On 26 Aug 2012, at 21:59, Stephen P. King wrote:

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On 8/26/2012 2:09 PM, Bruno Marchal wrote:On 25 Aug 2012, at 15:12, benjayk wrote:Bruno Marchal wrote:On 24 Aug 2012, at 12:04, benjayk wrote:But this avoides my point that we can't imagine that levels,contextandambiguity don't exist, and this is why computational emulationdoesnot mean that the emulation can substitute the original.But here you do a confusion level as I think Jason tries pointingon.A similar one to the one made by Searle in the Chinese Room. As emulator (computing machine) Robinson Arithmetic can simulate exactly Peano Arithmetic, even as a prover. So for example Robinsonarithmetic can prove that Peano arithmetic proves the consistencyofRobinson Arithmetic.But you cannot conclude from that that Robinson Arithmetic canproveits own consistency. That would contradict Gödel II. When PA usestheinduction axiom, RA might just say "huh", and apply it for thesake ofthe emulation without any inner conviction.I agree, so I don't see how I confused the levels. It seems to meyou havejust stated that Robinson indeed can not substitue PeanoArithmetic, becauseRAs emulation of PA makes only sense with respect to PA (in caseswere PAdoes a proof that RA can't do).Right. It makes only first person sense to PA. But then RA hassucceeded in making PA alive, and PA could a posteriori realizethat the RA level was enough.Like I converse with Einstein's brain's book (à la Hofstatdter),just by manipulating the page of the book. I don't become Einsteinthrough my making of that process, but I can have a genuineconversation with Einstein through it. He will know that he hassurvived, or that he survives through that process.Dear Bruno,Please explain this statement! How is there an "Einstein" theperson that will know anything in that case? How is such an entitycapable of "knowing" anything that can be communicated? Surely youare not considering a consistently solipsistic version of Einstein!I don't have a problem with that possibility per se, but you mustcome clean about this!

`What is the difference between processing the book with a brain, a`

`computer, or a book? This is not step 8, it is step 0. Or I miss what`

`you are asking.`

That is, it *needs* PA to make sense, and sowe can't ultimately substitute one with the other (just in somerelativeway, if we are using the result in the right way).Yes, because that would be like substituting a person by another,pretexting they both obeys the same role. But comp substitute thelower process, not the high level one, which can indeed be quitedifferent.Is there a spectrum or something similar to it for substitutionlevels?

`There is a highest substituion level, above which you might still`

`survive, but with some changes in your first person experience (that`

`you can or not be aware of). Below that highest level, all levels are`

`correct, I would say, by definition.`

`If your level is the level of neurons, you can understand that if I`

`simulate you ate the level of the elementary particles, I will`

`automatically simulate you at the level of your neurons, and you will`

`not see the difference (except for the price of the computer and`

`memory, and other non relevant things like that). OK?`

It is like the word "apple" cannot really substitute a picture ofan applein general (still less an actual apple), even though in manycontext we canindeed use the word "apple" instead of using a picture of an applebecausewe don't want to by shown how it looks, but just know that we talkaboutapples - but we still need an actual apple or at least a pictureto makesense of it.Here you make an invalid jump, I think. If I play chess on acomputer, and make a backup of it, and then continue on a totallydifferent computer, you can see that I will be able to continue thesame game with the same chess program, despite the computer istotally different. I have just to re-implement it correctly. Samewith comp. Once we bet on the correct level, functionalism appliesto that level and below, but not above (unless of course if I amwilling to have some change in my consciousness, like amnesia, etc.).But this example implies the necessity of the possibility of aphysical implementation,

In which modal logic?

what is universal is that not a particular physical system isrequired for the chess program.With comp, to make things simple, we are high level programs. Theirdoing is 100* emulable by any computer, by definition of programsand computers.I agree with this, but any thing that implies interactionsbetween separate minds implies seperation of implementations andthis only happens in the physical realm.

`No, this is not correct. You fail to appreciate that all`

`implementations and interactions are already emulated in arithmetic,`

`as shown by Gödel (in other terms, and implicity in 1931), and made`

`clear since.`

`Actually, since matiyasevich, we know that we can eliminite the`

`"A" ("for all") quantifier from the logic, and that a unique degree`

`four diophantine polynomial can already do the job.`

Therefore the physical realm cannot be dismissed!

`Nothing real need to be dismissed. But once an argument show that it`

`cannot be postulated, the "non-dismissing" takes the form of a`

`reduction of it to something else.`

Bruno Marchal wrote:With Church thesis computing is an absolute notion, and alluniversalmachine computes the same functions, and can compute them in thesamemanner as all other machines so that the notion of emulation (of processes) is also absolute.OK, but Chruch turing thesis is not proven and I don't consider ittrue,necessarily.That's fair enough. But personnally I find CT very compelling. Idoubt it less than the "yes doctor" part of comp, to be specific.How is Deutsch's version different?

`It is not a different version, it is a completely different thesis. It`

`assume a physical reality (primitive or not), and his thesis is that`

`there is a physical universal emulator capable of emulating all`

`physical processes. In the comp theory, this is an open problem.`

`CT assumes only arithmetic or equivalent, and postulates the existence`

`of a universal programming language. Actually it postulates that`

`lambda calculus is universal with respect of the ability to define`

`computable functions. Since then lambda calculus has been shown`

`equivalent with Turing machine, algol programs, game-of-life, very`

`elementary arithmetic, diophantine equations, etc. So the origian CT`

`is equivalent with`

All computable function can be computed by a fortran program All computable function can be computed by a algol program All computable function can be computed by a game-of-life pattern

`All computable function can be computed by a four degree polynomial`

`diophantine equation`

All computable function can be computed by a current computer etc. CT does not involve physics at all, contrary to Deutsch' thesis.

I don't consider it false either, I believe it is just a questionof whatlevel we think about computation.This I don't understand. Computability does not depend on any level(unlike comp).I don't understand either.Also, computation is just absolute relative to other computations,not withrespect to other levels and not even with respect to instantion ofcomputations through other computations. Because hereinstantiation anddescription of the computation matter - IIIIIIIII+II=IIIIIIIIIIIand 9+2=11describe the same computation, yet they are different forpractical purposes(because of a different instantiation) and are not even the samecomputationif we take a sufficiently long computation to describe what isactuallygoing on (so the computations take instantiation into account intheiremulation).Comp just bet that there is a level below which any functionnallycorrect substitution will preserve my consciousness. It might bethat such a level does not exist, in which case I am an actuallyinfinite being, and comp is false. That is possible, but out of thescope of my study.Bruno, this is exactly my argument against step 8; it failsexactly at the infinite case.

`The infinite case is exactly non-comp, which, as I just said in the`

`quote, is not the theory I am working on.`

COMP is omega inconsistent.

`That statement has been made by J. Lucas, and refuted since. The error`

`comes from a confusion between`

"[](ExP(x))", and "Ex[](P(x))"

`That is "I know it exists a number x having the property P true on x"`

`and "it exists a number x such that I know P is true on x".`

`But I have no clue why you say that comp is omega inconsistent in the`

`present setting.`

Bruno

Bruno Marchal wrote:It is not a big deal, it just mean that my ability to emulateeinstein(cf Hofstadter) does not make me into Einstein. It only makes meableto converse with Einstein.Apart from the question of whether brains can be emulated at all(due topossible entaglement with their own emulation, I think I willwrite a postabout this later), that is still not necessarily the case.It is only the case if you know how to make sense of theemulation. And Idon't see that we can assume that this takes less than beingeinstein.No doubt for the first person sense, that's true, even with comp.You might clarify a bit more your point.I am interested in benjayk answer too.

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