Le 24-juil.-12, à 19:07, Stephen P. King a écrit :

On 7/24/2012 7:52 AM, Bruno Marchal wrote:

 Le 23-juil.-12, à 20:30, Stephen P. King a écrit :

On 7/23/2012 6:00 AM, Bruno Marchal wrote:
If this is relevant for UDA, you should show to me. You start from an assumption of some primitive physical reality.

    Could you please explain to me why it is that you make this claim in spite of repeated explanation that show the contrary?

Because despite you repeat that physics is not primary, you argue that something is invalid in UDA by mentioning physical interactions, and by referring to papers which assumes physicalism (implicitly or explicitly). As I said you contradict yourself.


    It would be a contradiction if I where not qualifying the definition of "physical interactions". Have you noticed that I mention that I am putting the physical at the same level as the numbers, not by making the physical primitive but instead by making the numbers (the immaterial aspect as per your designation) occur (within my approach) at the same level. Neither numbers nor physical objects are primitive. Let me re-post something I wrote yesterday that you may have missed:

The natural numbers, or something recursively equivalent, have to be primitive (in my sense) by a theorem in logic. We cannot define the natural numbers by assuming less.

On 7/22/2012 2:41 PM, Stephen P. King  wrote:
   Many (as implied by the word plural) is not just a number. A plurality of 1p is a mapping function from some domain to some co-domain (or range), no? If there is no distinction between the domain and co-domain, what kind of map is it? Maybe it is an automorphism, but it is not something that allows us to extract a plurality over which variation can occur. You are talking as if the variation was present but not allowing the means for that variation to occur! The use of the word "plurality" is thus meaningless as you are using it: "first person plural view of physical reality".     You must show first how it is that the plurality obtains without the use of a space if you are going to make claims that there is no space and yet plurality (of 1p) is possible. In the explanation that you give there is discussion of Moscow, Helsinki and Washington. These are locations that exists and have meaning in a wider context. At least there is assumed to be a set of possible locations and that the set is not a singleton (such as {0}) nor does it collapse into a singleton.

Just use the plurality of the number relative situation among each other. That works fine for the multidreams, and that is enough to understand how the illusion of space and time occur (but not to get the measure, which needs the mathematical treatment of self-reference).


On 7/22/2012 2:41 PM, Stephen P. King  wrote:
  [SPK] If the computer is defined as a closed system then solipsism automatically follows.

It is not define as a close system. that is even why it is natural (but conceptually wrong) to put the infinite tape in the definition of the universal machine. But the universal numbers are open in a lot of sense. Now, even a closed computer, with a finite non extensible memory, can emulate a plurality of observers, defeating solipsim locally, if its memory is enough big.

    Ah! Exactly! "...even a closed computer, with a finite non extensible memory, can emulate a plurality of observers, defeating solipsim locally, if its memory is enough big." YES! Defeating solipsism locally. That is exactly what I am trying to discuss with you, that is what the verbosity about "local measures" is trying to convey. The "memory" is a resource, it is the computer's version of space. It is where the plurality is necessary.

But those are purely arithmetical concepts.

    Let us recap the idea so far: A Computer, defined abstractly, is a closed system.

But it is not closed (except for diagonalization, but I guess that is not in your sense).

It must be closed if it has a fixed point identity (ala Kleene theorems) ,

That has nothing to do, or it is the closure for diagonalization, but this makes the RE sets topologically open. You are quite confusing, and I don't see your point of invalidity.

but this closure causes it to be solipsist. It cannot name anything or have knowledge of anything that is not within the span of its being. How do we solve this problem? We first have to accept the problem. Like the alcoholic that wants rehabilitation, we must accept that we are - as observers - solipsists, but there is a chance that we are not doomed to this misery. If the memory of the computer is "big enough" then there is a non-zero chance that the memory of a separate and different computer has a state of its memory that is identical. This allows for a partial bisimilarity to exist between the two computers.     My idea is that if there is sufficient bisimilarity between a disjoint pair of closed computational systems and if there is a smooth transformation that allows homomorphisms of arbitrary states within a memory, then the appearance of plurality of computational observers is possible. The Stone duality then implies that if a homomorphism between a pair of Boolean algebras exists then there is a transformation between a pair of Stone spaces that exists. If physics can be defined in terms of Stone spaces and abstract computations in terms of Boolean algebras then the mind-body problem is solved. There is no need to "reduce" the mind-body problem to a body or a mind problem (in the singular sense). There is a reduction to a Minds (plural) or Bodies (plural) problem, and this is the interaction problem that I am trying to explain. If you would only read that article on the Concurrency Problem in Wiki, this might have been an easier journey.

    The key is that I am considering the body problem (as you define it in your discussion of UDA) to be the dual of the mind problem for materialism.

Too vague. AUDA shows the existence of such a dulaity, but the mind is not just the dual of matter, for the mind reality is a priori vastly bigger than the physical realm. How do you treat the first person indeterminacy in that duality?

Perhaps the only problem in our mutual understanding is vocabulary and definitions of words. What we are considering is very subtle and hard (almost impossible!) to define exactly. I need to be more patient in my explanations.

The problem is typical in the dialog between science and philosophy, and more servere when a point of philosophy is tretated with the scientific method. We can discuss only when you grasp the technical point, really (or find a possible flaw).

    Do you understand the key isomorphism that is being postulated to "connect" the physical with the mental aspects?

With comp it is not an isomorphism a priori. It might be, but that is an open very hard problem (even to just formulate it).

It is the identification of a physical object with its best possible computational simulation.

But we can't do that. If we do it for a mind person, its brain *is* an emerging pattern on infinities of computations, interfering statistically. Keep in mind that comp makes both matter (apparent primitive matter) and consciousness not Turing-emulable a priori.

It for this reason that I insist that we cannot disconnect the mental world of mathematics (including any form of number or arithmetic - including {N, +, *} - from the physical world of objects.

Logically you are right, for the first implies the second, but only at the epistemological level.

There must be at least one physical system that can implement a given computation for that computation to qualify for universality.

That is plain wrong. I guess you are changing the sense of universality. I use it in the usual Post-Turing-Church-Kleene-Markov sense. Given that ypou say "physical suystem are not primitive", I don't know what you mean by physical.

Of course universality demands that the computation can operate on any functionally equivalent system, so there is an invariance with respect to function, but the equivalence class "pivots" on the necessity that it can actually be run on a physical system.

Which physical system? Where does it come from. What is it? What is your theory?

Otherwise computations (as per the abstract theory of Universal Turing Machines) would have nothing at all to do with physical computers and be a purely mental exercise of fantasy.

You still evade to criticize UDA which shows that if we are machine (even just physical machine) then physics is derivable from aritthmetic. It is a theorem in applied logic, once you accept the classical very wide definition of knowledge and belief. Have you understand the step 7? It shows that comp + robust physical universe already makes physics a branch of number theory. Then step 8 shows that the assumption of a robust physical universe (or any primary physical universe) is a red herring: it simply cannot work, making observable matter necessarily non primary (making primitive matter into an epinoumenon).



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