On 25 Jan 2010, at 07:52, Brent Meeker wrote:

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Bruno Marchal wrote:

Now, having postulated the natural numbers with addition andmultiplication, they organized themselves, independently of ourwhishes, in a way which escapes *any* attempt of *complete*unification. They defeat all our theories, in a sense. Once wepostulate them, they get a life of their own. To understand them,we have literally no choice, in general, than to observe them andinfer laws.We can prove that they have definite behaviors, but we can prove(assuming mechanism) that we cannot predict them, in general.ISTM that can be read as a reductio against the reality ofarithmetic.On the contrary. It shows that arithmetical reality kicks back. Wemay also know greater and greater portion of it. We may discovernew interesting properties, and we progress indeed since a longtime. From Diophantus to Matiyasevitch, to mention a beautiful line.Are you alluding to fictionalism? Do you defend the idea that "3is prime" is a false proposition?No, I just don't think it's truth implies the existence of "3".

So you believe that the proposition "9 is not prime" is false?

`To say that "9 is not prime" is the same as saying that It exits a`

`number different from 1 and 9 which divides 9.`

`To believe that "9 is not prime" you need to believe that Ex[x =`

`s(s(s(0)))]. i. e "3 exists" (and divides 9).`

I have no real clue of what that could seriously mean.Of course I would never expect that someone who doesn't believethat 3 is prime can say anything about the consequence of DIGITALmechanism. Such a move cut the uda (and the auda) at their roots,and everything becomes infinitely mysterious. Frankly I would notask him to compute my taxes either.So why not suppose that the natural numbers are just a model ofperceptual counting; and their potential infinity is a convenientfiction whereby we avoid having to worry about where we might runout of numbers to count with?You can do that. But assuming you are not fictionalist, if you saythat the infinity of natural numbers is a fiction, you are lead,ITSM, to ultrafinitism.What's the difference between finitism and ultrafinitism? Doesn'tpostulating the integers plus ZF also commit you to existence of thewhole hierarchy of infinite cardinals?

`Finitist believes in all finite numbers or things. And nothing else. A`

`finitist believes in 0, and in s(0), and in s(s(0)), etc ... But he/`

`she does not believe in the whole set {0, s(0), s(s(0)), ...}. He/She`

`does not believe in infinite objects.`

`An ultrafinitist believes in 0, s(0), s(s(0)), ..., but he/she does`

`not believe in all finite numbers. He believes that the set of all`

`positive integers is a finite set. I think that Tholerus argued that`

`there is a bigger natural number. This makes sense for some strong`

`form of physicalism: a number exists if and only if it is instantiated`

`in the physical reality (which has to be postulated, then, and assumed`

`to be finite).`

With fictionalism, I think that you can say "yes" to the doctor,and reject the reversal consequences. This leads to a matterproblem, a mind problem, and the usual mind/matter problem. I wouldtake this as a defect of fictionalism.Brent, I am not saying that ultrafinitism and fictionalism arefalse. I am just saying that IF you say yes to your doctor'sproposal to substitute the brain for a computer, and this with areasonable understanding of what a computer is (and this asks for aminimal amount of arithmetical realism) then the laws of physicsare necessarily a consequence of the (usual, recursive) definitionof addition and multiplication. Indeed it is the global couplingconsciousness/realities which emerges from + and * (and classicallogic). (or from K and S and the combinators rules, + equalityrules (this is much less)).A sentence like "naturals numbers are just a model of perceptualcounting" already assumes (postulates) arithmetic. And with digitalmechanism you can explain why universal number can use naturalnumbers as "model of their perceptual counting".You should not confuse the numbers as thought by the philosophicalhumans (what are they? does they exists?) with the numbers as usedby mathematicians, physicists or neurophysiologists, like in "thisflatworm has a brain constituted by 2 * 39 neurons" or "allpositive integers can be written as the sum of *four* integerssquares.(Then the number takes another dimension once you say "yes" to thedoctor, because in that case, relatively to the (quantum)environment, you say "yes", not for a "model", but because you betthe doctor will put in your skull the actual thing "you", yetthrough "other matter", and all what counts is that he put theright number, relatively to the current environment. That otherdimension is somehow the object of all our discussions).May be I can ask you a question, which I asked to Peter Jones, andwhich is this. Do you see that NON-COMP + arithmetical realismentails the existence of a realm full of zombies?No, I don't see that.

`Probably my fault. Let us call "WEAK AI thesis" the thesis that we can`

`build a machine which behaves like a human, but that such a machine`

`has no consciousness, so it can be seen as a zombie. This is plausibly`

`true concerning some actual japanese androïds, or for some "fake`

`policeman" that some states put on the road as preventing measure.`

I find plausible that the following shows a zombie: http://www.youtube.com/watch?v=WbFFs4DHWys&NR=1&feature=fvwp I rephrase the question:

