Hi Stephen,

    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 the metaphor of “dreams shared by a continuum of running machines, and they can define (non constructively) notion of worlds, and proximity of worlds” and agree with it if I weaken the definition of the word “machine” to be something far removed from the concrete idea that most persons have.
Yes. A machine is just a number interpreted by a universal number. A universal number is a number u such that there is an arithmetical relation R with R(u, x, y, z) <-> phi_x(y) = z provable in PA (say).


Is there a commutative diagram for that relation? I can better understand 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 represent 1) a plurality of distinct 1-p (merely postulating a plural 1-p is insufficient reasoning for me.), 2) the evolution of those 1-p.
The plurality comes from the fact that the UD, or the true (and thus provable) Sigma_1 relation generates them all. easy consequence of Church thesis and Mechanism. The evolution comes from the fact that (Sigma_1) arithmetic emulates their (infinitely many) computable evolution.


I have no difficulty whatsoever with the UD per say, I just fail to see how the mere existence of Sigma_1 (or Sigma_n) –> evolution of 1-p. This is a “bridge to far for me” as it tells me nothing of the vertical relations between UD (existing in Platonia) and 1-p (existing at the immediate finite expression of the individual observer (the entity that reports to having 1-p)). This reminds me of Julian Barbor’s attempts to eliminate time from physics by using the H=0 relation of the “universal wavefunction” to “prove” that time does not exist. His thesis fails because there is a little thing called computational complexity that makes his machinery grind to a halt by proving that the computational resources (walls of Platonia are not enough!) will always be less than what is needed to compute the infinite NP-Complete problem which is the generation of the contents of the “time capsules” that his theory requires to replace 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’ Monadology where the “pre-ordained harmony” upon which Leibniz’ Monadology rests its explanation of how all of the internal evolutions of the Monads will be synchronized with each other. OTOH, we can still use the Monadology if we replace the need for a computation of the 3-p “initial conditions necessary” with a plurality of ongoing 1-p type computations within each Monad that act to continuously align pairs of Monads with each other. This is the distinction between 1 computation that must occur prior to the existence of Monads and many computations that co-exist with the monads. I can see that we can reword this idea into a form that is identical to your UD and UDA, but there is still an infinite tower structure that connects each individual 1-p with the ideal 3-p. One thing that proves this to me is that at the limit of the 3-p we find that our structure is identical to a “zero information system”, as any 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
No problem. I agree with term, because I think that numbers are ideas, indeed. relatively to universal numbers, numbers are ideas creating ideas, even analytical ideas.


OK, let me ask the question another way: How can numbers interact with each other without the interface that physicality allows?

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 separable existence 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 lead astray by the mathematization of the idea of causality based on an unrealistic toy model. We can say that X causes Y, if and only if Y occurs only when X is present, but this neglects to mention that X and 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 instantiation of objects that somehow escapes the reality of the plurality of the 1-p. Just as we can prove that there exist an infinite number of equivalent physical Machines that can code the same computer program, there are infinitely many X_i and Y_j where i =/= j, this is the heart of the NP-Complete problem that I mentioned above. I propose 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 the mathematics of special and general relativity (and quantum field theory) tells us is that for any physical object there are an infinite number of 3,1 dimensional coordinate frames that can instantiate an object and the mapping (diffeomorphism) between these was proven to be NP-Complete. Until and unless we can show that Integers are non-commutative then we cannot treat them as if they obey the same kind of statistics as fermions. But there is hope, fermions need bosons to interact with each other and bosons need fermions to be distinct from each other. We can play with Supernumbers, but they are dualistic 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 this because I cannot figure out how your theory explain a common illusion of a physical world necessarily emerges within the dreams of the “running” machines. How do the many dreams have sufficient structure to act to supervene inertia?
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 the machine, even when ideally correct, they are unable to relate the different internal views (p, Bp, Bp & p, Bp & Dp, Bp & Dp & p + their G/G* splitting).


Then it is my failing to understand how to get UDA and AUDA to prove 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 figure out how the Movie Graph idea is not being used a device to amplify a refutation of Comp in the paper.

Maudlin and me gives different proof that mechanism is incompatible with materialism. We show that


equivalently  MAT -> ~MEC, or MEC -> ~MAT.

You can use the movie-graph to refute MEC starting from MAT, or to refute MAT starting from MEC, or to prove that MAT and MEC are logically incompatible, starting from nothing (= classical logic and arithmetic).

OK, but please understand that this proof is just a restatement of 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” problem will remain. Just because Descartes screwed up with his version of "substance dualism” does not necessitate that all forms of dualism suffer the same problem! We can see that the dualism will vanish at some appropriate level into a neutral monism, but the dualism need not self-stultify so long as we have a model of interaction that is not inconsistent at all levels. We can get MEC and MAT to co-exist peacefully if we use Pratt’s idea, but to do so will require us to give up on our hopes for a single theory of everything that can be finitely 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 :)




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