On 7/14/2012 4:25 AM, Bruno Marchal wrote:

On 13 Jul 2012, at 21:59, Stephen P. King wrote:

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?

This is a consequence of the invariance of consciousness (for delays, virtual/real shifts, ...). I do not decide this.

Hi Bruno,

Might you see that this is problematic? Because you are using a particular infinite domain and codomain (N -> NxN) as primitives and these are ordered, you are stuck. This is one of the many weaknesses of Plato's program. I admit that the general idea is brilliant and valuable, it is far to limited and thus constraining on what can be accomplished.

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?

UD* does not bound the measure, and so such requirements can't be applied.

I know this! It is for this reason that I make my claim that your result is for solipsistic systems only. One cannot hope to define an explanation of interaction with this method. As Peter Wegner et al point out here <http://www.cs.brown.edu/people/pw/papers/bcj1.pdf>, it is defined a priori to only be one thing. Interactions, to be modeled well, cannot be constrained a priori in this way.

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?)

This is just an insult in disguise. Please Stephen , just do the math.

I did not intend it as an insult, but that possibility of interpretation is present. Why are you taking that option? You are avoiding my point. Why do you dismiss the SAT issue?

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".

In which theory? This cannot work if "we are machine", by the invariance result.

    Right, and that is the problem that I see.

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!)

Not at all. "I", the first person one, is not a number, and cannot be associated to any number.

Is it independent of all the numbers? Can it be severed? No! I am arguing the same thing for computations. Severing computations from physical implementation is a mistake. You are going to far. I think that it is like the difference between going to the limit of a function and jumping the gap to the "at infinity" itself.

How can one ignore the necessity of a (relatively) persistent medium to communicate? You are still falling into the solipsism trap!

You make a lot of statement without any justification, and ignoring all previous patient explanations.

Turing Machines operate by a priori definitions, thus they cannot make good models of interaction. I am just using Peter Wegner's claims and proofs. See http://www.cs.brown.edu/people/pw/strong-cct.pdf

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.

It seems you come back with primitive (assumed) matter. I have no clue what that could be, and it cannot work by UDA.

No, I am arguing against primitives entities altogether. I am claiming that neither matter nor numbers can be truly primitive, both have to emerge from a common neutral ground. It is the common neutral ground tht is primitive, not matter nor numbers. Bertrand Russell already has worked this out in his considerations of neutral monism, you are simply refusing to consider this possibility.

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").

That is a consequence of arithmetical realism without which Church thesis and the notion of digital machine cannot be defined.

The fact that they can possibly have hallucinations or dreams must be accounted for!

It is a theorem of arithmetic. All finite pieces of computations exist in arithmetic, the first persons cannot not glue them, by what is explained in the first six step of UDA.

That they are "collective" is an additional matter. You are glossing over very difficult problems!

I formulate them in a way we can test precise answer.

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.

Here you seem to ignore theoretical computer science.

Theory does not exist independent of minds with the capacity to discover it. You cannot sever the continuity of the connection between the two and imagine that they can still connect together. Platonism only works when its weak dualism is undisturbed. Minds that are completely severed from the means of interfacing with each other lose their ability to know anything other than themselves.

You say that computations are totally independent of physical systems,

In the same sense that the content of "17 is prime" is independent of physics. You have fail to explain the dependence that you suggest.

Independence of a particular physical system is not the same as independence of physicality. I am arguing for the former and you for the latter.

therefore computations have the same properties and actions if we eliminate the physical systems altogether. Is this correct?

The "therefore" is too quick. the independence is a consequence of strong Occam + step seven, or weak occam + step 8.

    Step 8 is a monstrosity.

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.

That is Putnam functionalism, and is part of comp. What I say go well beyond that.

    Yes, and I am trying to get you to see that this is a mistake.

To make your claim valid you have to tell me what is not valid in UDA.

You ignore the fact that UDA is required to be communicated and the means of its communication. It is a castle floating in mid air, after its scaffolding has been pulled away. It floats for a moment and then crashes down to the ground.

I am putting computations (the abstract bit strings)

Computations are not bit strings. You confuse a computation with a description of computation.

at the same ontological level as the physical systems. Neither is taken as primitive.

So what is your theory? Don't tell me "existence", for that means nothing at all.

Only the neutral ground of necessary possibility is primitive.

"necessary" and "possibility" are high level notion, and we don't even have a clue to what you apply it.

    You don't, that is obvious.

To rephrase this in more philosophical terms: neither minds nor bodies can be ontologically primitive.

Like in comp. But numbers (or combinators, ...) can be.

No, because they have particular properties they cannot be taken as neutral. Neutrality here admits no particularity of property. At best one can use "all possible properties" or a bare "hanger" like substance that we can hang properties upon. This is already well known in philosophy. This article cover this in great detail: http://plato.stanford.edu/entries/substance/ You might do well to read all of it.

They co-emerge from the undifferentiated Being-in-itself simultaneously and equally.

That is the kind of jargon which gives philosophy its bad reputation. You can't use this to invalidate proof.

    Rubbish; it is susceptible to disproof by reduction!

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" ".

That does not make sense. Sorry.

This is discussed in Stephen Wolfram's article: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html

"...many physical systems are computationally irreducible, so that their own evolution is effectively the most efficient procedure for determining their future."

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.

I partially disagree, but that is another debate.

    I would very much like to have that debate.

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.

You contradict again yourself.

Where? Are you back to claiming that I am assuming "primitive matter"? Please, that is stale and already refuted. You simply fail to want to understand. I have no need to argue what others have already argued better. It was, among others, Bertrand Russell himself that argued this case for neutral monism. I can do no better. My problem is that I cannot cut and paste his text to this media.

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?

Category confusion. Numbers are not located in any space.

Correct, and thus there is no possibility of multiplicity of a number. There is only one number of each kind. Godel's diagonalization is a form of "semantic externalization" if you stick to your argument, therefore your step 8 collapses. This is also explained as the problems that the "skeptical hypothesis" has: http://en.wikipedia.org/wiki/Skeptical_hypothesis#Skeptical_hypotheses

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.

Space and location emerge from arithmetical relations.

Emerge into what? There is no "there" there! There is no a priori possibility of anything external to the arithmetic relations, there is literally no room to put the copies therefore you cannot make copies or claim properties that only exist in functions on copies.

You reject the arithmetical realism, which makes you coherent, but non computationalist.

Non-computationalist only because I claim that computations are not just those that exist on N -> NxN.

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.

I have answered this many times, and you did not make any specific critics.

    Please cite one.

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.

But then do it. What i say has been explained consistent with what Pratt says. Not Deutsch, who indeed, reify the physical reality, and makes it primary, as he want keep physicalism intact. He just contradict elementary computer science, and makes a sort of revisionism of the Church Turing idea.

You fail to address Deutsch's criticisms directly; they are laid out explicitly in his new book. I have a copy ( of Beginning of Infinity) siding on my desk next to me now and have read the passages regarding this issue many times, Deutsch is not making the physical as necessarily primary, as you seem to imply here, but he can defend himself if he chooses to. So far he seems to be explicitly ignoring you. :_( My point is that you cannot assume all of the properties of matter and claim that matter is not involved. You are suggesting tacitly that matter is something separate from its bundle of properties. I disagree!



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

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