On 22 Nov 2012, at 18:38, Stephen P. King wrote:

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How exactly does the comparison occur?By comparing the logic of the observable inferred from observation(the quantum logic based on the algebra of the observable/linearpositive operators) and the logic obtained from the arithmeticalquantization, which exists already.How does the comparison occur? I will not ask what or who isinvolved, only how. What means exists to compare and contrast a pairof logics?

`The logic exists, because, by UDA, when translated in arithmetic,`

`makes a relative physical certainty into a true Sigma_1 sentence,`

`which has to be provable, and consistent. So the observability with`

`measure one is given by []p = Bp & Dt & p, with p arithmetical sigma_1`

`(this is coherent with the way the physical reality has to be`

`redefined through UDA). Then the quantum logic is given by the`

`quantization []<>p, thanks to the law p -> []<>p, and this makes`

`possible to reverse the Goldblatt modal translation of quantum logic`

`into arithmetic.`

`Comparison is used in the everyday sense. Just look if we get the`

`quantum propositions, new one, different one, etc.`

Comp seems to necessitate all possible physical worlds in anequiprobable way.?Does not comp require all possible 1p to exist?

`Comp makes all possible 1p existing in arithmetic, from the possible`

`arithmetical pov.`

There is a deep problem with notions of priors as it seems that wecannot escape from the problem of subjectivity as we see in the(so-called) anthropic principle: each observer will necessarilyfind itself in a world what has laws compatible with itsexistence. It seems to me that the observational act itself is abreaking of the perfect symmetry of equiprobability of possibleworlds.?But this claim implies violence to the idea of a 3p.I found at http://higgo.com/qti/Mallah.htm an exchange betweenMallah and Standish that seems to illustrate this problem:"Russell Standish: The predictions can easily depend of the'picture' but must be consistent with each other. Let me give asimple example: In one picture, observer A decides to measure thespin of an electron in the x direction. In the other, observer Bdecides to measure the spin of the electron in the y direction.Observer A will see the spin of the electron aligned with x axis,and Observer B will see it aligned with the y axis. Bothobservations are correct in the first person picture of thatobserver. A "person" with the third person perspective, seesobservers A and B as inhabiting separate `worlds' of a multiverse,each with appropriate measure that can be computed from QuantumMechanics.Jacques Mallah: On the contrary, this is a textbook example of theway I said it works. The theory predicts some measure distributionof observers; an individual observer sees an observation drawnfrom that distribution. There are no different sets of predictionsfor different pictures, just the measure distribution and thesample from it.Russell Standish: It sounds to me like you don't think theprediction changes according to what the observer chooses toobserve? An electron cannot have its spin aligned with the x axisand the y axis at the same time. Once the experimenter has chosenwhich direction to measure the spin, the history of thatparticular is observer is constrained by that fact, and thepredictions of QM altered accordingly. This is true both in MWIand the Copenhagen interpretation, and is the "spooky" nature ofQM. I used to think that QM gave predictions in terms ofdistributions, and that because one didn't see isolated particles,rather ensembles of such particles, I didn't see a problem. Theproperties of an ensemble are well defined. However, the abilityof experimenters to isolate a single particle, such as a photon,or an atom, means we have to take this "spookiness" seriously."The idea of a 3p cannot be applied consistently to the notionof a 'person' or observer if one is considering the 1p ofobservers in separate 'worlds' of a multiverse unless, forexample, A and B have observables that mutually commute and thushave some chance of being mutually consistent and capable of beingintegrated into a single narrative. I think that this problem isbeing overlooked because the problem of Satisfiability is beingignored.?I hope that we can agree that there is at least an illusion of aphysical world that 'we' - you, me, Russell, .... canconsider... Is it necessarily inconsistent with comp?? ? ?Not at all. The whole point of UDA is in explaining why thephysical reality is unavoidable for the dreaming numbers, and howit emerges from + and * (in the "number base"). It is indeed afirst person plural product, with the persons being all Löbianmachines, etc.I am coming at the idea of a 'physical reality' as an emergentstructure and not some pre-defined ordering.Good.Comp gives the complete algorithm to extract bodies and physicallaws, making comp testable, even if that is technically difficult,I claim that it is not even technically difficult; it isimpossible for the simple reason that there does not exista unique Boolean algebra for all possible 1p.? (I agree such BA does not exist, but this is exactly what we needto find a measure theorem à-la Gleason). We need a sufficientlygood quantum logic, and up to now the comp quantum logic fitsrather well.Gleason's theorem is interesting: http://en.wikipedia.org/wiki/Gleason%27s_theorem"For a Hilbert space of dimension 3 or greater, the only possiblemeasure of the probability of the state associated with a particularlinear subspace a of the Hilbert space will have the form Tr(μ(a)W), the trace of the operator product of the projection operatorμ(a) and the density matrix W for the system."We sidestep the problem of how we define the transition frompure states to density matrices. Andrew's discussion might be seenas addressing this...

