Hello Stephen,

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At 13:18 -0500 29/01/2003, Stephen Paul King wrote:

Could you translate these symbols into words so that I could better wrap my mind around them and spin them around in my head?

BM: Basically []p = provable p in such a precise way that 1) you can verify the proof in a finite number of mechanical steps 2) grosso modo p is made true in all recursively enumerable maximal extension of the machine/theory <>p is -[]-p you should read <>p by consistent p. That is the fact that -p is not probable, so that you get no contradiction by adding p as a new axiom to the theory or to the machine roots belief.

BM:> BM: Here I gave a little sketch of the translation of UDA in a "consistentmachine's language".[SPK] I hope that you realize that there are many ideas that you are assuming tacitly that I and others are not familiar with and/or may have other definitions for.

I constantly refer the interested lister to Boolos 1993 book. Or Smorynski 1985.

SPK:

For example: exactly what do the words "consistent", "machine" and "language" mean?

BM: See above. SPK:

I take "consistent" means that given some formal model, whose exact definition must be given somehow ...

BM: Any machine or theory extending classical logic and capable of proving elementary arithmetical theorems. SPK:

... or, at least, must be familiar to your readers, a "consistent machine's language" is one where there is no contradiction obtainable given any possible combination of the machine's language.

BM: Not "any possible combination", only those who respect classical logical inference rule. I interview (in AUDA) the platonist computationalist machine! SPK:

We may note that "machines" are usually defined by some set of functions N -> N, where N are the Natural numbers.

BM: Read my to diagonalisation post for making this precise. I would say that controlable machine, constructive reals, and total computable function (where total means defined on all N, can be, in our context, identified. But such a set is not *recursively* (mechanically) enumerable!!!! All "my" enterprise, and actually Church thesis, are made consistent by the fact that the set of total computable function is a necessarily fuzzy set include in the set of all computable functions. SPK:

BM:I am very skeptical that this (countable) set of numbers alone is sufficient in itself to cover the range of all possible systems in Nature (the Totality of possible existential expressions, including all mathematics). Given this caveat, is this within your notion of a definition of these words?

Please read carefully the diagonalisation post. Church thesis is really the

"schroedinger equation" of comp. I mean a highly non trivial statement in the

fundamentals of mathematics. It is the roots of the incompleteness phenomenon.

Before Church thesis you could have believed that "to be a machine" is a

simplifying assumption. After Church thesis we know that machines, and universal

machines in particular" have unbounded complexity. Universal machines are

mostly lucky unpredictable being.

> >SPK:> Ok, I am not questioning whether or not there "exists"self-referential>programs (plural???) or a "Univiversal program" (singular???), I am >wondering about how do we go from formal existence postulation to the >possibility of "maniferstation" itself. This is where I think that thereis>a problem if only in that the domain of explanatory power of such models >only applies to a very narrow range.

BM: I am really afraid you don't take Church thesis into account. The explanatory power applies to range which you can not even bound by formal tools. Even the whole Cantor Paradise is too poor to explain *in general* universal machine behavior. Some people still believe that the computer industry will make our life more simple. They will be disillusioned. A good thing perhaps. Now, for an explanation of the qualitative aspect of the "manifestation", well this is all the purpose of my thesis. Note that I acknowledge an explanatory gap, but I show that comp justifies the existence of a talk on explanatory gap by the machine's first person.

> BMNot with comp by hypothesis. Manifestation are indexicals. Strictlyspeakingthis follows from the UDA + OCCAM RAZOR, or better UDA + MOVIE GRAPH. (we can come back on this latter). See Maudlin 89 for something equivalent to the movie graph. Maudlin realises the incompatibility between the "physical supervenience thesis" (sup-phys) and comp. Because he want sup-phys, he abandons comp. Because I postulate comp, I abandon sup-phys.[SPK] What I am trying to argue is that we can not abondon eiter sup-phys nor comp except in the very very special case where the distinguishability between the two vanishes, e.g. a neutal monism that obtains in the infinite limit of all possible existential (or ontological) expressions and, additionally, we must not be so cavalier in our postulations. As I have tried to argue before, the notion that the mind is UTM emulable is not a proven fact and at this point should be considered to be merely a conjecture.

