On 7/13/2012 9:04 AM, Bruno Marchal wrote:

On 13 Jul 2012, at 11:55, Stephen P. King wrote:
How exactly does one make a connection between a given set of resources and an arbitrary computation in your scheme?

From the measure on all computations, which must exist to satisfy comp, as the UDA explains with all details, and as the translation of UDA in arithmetic (AUDA) makes precise. We still don't have the measure, but AUDA extracts the logic of measure one (accepting some standard definitions). And that measure one verifies what is needed to get a linear logic à-la Abramski-Girard which makes a notion of resource quite plausible. Anyway, we have no choice. If the measure does not exist, comp is false (to be short).

Dear Bruno,

Why do you seem to insist on a global ("on all computations") measure? I think that this requirement is too strong and is the cause of many problems. What is wrong with a "on some computations within some bound" measure? It seems to me that if you would consider the Boolean SAT problem you would see this... I still do not understand why you are so resistant to considering the complexity issue. Was not Aaronson's paper sufficient motivation? A possible solution is a "local" measure (as opposed to global measures), but this idea disallows for any kind of global regime or Pre-Hstablished Harmony. (Is this why you are so dogmatic?) It allow also for the possibility of pathological cases, such as omega-inconsistent logical algebras, so long as the contradictions do not occur within some finite bound. In other words, it may be possible to achieve the goal of the ultrafinitists without the absolute tyranny that they would impose on the totality of what exists,. but at the small price of not allowing abstract entities to be completely separate ontologically from the physical systems that can possibly implement them. Please notice that I am only requiring the connection to occur within the "possibility" and not any arbitrary actual physical system! I distinguish "actual" from "possible".



I am not sure what you mean by "explanation" as you are using the word. Again, AFAIK abstractions cannot refer to specific physical objects

It is better, when working on the mind-body problem, to not take the notion of physical object as granted, except for assuming that the physical laws have to be rich enough to support brain and computer execution, that is, to be at least Turing universal.

This is a bit hypocritical since it is an incarnated number(up to isomorphism) that is writing this email! (per your result!) How can one ignore the necessity of a (relatively) persistent medium to communicate? You are still falling into the solipsism trap! Maybe you are trying to claim some kind of excuse via "semantic externality"! But that argument is self-stultifying also... Words cannot exist as mere free-floating entities.



unless we consider an isomorphism of sorts between physical objects

After UDA, and the usual weak Occam rule, we *know* (modulo comp) that physical "objects" are collective hallucination by numbers.

You must show why some particular class of numbers (or equivalent) is the class of primitive entities capable of having "hallucinations" (or "dreams"). The fact that they can possibly have hallucinations or dreams must be accounted for! That they are "collective" is an additional matter. You are glossing over very difficult problems!


You have more than once acknowledge that the physical reality is not primitive (= cannot be assumed), so I am not sure to see why you come back with it to challenge the comp consequences.

You are not understanding the definition that I have made here. It is not a "matter is primitive claim", it is a limit on the way you are defining computational universality. You say that computations are totally independent of physical systems, therefore computations have the same properties and actions if we eliminate the physical systems altogether. Is this correct?

My claim is that universality entails that any universal computation is not restricted to a particular physical system, but there must be at least one physical system that can implement it. I am putting computations (the abstract bit strings) at the same ontological level as the physical systems. Neither is taken as primitive. Only the neutral ground of necessary possibility is primitive. To rephrase this in more philosophical terms: neither minds nor bodies can be ontologically primitive. They co-emerge from the undifferentiated Being-in-itself simultaneously and equally. This is just a restatement of the duality that I am advocating.

I previously wrote: "[there exists a] isomorphism of sorts between physical objects and "best possible computational simulations thereof" ". This is the link between mind and body that Descartes was unable to define in his substance dualism. Descartes' dualism failed because it could not see process; it saw minds and bodies strictly as "things" that somehow had to interact on each other and thus it was the substance assumption is what blew up Rene's beautiful project.



and "best possible computational simulations thereof" as I am suggesting, but you seem to not consider this idea at all.

Because such an idea has been shown to be inconsistent with comp (UDA).

No! It most certainly has not. You are taking liberties with definitions, particularly in the MGA and strobe argument, to make claims that are simply wrong. You cannot communicate nor even refer to any kind of "action" if there is no means to by-pass the Identity of indiscernibles <http://en.wikipedia.org/wiki/Identity_of_indiscernibles>. It is not permissible to assume multiple or plural cases of identical entities unless there is some means that allows for an "external" differentiation between them. For example, we can have multiple electrons in physics because there is a possible variation in their possible location relative to each other in some "space". If there is no space (up to isomorphism) assumed to exist at the same level as numbers, how can there exist multiple versions of the same numbers? How is the notion of a plurality of possible versions of the same number represented in your primitive arithmetic? (+, *, N) does not have enough room unless you are appending additional structure to it and if you are going to do this then you must withdraw the claim of primitivity of numbers (or equivalents) because all of the structure must be at the same level if only for the sake of access.



Your statement "just study the proof and criticize it" begs the question that I am asking!


It does not. UDA *is* the explanation why if the brain (or the generalized brain) works like a digital universal machine, (even a physical one, like a concrete computer) then the laws of physics HAVE TO emerge from the laws of the natural numbers (addition and multiplication) law.

NO! You cannot rest all of the necessity of the physical world on just one brain and its actions. You are completely neglecting the important and none negligible role of interactions between many physical systems.


You might study any textbook in mathematical logic to see that a computation is a purely arithmetical notion (accepting the Church-Turing thesis). I am currently explaining this in FOAR, so you can ask a precise question for anything you would have some problem with in that list (that you already follow). I can no more explain this here, as I have done this more than once before.

I am studying the materials that I can access. The problem is that I have questions that the authors do not consider. The exceptions are those authors, like Vaughan Pratt and David Deutsch, that you are discounting. Therefore I have to address you directly.


Bruno


--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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