Hi Stephen,

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Thank you for you kind and thoughtful comments. Interleaving... From: Bruno Marchal Sent: Saturday, January 22, 2011 4:05 AM To: everything-list@googlegroups.com Subject: Re: A paper by Bas C. van Fraassen Hello Stephen, On 21 Jan 2011, at 23:15, Stephen Paul King wrote:Dear Bruno,Thank you for writing further on this. I can understand themetaphor of “dreams shared by a continuum of running machines, andthey can define (non constructively) notion of worlds, andproximity of worlds” and agree with it if I weaken the definitionof the word “machine” to be something far removed from the concreteidea that most persons have.[BM]Yes. A machine is just a number interpreted by a universal number. Auniversal number is a number u such that there is an arithmeticalrelation R with R(u, x, y, z) <-> phi_x(y) = z provable in PA (say).[SPK]Is there a commutative diagram for that relation? I can betterunderstand complicated equations expressed in Category Theory terms.

`Gosh. Categories with *partial* functions, as needed for Turing`

`universality, are hard to manage, for me at least. Not sure I can even`

`build the product and coproduct!`

`You might take a look at the dominical categories of Di Paoloa and`

`Heller: see`

`http://www.jstor.org/pss/2274352 (The Journal of Symbolic Logic ©`

`1987 Association for Symbolic Logic)`

`But you might just add difficulties to recursion theory, which is`

`already not so easy. In my opinion.`

**The concern that I continue to have is how do our models represent1) a plurality of distinct 1-p (merely postulating a plural 1-p isinsufficient reasoning for me.), 2) the evolution of those 1-p.[BM]The plurality comes from the fact that the UD, or the true (and thusprovable) Sigma_1 relation generates them all. easy consequence ofChurch thesis and Mechanism.The evolution comes from the fact that (Sigma_1) arithmetic emulatestheir (infinitely many) computable evolution.[SPK]I have no difficulty whatsoever with the UD per say, I just failto see how the mere existence of Sigma_1 (or Sigma_n) –> evolutionof 1-p. This is a “bridge to far for me” as it tells me nothing ofthe vertical relations between UD (existing in Platonia) and 1-p(existing at the immediate finite expression of the individualobserver (the entity that reports to having 1-p)). This reminds meof Julian Barbor’s attempts to eliminate time from physics by usingthe H=0 relation of the “universal wavefunction” to “prove” thattime does not exist. His thesis fails because there is a littlething called computational complexity that makes his machinery grindto a halt by proving that the computational resources (walls ofPlatonia are not enough!) will always be less than what is needed tocompute the infinite NP-Complete problem which is the generation ofthe contents of the “time capsules” that his theory requires toreplace time’s flow”.

`This is unclear. You allude to the general problem of indexical.`

`Remember that my assumption is mechanism. From that you are conscious`

`here and now because some Sigma_1 proposition is true (and thus`

`provable, even by tiny RA (Robinson arithmetic). Now the problem we`

`have to solve is that we have to isolate a measure on the Sigma_1`

`proposition true proposition, actually, on their proofs. They are`

`accessed by the UD an infinity of times, through an infinity of`

`computations. This is handle technically by the logic of Bp & Dp (& p)`

`with p restricted to Sigma_1 proposition. Bp & Dp is definable and`

`third person (the intelligible matter), and the first person`

`"matter" (sensible matter, physical sensations) is handled by Bp & Dp`

`& p, which is not definable by the person. This should give the`

`qualia, including the "qualia of time". Formally, this works, but`

`leads to open problem in logic.`

This problem can be traced even back to Leibniz’ Monadologywhere the “pre-ordained harmony” upon which Leibniz’ Monadologyrests its explanation of how all of the internal evolutions of theMonads will be synchronized with each other. OTOH, we can still usethe Monadology if we replace the need for a computation of the 3-p“initial conditions necessary” with a plurality of ongoing 1-p typecomputations within each Monad that act to continuously align pairsof Monads with each other. This is the distinction between 1computation that must occur prior to the existence of Monads andmany computations that co-exist with the monads.I can see that we can reword this idea into a form that isidentical to your UD and UDA, but there is still an infinite towerstructure that connects each individual 1-p with the ideal 3-p. Onething that proves this to me is that at the limit of the 3-p we findthat our structure is identical to a “zero information system”, asany part of it is isomorphic to any other part and to the whole.There is no “difference that makes a difference” there.I see your theory as a very sophisticated form of idealism[BM]No problem. I agree with term, because I think that numbers areideas, indeed. relatively to universal numbers, numbers are ideascreating ideas, even analytical ideas.[SPK]OK, let me ask the question another way: How can numbersinteract with each other without the interface that physicalityallows?

