an emerging pattern from the elementary arithmetical truth seen from inside. That makes mechanism a testable hypothesis, and that can already explain many qualitative features of the observable worlds, like indeterminacy, non-locality, non-clonability of matter, and some more quantitative quantum tautologies.I thought non-locality is solved with Everett's interpretation, or doyou 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.Also, I am curious how mechanism accounts for the non-clonability ofmatter.By UDA, any piece of observable matter is determined in totality onlyby an infinity of computations. That is why the physical reality isNOT Turing emulable, and not describable by anything finite. To copyexactly any piece of matter, you would need to copy the results of theentire running of the UD (and extract the first person pluralperception from it). Only your first person experience can interactwith such piece of matter, but your digital mind always makes adigital truncation of that reality. That truncation leads to copiablethings, but there are always approximation of the "real physicalreality", which is really an infinite sum of computations. That's therough 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 ofuniverses/computations.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).Likewise, PA cannot prove (believe) in its own consistency, but PA canemulate/compute completely the proof by ZF that PA is consistent.There is just no reason that PA begin to believe in the axiom of ZF.PA can emulate ZF, like Searle can emulate the chinese guy, but theykeep different beliefs.Here RA = Robinson Arithmetic, PA = Peano Arithmetic, ZF =Zermelo-Fraenkel set theory, ZFC = ZF + axiom of choice, ZF+K = ZF +the axiom of existence of inaccessible cardinals.Emulation/computation is a universal notion, independent of any formalapparatus needed to describe those computations. But belief/proof ishighly dependent of the system used. It is not because I can emulateEinstein's brain that "I" will have Einstein's beliefs. But I willhave Einstein computability power. And also, by emulating Einstein'sbrain, 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 provability abilities,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, butPA, ZF, ZFC, ZF+K, are Lobian numbers, and RA can emulate all of them.The key point is that RA cannot believe in general what they say. RAcannot prove its own consistency, but PA can already prove that RA isconsistent, and RA *can* prove that PA can prove that RA isconsistent. But that does not help RA, except if it feels alone andwant 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 no suchinvariance for provability power. All theories (Löbian numbers) grasponly a tiny part of the Arithmetical truth, and all grasp a differentparts (except ZF and ZFC). But they all compute the same computablefunctions.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 by suchor such reasoner. The UD emulate (like RA proves) all the (conscious)beliefs of all machines, including ZF, ZF+K, etc. Consciousness isrelated to those computation/emulation of beliefs, not to thecomputations themselves. In a sense, a machine or a brain is neverconscious: a relative machine, or a relative brain, just correlateconsciousness experience relatively to plausible computation.> No. The running of a program does NOT create a mind. It just makesit 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 unclear whatyou 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 to thelogical number-theoretical relations describing that computation ...and all similar (with respect to the relevant levels) computationswhich exist in Sigma_1 (computational) arithmetical truth (and whichmight bear on beliefs and proofs which extends far beyond the computable).

`But do you mean to assert that all computations have consciousness`

`attached? In what sense does this allow us to distinguish human`

`introspection from human perception from my dog's awareness from a`

`snail's awareness from a rock's awareness?`

Brent

Of course this is a delicate point. The notion of "a single program"is ambiguous. If it is a concrete physical instantiation of a program,then with digital mechanism, but also already quantum mechanism, it isalready unclear if we speak about real infinities of indistinguishablehistories/computations or of something unique (by taking some quotientof some equivalence relation).Consciousness is never created. Consciousness comes from the fact thatuniversal numbers can develop true (relative) beliefs, and that suchtrue beliefs appears to be stable with respect of infinities of sharedcomputational histories. >From our point of view this consciousness*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, andwith the content of consciousness as lived by entities with which weshare computational histories. It is, and has to be, counterintuitive.From "outside arithmetical truth" physical realities are "just" theintersubjective correlation of infinities of universal numbersbeliefs. That is why I can understand very well Rex's first personfeeling that consciousness is fundamental or basic. But numbersexplains that feeling can be justified by the numbers relations, andhave to, if we accept the existence of the substitution level.Hope this helps. Bruno http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/> --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 toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en.

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