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

On 27 Aug 2012, at 15:32, Stephen P. King wrote:

On 8/27/2012 8:48 AM, Bruno Marchal wrote:

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

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, context
and
ambiguity don't exist, and this is why computational emulation does
not mean
that the emulation can substitute the original.

But here you do a confusion level as I think Jason tries pointing on.

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 arithmetic can prove that Peano arithmetic proves the consistency of
Robinson Arithmetic.
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.
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).

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.

Dear Bruno,

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!

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.

Dear Bruno,

The question that I am asking is how you deal with multiple minds. SO far all of your discussion seems to assume only a single mind and, at most, a plurality of references to that one mind.

?

After a WM duplication there is already two minds. The first person plural handled the many minds.

That is, it *needs* PA to make sense, and so
we can't ultimately substitute one with the other (just in some relative
way, 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 the lower process, not the high level one, which can indeed be quite different.

Is there a spectrum or something similar to it for substitution levels?

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.

OK. This seems to assume a background of the physical world...

Not at all. You need only a Turing universal system, and they abound in arithmetic.

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?

Yes, but that is not my question. When you wrote "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" these seems to be the implications that the mind of Einstein and the mind of Bruno are not one and the same mind, at least in the sense that you can be come him merely by reading a book just changing your name.

Yes. comp has no problem with many minds.

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.

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.).

But this example implies the necessity of the possibility of a physical implementation,

In which modal logic?

None so far that I know of. This is the problem that I see. We completely ignore the ubiquitous even to the point of believing that it doesn't exit at all!

?

what is universal is that not a particular physical system is required for the chess program.

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.

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.

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.

That is not my point. Any and all implementations and interactions must be "emulated in arithmetic" for the symbols of arithmetic to have meaningful content. I am asking a semiotics question. Is there a referent to which arithmetic refers to?

?  (the model of arithmetics?)

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.

All of which assumes that such can be communicated.

Why? Even if Matiyasevic found this on a desert islands his result would be true. Even if he did not found it, and was never communicated, it still would be true, or you defend an arithmetical idealism incompatible with comp.

But how does it get communicated? I am asking you to consider what is being taken from granted, that ideas, concepts, representations are communicated and asking you how that occurs - even as a toy model explanation.

It happens when a collection of universal machines are supported by some common universal machine. That happens all the "time" in arithmetic.

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.

This is not a reduction issue. The symbols string that you are reading now does not refer to the computer monitor that you are reading it on, or does it?

?

Bruno Marchal wrote:

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.
OK, but Chruch turing thesis is not proven and I don't consider it true,
necessarily.

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.

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.

Yes, of course it is! I claim that it is an open problem for comp because it assumes that it (physical reality) can be deleted from the discussion.

I say the exact contrary. If comp is true then the primitive physical reality is deleted from the ontology, and we have to explain the physical reality appearance from the ontology we keep, like numbers or combinators, etc.

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 think that you are simply failing to understand Deutsch' idea. one does not need to assume physical reality if one can merely assume that some kind of communication can occur. My claim is that interaction defines the equivalent to a physical reality;

it is the plenum of commonalities on which we communicate. I am trying to get you to see this such that you might see the easy solution to comp's open problem.

I don't consider it false either, I believe it is just a question of what

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 with
respect to other levels and not even with respect to instantion of
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).

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.

Bruno, this is exactly my argument against step 8; it fails exactly 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.

That is a nice Attaque au Fer! This is exactly why I make the claim that your result is omega-inconsistent.

I have no clue with a result being omega-inconsistent.

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.

Its meaningfulness vanishes when the medium which allows communication is removed. How can it be communicated? This is not an issue of consistency, it is something else. I would like to see more of J. Lucas' statement and the refutation.

There is a full chapter on this in "conscience and mécanisme", and thousand of papers in the literature.

Again, none of this address the issue of the flaw in UDA.

Bruno

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

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