OK.

Why? Because it cannot be proven to be satisfiable(aka globallyself-consistent) by any finite sequence of algorithms.Completeness and consistency for such cannot be assumed a priori.?Do you ever address the question of satisfiability?

`Which satisfiability? I use it all the time. p->p is satisfiable by`

`all interpretation, and this is used all the time. I do not use the`

`complexity of satisfiability, as if this needed to be used, it has to`

`be justified by the modal logic extracted from self-reference.`

but up to now, it fits remarkably, and that would not have beenthe case without QM. That would not have the case if "p->[]<>p"was not a theorem of the Z1* logics (matter).Your reasoning is correct only because you are assuming theimpossible to be true a priori: that there exists a solution tothe Satisfiability problemIt exists. "Satisfability" is non tractable, not insoluble. Thefirst persons don't care "waiting exponential time" by theinvariance of first person experience on delays.Of course, but an infinite BA requires eternity (infinitely manysteps) to solve its satisfiability problem.

`But no machine ever need to do that (and can't). The BA might be`

`infinite, but not the proposition, unless you are using infinitary`

`logic, which does not play a big role in comp up to now.`

I am not claiming non-solubility; I am pointing out that thecomputation of satisfiability must run to obtain a solution,

The 1p depends on truth, not on proof.

otherwise it is false to claim that the solution is accessible.

`The UD does "prove", or arithemtic proves, all the true sigma_1`

`sentences, which is enough for the computations to be emulated. then`

`the 1p are distirubuted non constructively on that, independently of`

`the complexity of the proofs. Without this, no measure problem.`

`And with no measure problem, you lost the reduction of physics to`

`computer science.`

It is a profound mistake to claim that the existence of the largestprime number defines the exact sequence of numerals that wouldenumerate that prime number.

`You need to decide in which base you write it, and then it is defined.`

`But we don't need this.`

Similarly, the mere possibility of satisfiability of a BA

Satisfiability concerns sentences, not BA.

cannot be used to argue about the particular distribution ofpropositions of the BA.You are considering first persons in the eternal and ideal case,but that does not connect omniscient machines to finite human brains.

The connection is explained by the UDA.

This is the challenge to Plato and Parmenides, how do we bridgebetween the Realm of Truth and the world of appearances?

`By the realtion between machines' belief and reality. With comp,`

`today, we can use the work of Tarski and others.`

We could make claims forever but showing a proof requires physicaleffort.

`And time, money, if not a sense of public relation. But that is`

`relevant at some meta-meta-level.`

There are no shortcuts to knowledge. You seem to be OK with the ideathat knowledge can obtain 'for free'.

`Free of physics, yes. Free of math? No. You need to postulate enough`

`to get Turing universality.`

Perhaps I am mistaken, but it seems that you are assuming theimpossible to be real.

`I don't. Unless you come back with the idea that 1+1=2 requires a`

`physical world, or thing like that.`

*and* that it is accessible for any finitely expressible logicalstructure.It is accessible, but then I don't see at all the relevance of this.Please explain how it is accessible.

You were using the term. I am the one asking the question here. 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.