BM: It cannot be taken as a conjecture. It is an hypothesis which has the curious feature that if you add it as an axioms it becomes false! (This is a known feature of modal logics or intensional mathematics). So "the notion that the mind is [consistently] UTM emulable" is not only not a proven fact, but it will never be a proven fact, even in the seemingly trivial sense as being provable in a theory which take it as axioms. I use modal logic because it is so easy to be wrong in intensional (modal) context. SPK:

The thought experiement using classical cloning and or teleporting of minds has several assumptions that are contrary to known physical facts, such as the imposibility of simulataneously measuring the position and momenta of all the required atoms of a brain such that a UTM could be defined that would emulate its behaviour. This, in itself, leads me to reject the entire notion of "brain cloning" and any idea that depends on it as simple idealistic. It is as fantastic as a pink unicorn. I see not way in which the classical teleportation is possible in the "real world".

BM: I use brain cloning (and the neuro hypothesis) to make my argument simpler. Then I explicitely eliminate that hypothesis. The elimination is based on the fact that the UD will generate all your digital quantum state. You can postulate that you are not a quantum digital machine, for example that you are some analogical quantum machine capable of handling in finite time infinite precision. But in that case you are no more in the context of the comp hypothesis. I have no problem with that.

SPK >Here we find the following: >http://www.cis.udel.edu/~case/slides/krt-consc-cs-slides.ps BM: Nice. I didn't see it! SPK: > Exactly what is the formal statement of "if she looks closely enough to >its probable local implementation" or equivalently, "near its comp >substitution level"? Are you assuming some kind of "delta-epsilonics"here?BM: It means that your substitution level are the neurons and you look at the molecules which constitute the neurons. Or your substitution level is the quarks and you look at anything apparently making up the quarks,etc.It happens when you look at a so much fine grain that you face the1-personundistinguishable stories. I am not assuming "delta-epsilonics" things,butit is an open problem if sort of "delta-epsilonics" is not dormant here. CF: the UD dovetails on the reals, oracles, ...[SPK] Umm, this confuses me! How can we think of UD as "generating" all of physicality via computational simulations but yet seems to require the prior existence of the reals (numbers), oracles, etc. This looks like a "chicken and the egg" problem!

BM: You always seem to forget that I don't postulate any form of physicality. For me term like "matter" or "universe" are like the term "phlogistic" or "God". That is very, very, very, ..., very vague term which confuses us on fundamental questions. Those term have local use but we will not progress if we reify them and take their referent for granted. It would be like to finally criticize a molecular biologist because he has not yet explain the vital principle.

> >SPK:> I still do not understand how you go from UDA to 1-uncertainty.Please>point me to the definitions again. ;-)

BM: See link to the Universal Dovetailer Argument (UDA) in my web page.

> BM: > See http://www.escribe.com/science/theory/m2978.html and follow up.[SPK] This is just more on the classical teleportation idea that I am arguing is impossible in the real world!

BM: That impossibility is not relevant for the demonstration. I insist. See above.

[SPK] Again, you can not do this "postulating" and make ontological claims. This is not like Euclid's postulation of points! But furthermore, why do you not postulate more than just N-> N and arithmatic operations? It seems to me that Goedel's incompleteness theorems necessitate and infinite nesting of metatheories to span the universe of mathematics such that a Totality of the "mathemacial universe" is not even enumerable!

BM: You are right. But Godel's theorems are provable by the machines, and that is the reason why I don't need to postulate explicitily those tranfinite progressions. Numbers in numberland also dream about infinite nestings of metatheories. There is a sort of SKOLEM paradox here. I postulate just the meaningfulness of the standard model of "Peano Arithmetics" (let us say), and then I show that this countable model, seen from inside (1-view), is bigger than what any machines can ever imagine, and is highly structured too. That 1-bigness will provide jobs for mathematical psychologists, for ... ever. SPK:

What is COMP other than N -> N functions? COuld you explain to us how you can generate SWE using only N -> N functions, or, equivalently, how to embed complex valued functions in N?

