On 10/7/2012 4:26 AM, Bruno Marchal wrote:

On 06 Oct 2012, at 21:27, Stephen P. King wrote:

On 10/6/2012 2:51 PM, Bruno Marchal wrote:

On 06 Oct 2012, at 17:40, Stephen P. King wrote:

On 10/6/2012 4:25 AM, Bruno Marchal wrote:

On 06 Oct 2012, at 09:35, Stephen P. King wrote:

Hi Bruno,

  You wrote:
As the cow-boy guessed right this is assuming too much, both for the formalism used (which is OK), and the ontology, so it uses implicitly non-comp hypothesis, which is less OK, as comp is also assumed implicitly. IT is not uninteresting for possible progress, but it is unaware that matter as to be explained by statistics on computations "seen from inside". The role of "Russell operator" is played by the Kleene second recursion theorem, which encapsulates the "non foundation" well enough.

I disagree. His operators are "looking from the outside" at A (the physical universe).

What do you mean here by "physical universe"?

What do you think it means? The common subject of observation by a collection of observers.

What are observers? Where do they come from?
Hi Bruno,

It depends on what feature you wish to find an explanatory model of. My point is that "what is an observer" depends on the features that one wishes to explain.

The context is the search of a TOE, which does not avoid the problem of explaining consciousness and matter, and the relation between, or put in another way the relation between first person views and third person views. You mentioned the "physical universe", but this is something that we cannot take for granted in such a context. You defined it by using the notion of observer, that's OK ... if you define the notion of observer without mentioning "physical universe" (or if you do it, you have to solve the recursion, with the second recursion theorem, or, if you want, with Set Theory + non foundation, à la Barwise, but this must be eliminable in comp, or put in the machine's epistemology).

In my thinking, a physical world = a reality = that which is incontrovertible (free of contradictions = Boolean Satisfiable) for some finite collection of observers, where observers are defined as "bundles of computations". Physical worlds are not actual in the absence of observers. I also stipulate that there are an infinite (uncountable) number of physical worlds. This demands that there exists an uncountable infinity of observers <=> an infinite number of bundles of computations. Please recall how I define "exist"; it is *necessary possibility*.

You like the modal logical explanatory model,

This is not correct. I just model "belief" by the "instantional" manner, à-la Dennet.

    One day I might be able to recall your terminology exactly. ;-)

A machine believes p if the machine assert p, which makes sense as I limit myself to machine talking first order language, ideally arithmetically sound, and being able to believe the logical consequences of its beliefs in arithmetic. Then modal logic just happens to describe completely, at the propositional level, the logic of provability of such machine, thanks to the work of Gödel, Löb and Solovay (and others). I have never choose to use modal logic, I use only machine self-reference, where a very special modality imposes itself (G).

    Sure, you use that is necessitated by non-contradiction principle. ;-)

so there we might think of observers as bundles of computations.

OK. That's nice, but what is a computation?

A computation is *_/*any transformation of information*/_*. Information = any difference between two that makes a difference to a third. It is interesting that this definition demand that there exists at least three entities or processes or whatever for information and thus computation to exist. I have not considered the further consequences of this idea so far. It might be completely fallacious.

Your preceding post were using a notion of physical computation, which would not cut the regress.

I disagree. I am arguing that only if we retain a connection between computation as a platonic abstraction and the requirement of physical resources we will have a viable cut off for the regress. A computer that can only process a finite number of recursions or iterations of self-modeling will not have an infinite regress for obvious reasons. What I am trying to do to make this a more formal statement is to tie together the Kolmogorov complexity of a description a system <http://en.wikipedia.org/wiki/Kolmogorov_complexity>, abstract or physical, with the physical degrees of freedom of a physical system (for example the dimensions of its Hilbert space or Hamiltonian). In this way we have a way to define a physical system as a bounded bundle of computations. This would be a lower bound on the necessary physical resources required to implement an arbitrary computations. Following this idea we can see that it implies that physical systems that require infinite computations to be exactly simulated only can exist is very special circumstances!

But as I answered you can take the original definition of computation (by Post, Turing & Co.), in which case you can assume only arithmetic, and the regression is cut, by defining the "bundle of computations" with the first person indeterminacy. Then you are back to sane04, and you describe the comp theory.

    This is where I agree with comp. I only disagree with your step 8:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf <http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf>

"what if we don't grant a concrete robust physical universe? Up to this stage, we can still escape the conclusion of the seven preceding reasoning steps, by postulating that a ''physical universe'' really ''exists'' and is too little in the sense of not being able to generate the entire UD*, nor any reasonable portions of it, so that our usual physical predictions would be safe from any interference with its UD-generated ''little'' computational

Here you seem to only consider a "physical universe" to be an entity that "exists" with no observers associated with it and reason that such is an irrelevant concept that can and should be dismissed from consideration. I am OK with that! I define a "physical universe" differently! (see above) I am only asking for a weaker version of a "physical universe" to exist; one that is not ontologically primitive, but to demand this is to also demand that arithmetics and numbers are not ontologically primitive as well. Both abstractions, such as numbers and their truths, and physical worlds must emerge together from a primitive ground which is neutral in that it has no innate properties at all other that necessary possibility. It merely exists.

from your paper:

"It will follow that a much weaker and usual form of Ockham's razor can be used to conclude that not only physics has been epistemologically reduced to machine psychology, but that ''matter'' has been ontologically reduced to ''mind'' where mind is defined as the object study of fundamental
machine psychology."