`Do you see that NON-COMP + WEAK AI thesis entails the existence of`

`zombies in arithmetic?`

`Of course they would exist in the same sense that numbers exists (and`

`programs or digital machine, together with their computations, exist`

`in arithmetic, except that a zombie androïd will be more tedious to`

`define). Well, for the Japanese zombie (plausibly) you may ask for the`

`(digital) code source.`

`A more simple reason is that all rational approximations of the`

`quantum state evolution of the Milky Way up to some fixed moment,`

`exist in arithmetic, like any finite pieces of any computations exists`

`in arithmetic (and is executed by the UD).`

`The laws of arithmetic do emulate all those computations. In`

`particular the proposition "all digital approximations of dynamical`

`movement of Brent's body are emulated in arithmetic". But if you don't`

`attribute a consciousness to such virtual and arithmetical "Brent",`

`then they will be abstract (arithmetical, virtual) zombies, and this`

`despite some of them will write the same mails, and invoke the same`

`thoughts and idea. I assume classical (non relativistic) quantum`

`mechanics, for the sake of the illustration, here.`

Yet, like in the empty wave of the Bohmians, those zombie acts andtalk like you and me, have thought processes, and asks themselvesabout mechanism, consciousness, realities, and what constitutetheir environment (matter), and all this in a genuine way, asdefined by the logics of (correct/consistent) (relative) self-references. With NON-COMP, I would be tended toward fictionalismmyself, because I would wish those zombies could not exist.Such zombies seem like an incoherent concept to me.

`With comp, the problem of the zombie, or of the movie of a computation`

`is solved by the fact that consciousness cannot really be attributed`

`to anything observable. My current consciousness is not related to my`

`observable body, only to my "real body" which emerges from ALL`

`computations going through my state related to "my`

`consciousness" (which exists assuming comp).`

`But then, with QM, we are described by infinite (or very big) tensor`

`products, and this suggest we may "observe" or infer from the simplest`

`theories of the empirical facts, a part of our unobservable "real`

`body". The "real body" is really an infinite (or big) tensor products`

`of bodies. The fact that quantum indeterminacies are sharable`

`(explained in Everett by the multiplication of worlds, or the`

`contagiousness of the superposition states (entanglement)) may suggest`

`also that our substitution level is determined by the Heisenberg`

`uncertainties.`

`The quantum aspect of reality (by which I mean mainly the many worlds`

`and the constant multiplication (or differentiation) of large`

`populations of universal machine/subject) saves both QM and comp from`

`solipism. It makes possible the notions of first person plural.`

In a sense, there *exist* local zombies, because from their ownfirst person points of view, they belong to the projection of theset of all computations. Their first person indeterminacy bears onthe whole computational space, and what is observable in any stableway can only belong to the border of that space.How do you define the border of computational space?

`Hmm... Imagine a affine line. You can see it as a point in the`

`projective space. Now consider your current relative computational`

`state, describes at *a* correct level of substitution. In arithmetic`

`it exist an infinity of computations going`

`through that relative state (and the UD generates them all). You don't`

`know in which computation "you are", and by the first indeterminacy,`

`it does not matter, given that the next "moment" is given by a measure`

`on the set of all possible "next states". The math suggests there is`

`no "next state" from the first person view, but more a continuous`

`neighborhood. Now for each computation you are in, you have to predict`

`your "observable reality" by the infinite union of all infinite`

`computations going through that state. Example the Milky way, in the`

`position base, will give a continuum of different computations,`

`distinguished by the position of the electron on any atom. Now many`

`computations stop and many computations don't stop, and the`

`interesting things happen in between, a bit like the border of the`

`Mandelbrot set. If the`

`set M inter Q x Q is creative in the sense of Emil Post, then the`

`border of the M set is (recursively isomorphic to ) the border of the`

`computational space. I have still some doubt, but the M set`

`illustrates the self multiplication, and self complexification (self`

`mixing).`

`(power of two for the M set) look at this beautiful (8 minutes) deep`

`and interesting zoom:`

http://www.youtube.com/watch?v=Pzg4XvaBnT4

`Eventually the border is described by the arithmetical "hypostases".`

`The eigth basic person points of view. I guess there will be`

`opportunity to come back on this. The border of the computable is the`

`boundary between the computable and the uncomputable. It is`

`arithmetical truth minus the Sigma_1 complete set(s).`

This is really just a consequence of the impossibility to be awareof the UD delays, or of where "we" are in (Sigma_1)-reality, orcomp-reality. The comp supervenience thesis is hard to explainwithout digging in the details, but consciousness, ourconsciousness, is related to a big infinite cloud of intricatenumber relations. The "identity thesis" is partially justified onlyin a very relative and local way. It is a bit like the appearanceof a collapse in the QM without collapse.I don't find the multiple-worlds interpretation of QM veryconvincing either. In conventional QM it implies that a singleradioactive atom causes a continuous splitting of the world. Isuspect that real numbers should not be taken seriously.

I have never understood the one world interpretation of QM.

`I think that there is no many worlds interpretation of QM. Linearity`

`of evolution and tensor product multiplies or differentiates the "set`

`closed for interaction".`

a(b + c) = ab + ac

`Feynman says that the collapse of the wave is a collective`

`hallucination. And Everett showed that any machine capable of`

`memorizing the result of its observation will describe those`

`hallucinations in their diaries.`

`And I think that once we assume comp then the wave itself appears to`

`be, not really an hallucination, but a sum on all hallucinations, if`

`you want. Technically, this means we have to justify the discourses on`

`the wave itself, by the necessities and possibilities and`

`(arithmetica) truth for the (Lobian) universal machines. Physics has`

`to be invariant for the choice of phi_i bases so that postulate the`

`quantum becomes treachery, with respect of the comp mind body problem.`

`We have to justify the quantum from the stable limit discourse of the`

`universal machine (which observes itself).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.