`Numbers do not interact. But universal numbers simulates, even`

`emulate, everything Turing emulable, including interacting bodies.`

`Physical reality emerges from the gluing of those emulation, as`

`observed by the internal machine. That universal numbers exist is just`

`due to the turing universality of a tiny part of arithmetic. It is`

`long to prove, but is already in Gödel's 1931 paper. You need the`

`fundamental theorem of arithmetic, the remainder chinese lemma,`

`Gödel's beta function, etc.`

Numbers are like bosons in a condensate, they have no separableexistence from each other nor any thing like causal efficacy.

`Cute analogy. But analogy in interdisciplinary fields can be very`

`misleading.`

They merely exist. That they encode relationships is not a surprise,that is the essence of their existence! Perhaps we have been leadastray by the mathematization of the idea of causality based on anunrealistic toy model. We can say that X causes Y, if and only if Yoccurs only when X is present, but this neglects to mention that Xand Y are not unique singletons in the universe of possibilities.

`Each hypostases defines a notion of causality, by B(p->q), with B the`

`modal operator corresponding to the hypostase.`

This Humean model presumes that there is only a single instantiationof objects that somehow escapes the reality of the plurality of the1-p.Just as we can prove that there exist an infinite number ofequivalent physical Machines that can code the same computerprogram, there are infinitely many X_i and Y_j where i =/= j, thisis the heart of the NP-Complete problem that I mentioned above. Ipropose Pratt’s “process dualism” as a way to cut this Gordian knot,but I am only weakly able to explain someone else’s theory. What themathematics of special and general relativity (and quantum fieldtheory) tells us is that for any physical object there are aninfinite number of 3,1 dimensional coordinate frames that caninstantiate an object and the mapping (diffeomorphism) between thesewas proven to be NP-Complete.Until and unless we can show that Integers are non-commutativethen we cannot treat them as if they obey the same kind ofstatistics as fermions. But there is hope, fermions need bosons tointeract with each other and bosons need fermions to be distinctfrom each other. We can play with Supernumbers, but they aredualistic and do not have a natural Monotonicity!!!!**

You substantialise the numbers too much.

`Remember that I am using numbers because they are taught in high`

`school. I would talk to computer scientist, I would use the S and K`

`combinators. The point is that with comp the laws of physics are`

`invariant for the change of the basic "ontology". Any first order`

`specification of a universal system will do. Numbers are quite cute`

`for doing that, but they are not intrinsically important at the start.`

that still suffers from the problem of epiphenomena. I say thisbecause I cannot figure out how your theory explain a commonillusion of a physical world necessarily emerges within the dreamsof the “running” machines. How do the many dreams have sufficientstructure to act to supervene inertia?[BM] They have too. That is the point of the UDA. They can. That is the point of AUDA.The fact is that the number relations are highly non trivial,especially when you realize that from the point of view of themachine, even when ideally correct, they are unable to relate thedifferent internal views (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p +their G/G* splitting).[SPK]Then it is my failing to understand how to get UDA and AUDA toprove P=NP, for that is what you are in essence proposing!

`I have no clue what P=NP has to do with all this. Machine's theology`

`need the whole arithmetical hierarchy and beyond.`

`Also. Matter is not an epiphenomenon. Matter just don't exist. Think`

`of arithmetic as a video game, or Matrix. Except that we are`

`distributed in it, in a very complex way.`

I show ~MEC v ~MAT.