BM:

Please, comp is PI (Personal Implication: you say "yes doctor" for his

proposition of a artificial brain)

TC (Church Thesis, see what I say above on it)

RA (the believe that arithmetical truth is atemporal,

aspatial, .... and that it does not depend on you, me...)

Real numbers enters the show in two different ways: as constructive real,

which can be identified with total computable function from N to N, and as

being generated in the limit by the UD. This include the non constructive reals.

Complex, quaternion, octonions, should be explained by Z1* (and *that* is a

conjecture!).

SPK:

The manual containing an enumeration of all of the brain states of Einstein is impossible by the Heisenberg Uncertainty principle.

BM: Only if you postulate that einstein brain is an infinite *analogical* quantum computing machine. SPK:

This is a "red herring"!

BM: That is your opinion, which I respect. SPK:

I do give Searle some credit for trying to point out something amiss with the "Emperor's New Clothes" but not much. ;-) The key that strong AI and COMP believers in general seems to neglect the fine point that 1-person expereice is not 3-person observable.

BM: But that was what I said in my last post to Colin Hales. Remember? I even have compared the first person to the vampire! It is the most striking feature of the first person: it is not a 3-machine! SPK:

Just because for some finite testing there could be no difference between a Machine's behavior and a "human" does NOT necessitate that they have equivalent 1-person content.

BM: Sure. SPK:

As a matter of fact, I have no way to prove that you are not a machine and you can not prove that this post is not just the output of a random letter generator. All we have is likelyhoods and assumptions. ;-)

BM: Sure.

SPK: I fail to see how notions such as "time", " casuality" and "1-person / 3-person distinctions are shown to be necessary by your model. My point is that if our 1-person experience of a world is nothing more that a string of symbols existing a priori in Platonia,

BM: But it is not! A first person is a person with her feelings, pains, hopes, joys, headache, and many personal memories. Nothing else. Certainly not a 3-string, not a 3-bunch of 3-particles, not a 3-machine, neither a 3-brain. The magic of comp, is that you can 3-study the 1-person discourse. The 1-person are much more than the arithmetical platonia, even if that much more is just platonia seen from inside. SPK:

why do we have enless debates about the notion of a "flow of consciousness"? It can not be "explained" away as just an illusion or "intensional stance". Immaterial strings might be capable of encoding each other as subsets but unless we have some means to explain how Nature solves mathematical problems that are both intractible by finite TMs and require that we include the means of explaining concurrent computations, e.g. we have to explain, at least, the appearence of interactions between a plurality of systems not just a single computational system.

BM: That's exactly what I begin to do in my thesis. SPK:

I am sorry, Bruno. But unless you can recover your proof independent of "classical teleportation" your explanation is grossly insufficient, at least, for me. :_(

BM: Read very carefully the UDA, and you will see that I explicitely eliminate the "classical teleportation". It is the point 13 in the m1726. SPK:

Our ideas seems to be very similar but I think that you have truncated a lot of ideas into COMP that need to be more carefully examined. The possibility that we need to define a generalization for COMP that involves, at least C -> C functions (C = complex numbers) obtains in my thinking. Pratt's notion of Chu spaces with k = Complex seems to get close. I am working on a post on Pratt's ideas but have many distractions and so do not know when it will be ready to post.

BM: Take your time. I am busy too. Apparently, also, my computer is again sick (damned).

SPK: Let us continue our explorations of ideas and I hope to explain to you how I am neither a PHYSICAList nor a COMPutationalist. I have a thought that might show how there might be a flaw in your reasoning and it is that just because UTMs are independent of any particular physical implementation does not obtain that UTMs do not require, at least, some approximate implementation in physicality. Numbers are meaningless if there does not exist some 1-person notion of "numberness". Like the number three is a meaningless symbol, at best, if there is not some set of objects that is associable with "threeness". More on this in the next post. ;-)

BM: I am not sure there is any problem between us. You don't like very much neither comp, nor what I derive from it. People who postulates comp and who does not like the consequence are more troubled, like most monist materialist. I have skip the "Finkelstein part of the post" because I prefer to reread him before). I am a little less finitist than Finkelstein, I think). Apology also for having (non purposefully) attribute some of my prose to you ;-). Bruno -- http://iridia.ulb.ac.be/~marchal/