On 14 Aug 2012, at 07:26, Stephen P. King wrote:

On 8/13/2012 9:19 AM, Bruno Marchal wrote:

On 12 Aug 2012, at 20:05, Stephen P. King wrote:

Hi Roger,

    I will interleave some remarks.

On 8/11/2012 7:37 AM, Roger wrote:
Hi Stephen P. King

As I understand it, Leibniz's pre-established harmony is analogous to
a musical score with God, or at least some super-intelligence, as

Allow me to use the analogy a bit more but carefully to not go too far. This "musical score", does it require work of some kind to be created itself?

This prevents all physical particles from colliding, instead they
all move harmoniously together*. The score was composed before the
Big Bang-- my own explanation is like Mozart God or that intelligence
could hear the whole (symphony) beforehand in his head.

I argue that the Pre-Established Harmony (PEH) requires solving an NP-Complete computational problem that has an infinite number of variables. Additionally, it is not possible to maximize or optimize more than one variable in a multivariate system. Unless we are going to grant God the ability to contradict mathematical facts, which, I argue, is equivalent to granting violations of the basis rules of non-contradiction, then God would have to run an eternal computation prior to the creation of the Universe. This is absurd! How can the existence of something have a beginning if it requires an an infinite problem to be solved first?
    Here is the problem: Computations require resources to run,

That makes sense, but you should define what you mean by resources, as put in this way, people might think you mean "primitively physical resource".

Dear Bruno,

"A bounded Turing machine has been used to model specific computations using the number of state transitions and alphabet size to quantify the computational effort required to solve a particular problem." Let us supposed that the states are physical as defined in your resent post:

"This define already a realm in which all universal number exists, and all their behavior is accessible from that simple theory: it is sigma_1 complete, that is the arithmetical version of Turing-complete. Note that such a theory is very weak, it has no negation, and cannot prove that 0 ≠ 1, for example. Of course, it is consistent and can't prove that 0 = 1 either. yet it emulates a UD through the fact that all the numbers representing proofs can be proved to exist in that theory. Now, in that realm, due to the first person indeterminacy, you are multiplied into infinity. More precisely, your actual relative computational state appears to be proved to exist relatively to basically all universal numbers (and some non universal numbers too), and this infinitely often. So when you decide to do an experience of physics, dropping an apple, for example, the first person indeterminacy dictates that what you will feel to be experienced is given by a statistic on all computations (provably existing in the theory above) defined with respect to all universal numbers. So if comp is correct, and if some physical law is correct (like 'dropped apples fall'), it can only mean that the vast majority of computation going in your actual comp state compute a state of affair where you see the apple falling. If you want, the reason why apple fall is that it happens in the majority of your computational extensions, and this has to be verified in the space of all computations. Everett confirms this very weird self-multiplication (weird with respect to the idea that we are unique and are living in a unique reality). This translated the problem of "why physical laws" into a problem of statistics in computer science, or in number theory."

    And you also wrote:

"...from the first person points of view, it does look like many universal system get relatively more important role. Some can be geographical, like the local chemical situation on earth (a very special universal system), or your parents, but the point is that their stability must be justified by the "winning universal system" emerging from the competition of all universal numbers going through your actual state. The apparent winner seems to be the quantum one, and it has already the shape of a universal system which manage to eliminate abnormal computations by a process of destructive interferences. But to solve the mind body problem we have to justify this destructive interference processes through the solution of the arithmetical or combinatorial measure problem."

Does the measure cover an infinite or finite subset of the universals?

It covers the whole UD* (the entire execution of the UD, contained in a tiny constructive part of arithmetical truth). It is infinite. This follows easily from the first person indeterminacy invariance (cf step seven).

Does the subset have to be representable as a Boolean algebra?

This is ambiguous. I would say "yes" if by subset you mean the initial segment of UD*.

A physical state might be one that maximally exists

... from the local first person points of view, of those dropping the apple and trying to predict what they will feel. But there is no physical state, only physical experience, which are not definable in any third person point of view. A physical state, with comp, is not an object.

in universal numbers, but this does not really answer anything.

Indeed, it is *the* problem, which comp formulate mathematically (even arithmetically).

The body problem is still open.

But a big part is solved.

But the body problem vanishes if we follow Pratt's prescription!

Explain how you derive F= ma in Pratt. I don't see any shadow of this, nor even an awareness that to solve the body problem in that setting. Pratt shows something interesting, not that the body problem has vanished. Or write a paper showing this. None of the ten problem on consciousness exposed in Michael Tye book are even addressed, not to mention the body problem itself.

By making physical events and abstract/mental/immaterial states the Stone dual of each other, neither is primitive in the absolute sense. They both emerge from the underlying primitive []<>.

With wich "[]<>"?

With comp, the universal arithmetical being already got the answer, and answered it.

[]p = Bp & Dt
<>p = Dp V Bf

Bp = the sigma_1 complete arithmetical Beweisbar predicate (Gödel 1931)
Dp = ~B~p

Then we get for the sigma_1 p: []p -> p, p -> []<>p, and all we need to show that p -> []<>p. It is just my incompetence which provides us to know if this gives quantum mechanics or not. But the theory is there. Comp gave no choice in this matter (pun included!).

and if resources are not available then there is no way to claim access to the information that would be in the solution that the computation would generate. WE might try to get around this problem the way that Bruno does by stipulating that the "truth" of the solution gives it existence, but the fact that some mathematical statement or sigma_1 sentence is true (in the prior sense) does not allow it to be considered as accessible for use for other things. For example, we could make valid claims about the content of a meteor that no one has examined but we cannot have any certainty about those claims unless we actually crack open the rock and physically examine its contents. The state of the universe as "moving harmoniously together" was not exactly what the PEH was for Leibniz. It was the synchronization of the simple actions of the Monads. It was a coordination of the percepts that make up the monads such that, for example, my monadic percept of living in a world that you also live in is synchronized with your monadic view of living in a world that I also live in such that we can be said to have this email chat. Remember, Monads (as defined in the Monadology) have no windows and cannot be considered to either "exchange" substances nor are embedded in a common medium that can exchange excitations. The entire "common world of appearances" emerges from and could be said to supervene upon the synchronization of internal (1p subjective) Monadic actions.

I argue that the only way that God could find a solution to the NP-Complete problem is to make the creation of the universe simulataneous with the computations so that the universe itself is the computer that is finding the solution. <snip>

Even some non universal machine can solve NP-complete problem.

Yes, of course. But they cannot solve it in zero computational steps.


Leibniz' PEH, to be consistent with his requirement, would have to do the impossible. I am porposing a way to solve this impossibility.


To be sure I am still not knowing if you have a theory, and what you mean by "solve" in this setting.



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