`But the form MEC -> ~MAT is constructive. It explains why matter is`

`phenomenologically observed by persons.`

`Only with MAT consciousness becomes epiphenomenal. This usually ends`

`up with the elimination of the person. Brrr...`

**I have been re-reading the Mauldin paper and trying to figureout how the Movie Graph idea is not being used a device to amplifya refutation of Comp in the paper.[BM]Maudlin and me gives different proof that mechanism is incompatiblewith materialism. We show that~MEC v ~MAT equivalently MAT -> ~MEC, or MEC -> ~MAT.You can use the movie-graph to refute MEC starting from MAT, or torefute MAT starting from MEC, or to prove that MAT and MEC arelogically incompatible, starting from nothing (= classical logic andarithmetic).[SPK]OK, but please understand that this proof is just a restatementof the epiphenomena problem that any monism will have.

`Only material monism has that problem, because materialist postulate a`

`primary-material world causally closed, so that consciousness is an`

`epiphenomena.`

`But immaterial monism has no epiphenomena. Primary matter really don't`

`exist att all (unlike consciousness before the materialist becomes`

`eliminativist!), only numbers (or combinators, fortran programs,`

`choose your favorite basic universal ontology) and their "execution"`

`relative to universal numbers). Consciousness is then related to the`

`natural belief in a reality which grows when universal numbers looks`

`inward and get Löbian. It is a sort of "Dt?", with the "?" being`

`unconscious or instinctive. And this gives a fundamental role of`

`consciousness: the relative speeding universal execution. Useful for`

`"self-moving" entities and persons. It makes consciousness playing a`

`fundamental role, even in the origin of the physical role, and this`

`without any kind of magic.`

`There is still matter, but matter is not substancial. It is a`

`persistent observable, explained by a precise phenomenology. That`

`phenomenology explains the first person plural sharable quanta and the`

`first person non sharable qualia.`

`I am not saying that this is true, only that this follows from the`

`assumption that "I" am Turing emulable and the use of the classical`

`theory of knowledge.`

Unless we have some form of duality at some level the “hard” problemwill remain. Just because Descartes screwed up with his version of"substance dualism” does not necessitate that all forms of dualismsuffer the same problem! We can see that the dualism will vanish atsome appropriate level into a neutral monism, but the dualism neednot self-stultify so long as we have a model of interaction that isnot inconsistent at all levels. We can get MEC and MAT to co-existpeacefully if we use Pratt’s idea, but to do so will require us togive up on our hopes for a single theory of everything that can befinitely encoded on a T-shirt that beautiful Olympia can model for us.

`By changing the definition, we can attribute new meaning to terms. If`

`by matter you mean the taste of coffee, the smoothness of velvet, the`

`perfume of flowers, ... There is no worry. That abounds, from the`

`point of view of relative numbers, in Platonia, including typhoons and`

`taxes (alas). If by matter you mean any reification of particular`

`universal numbers (like in Digital physics approach) then that does`

`not exist, if my reasoning is correct, in the MEC frame. If you mean`

`by matter any sort of primitive substance, then that exists even less`

`(if I can say).`

`With comp there is a rather precise theory of mind (computer science/`

`number theory), and any universal machine/number can find it by`

`itself. The mind body problem is then reduced to the body problem`

`(UDA). And bodies appears as sum on all the computations going through`

`the mind states. If we impose the negation of solipism, this entails`

`we share computations and thus are multiplied collectively. This is`

`testable, and this gives an Everett-like sort of physics. In that`

`sense, Everett's formulation of QM confirms COMP + ~solipsisme. To`

`extract the first person plural from comp is more difficult, but seems`

`very reasonable, from the S4Grz1, X1* and Z1* logics. But such an`

`extraction has nothing to do with the fact that IF we are machine, we`

`*have to* do it to get the correct theory of both qualia and quanta.`

`I have discovered that in some people attributes me a proof of MEC ->`

`PHYSICS, when I have only proved the much more modest MEC ->`

`B(physics) where B = the modal necessity box, here. People confuse p -`

`> q with p -> Bq. It is radical (coming back to Plato's idealism),`

`but modest: we are just at the beginning. I only provide jobs for an`

`infinity of future mathematicians :)`

Best, 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-list@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.