But "physics" =/= "physical world". Here is where we diverge in our agreement! Physics is behavior not "being". Matter =/= "physical world". Matter is the spatial aspect of sets, once we remove all of the contingencies of physics explanations. You are claiming to "reduce" matter (Aristotelian "substance") to "mind" (that which fundamental machine psychology presupposes) and thus eliminate "matter". But this seems to be possible only if fundamental machine psychology allows the existence of a single machine and thus a singular mind. I have tried to point out that this is exactly consistent with Tennenbaum's Theorem <http://web.mat.bham.ac.uk/R.W.Kaye/papers/tennenbaum/tennrosser> and tried to argue that this is a huge problem as it makes comp (or UDA) into a description of the psychology of a consistent solipsistic machine. One possibility requires that we "relativize" countable models of PA using the non-standand arithmetics but in a way that perpetually "hides" the non-standard component, the constant, of the model from the machine itself. The inability for a computable model of consciousness to "know" which computations "it is", is an expression of this property, IMHO.

It might be helpful for you to examine the Zuckerman and Miranker paper <http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf> and discuss it with the members of the list. I will defend it against your critique, as I see the paper as a nice representation of part of the dual aspect monism (or "process dualism") idea that I have been advocating.

That's a technical implementation, which assumes too much from the point of view of foundational studies. It is OK, and rather cliché in my opinion, and is the kind of thing I let the Löbian machine too choose. It is not really relevant, given the results in the comp theory, as the regression cut are based, through comp, to the Kleene second recursion theorem (the double intensional diagonalization, or Dx = "xx").

Are you interested in solving the arithmetic body problem or not? I am interested in solutions! BTW, the regression cut that you are implementing is not flexible. My work requires a flexible regression cut to deal the"Heisenberg cut" problem of QM <http://www.phys.tue.nl/ktn/Wim/qm1.htm#Heis_cut> so we can consider observers in non-statistical ways (in contrast with the way that decoherence arguments treat observers). My proposal is to add some fine detail to Zuckerman''s model, specifically to the definition of "observation" in his model, in a way that is consistent with Pratt's model. Pratt's model has some open problems of its own, but these are solved by the requirement of physical resources for the bound on bundles of computations (aka observers). But this latter idea demands a weaker version of computational universality... We fight over that!

I am just trying to understand if your theory contradicts anything in what has already been done in comp, or if it contradict or is in opposition as you seem to believe or assert from time to time. Paper like Pratt, and now Zuckerman are just unaware of the comp reversal between physics and arithmetic, and completely ignore the mind body problem.

Why do Pratt and Zuckerman need to be aware of the comp reversal? Could it be that you are merely complaining that they are ignoring your work?

They use the term consciousness without motivating its use, or making clear what axioms they take for consciousness, and seems to build on the usual Aristotelian paradigm. They are simply unaware of the first person indeterminacy and its consequences. They are not alone, of course.

"...without motivating its use"? What is a more basic question that human ask than "what is the nature of my existence?"? Why complain that they are not stating the obvious?

You seem to accept the first person indeterminacy, and the seven first steps of UDA, so an interesting work would be to adapt their work (of Pratt, Zuckerman) to the comp reality, but this does not necessitate to change the limited arithmetical ontology, as set theory, with or without foundation, belongs to the number's many possible epistemologies. If not, it means they are implicitly assuming a non-comp theory, as it is necessitated by the Aristotelian frame.

Let us see that first and not prejudge the possibilities. Most people have never questioned the Aristotelian framework as you have; I appreciate that fact, but we can be OK with that fact. It need not stop our work.

What Zucker did is a modeling of some aspect of self-reference, partially coherent locally with comp.

I argue that local coherence is all that is necessary for the requirements of deriving physics!! In other words, local solutions of the arithmetic body problem are sufficient. We do not need a global solution. In fact, I argue that a global solution is impossible as such would contradict the finding of the Wheeler-DeWitt equation <http://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation>! What I am arguing for (within physics) is consistent with papers by Peres <http://arxiv.org/abs/gr-qc/9704061>, Kitada <http://arxiv.org/abs/gr-qc/0110066> and Dugic <http://arxiv.org/abs/quant-ph/9810029>.

He seems to ignore the arithmetical self-reference which has to be used when postulating comp. But what is more annoying is that they use implicitly a physical supervenience thesis, or are just unclear on this, and so some correction and adaptation needs to be added.

    Maybe Zuckerman is unfamiliar with Lob's work?

Such adaptation is very technical, and I hope you are not using this to escape the question I am asking you, due to your negative unclear remark on the step 8.

    I am trying to be precise, but I have constraints on my abilities. ;-)

That would be the case if you think that Zucker work contradicts the arithmetical or Turing universal restricted ontology, which is shown necessary and sufficient for the derivation of both consciousness and the matter collective hallucination brought by comp.

But you cannot ignore the open "arithmetical body" problem! We all have "motes" in our eyes!

By the way, are you sure that Pratt's approach work in set theories with non-foundation?

Yes. I confirmed this in conversations with Peter Wegner. It was he that pointed me to the work of Jon Barwise in 1998.

That does not seem entirely obvious to me, and should be justified. In this case you can point on some references if this has been already studied. It is not obvious because in the set/boolean algebra duality, the duality is working, as Boolean algebra are well founded structures.

One thing that I need to point out is that non-foundation theory works with normal sets. As you might see in the Youtube video of Zuckerman <http://www.youtube.com/watch?v=WJrhBVTs83o>, the Aczel Universe <http://www.blutner.de/AFA/liar3.pdf> is an extension of the ZF universe.



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