# Re: Simple proof that our intelligence transcends that of computers

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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:
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On 25 Aug 2012, at 15:12, benjayk wrote:

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Bruno Marchal wrote:
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On 24 Aug 2012, at 12:04, benjayk wrote:

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But this avoides my point that we can't imagine that levels, context
```and
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ambiguity don't exist, and this is why computational emulation does
```not mean
that the emulation can substitute the original.
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But here you do a confusion level as I think Jason tries pointing on.
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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 Robinson
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arithmetic can prove that Peano arithmetic proves the consistency of
```Robinson Arithmetic.
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But you cannot conclude from that that Robinson Arithmetic can prove its own consistency. That would contradict Gödel II. When PA uses the induction axiom, RA might just say "huh", and apply it for the sake of
```the emulation without any inner conviction.
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I agree, so I don't see how I confused the levels. It seems to me you have just stated that Robinson indeed can not substitue Peano Arithmetic, because RAs emulation of PA makes only sense with respect to PA (in cases were PA
```does a proof that RA can't do).
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Right. It makes only first person sense to PA. But then RA has succeeded in making PA alive, and PA could a posteriori realize that 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 Einstein through my making of that process, but I can have a genuine conversation with Einstein through it. He will know that he has survived, or that he survives through that process.
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Dear Bruno,

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Please explain this statement! How is there an "Einstein" the person that will know anything in that case? How is such an entity capable of "knowing" anything that can be communicated? Surely you are not considering a consistently solipsistic version of Einstein! I don't have a problem with that possibility per se, but you must come clean about this!
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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.
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```That is, it *needs* PA to make sense, and so
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we can't ultimately substitute one with the other (just in some relative
```way, if we are using the result in the right way).
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Yes, because that would be like substituting a person by another, pretexting they both obeys the same role. But comp substitute the lower process, not the high level one, which can indeed be quite different.
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Is there a spectrum or something similar to it for substitution levels?
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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?
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It is like the word "apple" cannot really substitute a picture of an apple in general (still less an actual apple), even though in many context we can indeed use the word "apple" instead of using a picture of an apple because we don't want to by shown how it looks, but just know that we talk about apples - but we still need an actual apple or at least a picture to make
```sense of it.
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Here you make an invalid jump, I think. If I play chess on a computer, and make a backup of it, and then continue on a totally different computer, you can see that I will be able to continue the same game with the same chess program, despite the computer is totally different. I have just to re-implement it correctly. Same with comp. Once we bet on the correct level, functionalism applies to that level and below, but not above (unless of course if I am willing to have some change in my consciousness, like amnesia, etc.).
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But this example implies the necessity of the possibility of a physical implementation,
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In which modal logic?

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what is universal is that not a particular physical system is required for the chess program.
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With comp, to make things simple, we are high level programs. Their doing is 100* emulable by any computer, by definition of programs and computers.
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I agree with this, but any thing that implies interactions between separate minds implies seperation of implementations and this only happens in the physical realm.
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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.
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```Therefore the physical realm cannot be dismissed!
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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.
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Bruno Marchal wrote:
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With Church thesis computing is an absolute notion, and all universal machine computes the same functions, and can compute them in the same
```manner as all other machines so that the notion of emulation (of
processes) is also absolute.
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OK, but Chruch turing thesis is not proven and I don't consider it true,
```necessarily.
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That's fair enough. But personnally I find CT very compelling. I doubt it less than the "yes doctor" part of comp, to be specific.
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How is Deutsch's version different?
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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
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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.

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I don't consider it false either, I believe it is just a question of what
```level we think about computation.
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This I don't understand. Computability does not depend on any level (unlike comp).
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I don't understand either.

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Also, computation is just absolute relative to other computations, not with
```respect to other levels and not even with respect to instantion of
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computations through other computations. Because here instantiation and description of the computation matter - IIIIIIIII+II=IIIIIIIIIII and 9+2=11 describe the same computation, yet they are different for practical purposes (because of a different instantiation) and are not even the same computation if we take a sufficiently long computation to describe what is actually going on (so the computations take instantiation into account in their
```emulation).
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Comp just bet that there is a level below which any functionnally correct substitution will preserve my consciousness. It might be that such a level does not exist, in which case I am an actually infinite being, and comp is false. That is possible, but out of the scope of my study.
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Bruno, this is exactly my argument against step 8; it fails exactly at the infinite case.
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The infinite case is exactly non-comp, which, as I just said in the quote, is not the theory I am working on.
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```COMP is omega inconsistent.
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That statement has been made by J. Lucas, and refuted since. The error comes from a confusion between
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"[](ExP(x))", and

"Ex[](P(x))"

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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".
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But I have no clue why you say that comp is omega inconsistent in the present setting.
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Bruno

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

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http://iridia.ulb.ac.be/~marchal/

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