On 28 Feb 2012, at 16:29, Stephen P. King wrote:

On 2/28/2012 4:33 AM, Bruno Marchal wrote:


On 27 Feb 2012, at 20:02, Stephen P. King wrote:

On 2/27/2012 12:26 PM, ronaldheld wrote:
What observations or measurements can I perform that would falsify
COMP?

Hi,

Any measurement of a physical process that cannot be simulated by a Turing Machine equivalent computation.

That would contradict digital physics. But digital physics is self- contradictory (indeed it implies comp which implies the falsity of digital physics). Roughly speaking: if "I" am a machine, then everything else is not.

Dear Bruno,

Let me see if my thoughts are correct as I can best write them. COMP is the conjunction of "Yes Doctor", the Church Thesis and Arithmetic Realism, correct?

Yes, but note that this is redundant. "yes doctor" means "yes" for a digital transplant. Church thesis is needed to make the term "digital" mathematically precise. And AR is needed to make Church thesis making sense.




I am now not sure of the definition of "Digital physics" given this thread so far... From what I can tell, Yes Doctor is built on the idea of functional substitutability at some level or scale for physical systems, such that a given algorithm will run on any functionally equivalent physical system; it is basically a restatement of computational universality.

I can say yes, to be short. but logically, universality is not used here. But this is a technical point on which I don't want to digress now. Primitive recursive function can have equivalent programs, despite there is no universal primitive recursive functions.



This idea shows us that our consciousness is not dependent on a particular form of physical system if and only if our consciousness is algorithmic or computable in the Turing sense. I am agnostic on this because I do not see any evidence (pace Tegmark) that our brain's implementation of consciousness does not involve quantum entanglement. My answer to Ronald's question was based on what I thought I understood of COMP, so it seems that I still do not understand COMP. Does not COMP require that any observation of our physical world be faithfully representable as a finite list of yes or no type questions and their answers?

See Quentin's comment.
Comp is a priori neutral on any question of physics, until physics is derived from comp.






IOW, any non-computational physical process.

Comp implies non-comp (non Turing emulable first plural person) physical processes. Indeed the "comp primitive matter" is not Turing emulable, it is an infinite sum on infinite computations.

But this definition (of "comp primitive matter") is fraught with the measure problem!

OK, but a precise one that we can handle with mathematical tools. That's the progress. Comp is fraught with tuns of problems. Comp is just a toll for making those problem precise.





Does this exclude an infinite collection of possible worlds to represent the physical systems that can implement that infinite computations?

A priori, no. Now in your sentence, the word "worlds" is ambiguous, so I chose favorable interpretations of it, to make sense of what you say.



I suppose that you could say that it does as the UD "will generate all possible Turing machine states, infinitely often (why?),

Due to the closure of the diagonalization, it can be proved that the phi_i sequence goes through all equivalent programs an infinity of times. It is called the "padding theorem". It is obvious for most computer scientists, because you can always add useless code, but it is also a consequence of Kleene's second recursion theorem.




which (by comp) includes all your virtual reconstitutions corresponding to (hopefully) consistent extensions of yourself, in all possible (locally) emulable environments or computational histories." The usual idea that I am considering is that a physical system will have to be potentially infinite to satisfy the requirements of a universal Turing machine, as it has to have at least an infinite tape.

The tape is not part of the universal machine. It is better to think about the universal machine as the code of such a machine on the tape (of some other one). Once a fixed ontological toe is given, a universal machine is a number. It is a finite object. This is important to keep in mind. i would not say that human or juming spider are Löbian (and thus universal) if that needs some infinity. For the 1p, it is different because the 1p is indeterminate on infinity of computations, and this structures the logic differently.




You write:

"Instead of linking [the pain I feel] at space-time (x,t) to [a machine state] at space-time (x,t), we are obliged to associate [the pain I feel at space- time (x,t)] to a type or a sheaf of computations (existing forever in the arithmetical Platonia which is accepted as existing
independently of  our  selves  with  arithmetical  realism)."

Yes, that's a conclusion of a reasoning. It shows that primitive matter lacks the ability to singularize matter out of the UD. So, even if it makes sense, it is empty of explanation power for the mind-body problem.




This seems to bypass the requirement of the concrete implementation of the UTM by appeal to the independent of the truth value of sigma_1 sentences (or equivalent) such that you can then claim 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."

Yes. The reasoning shown that the concrete implementation has to be bypassed, which save us from the problem of defining what that could mean. It is the result, not something added to the assumptions.




Therefore any considerations of, for example, thermodynamics is irrelevant as such would be derivable from the "accidental correctness" of Sigma_1 sentences.

Exactly.



This is interesting on its own as it strongly resembles the "occasionalism" of Malebranche and others that was proposed to explain psycho-psychical parallelism between mental and physical events.

OK.




Pratt's residuation solves this problem without AR's idealism,

If you can prove that, then Pratt's theory has been shown incompatible with comp, given that the AR *idealism* is a consequence of comp, as opposed to AR which is part of the assumption of comp, and of any theory capable of defining a (Turing) universal system.




among other things, by reducing global computations to pairwise interactions between a potentially infinite number of computations. This is a form of accidentalism, but is more subtle as the relationship between mental and physical states/events does not need a causal explication. Additionally, Pratt's residuation proposal (similar to this concept) generates only consistent extensions of first person indeterminacy modulo arbitrarily large memory resources. It is only when memory resources are limited to being finite ("Forgetfulness" as what occurs in the Telephone game) that inconsistent extensions might occur.

Perhaps. I cannot judge. You might write a paper on that.




My skepticism of your interpretation of COMP has always turned on the allegation of eliminatism (in the sense of "that ‘‘matter’’ has been ontologically reduced to ‘‘mind’’") that you seem to derive from the independence of truth valuation, for example that because the primeness of 17 is completely independent of our knowledge of 17ness or primeness properties, that the truth value alone of "17 is prime" is sufficient to determine the properties that the sentence "17 is prime" implies to the exclusion of all others.

This is not quite clear. I don't see what is special with the interpretation of comp. It is the standard one. The result might be startling, but we can say we get a contradiction so far. It is perhaps weird, but not much weirder than physics, up to now.



I have looked at your Strobe argument and MGA but I still do not see how it is that the reduction follow. I have not had the "aha" moment. :-( I am not convinced by Maudlin's arguments. How does the truth value determine the properties of a referent absent the possibility of prior identification of the referent?

You lost me completely. I think you introduce philosophical problems, which might be of some interest, but which distract you from looking at the validity of the argument.



How can the exactness of the properties of an entity follow only from its potential existence as an entity?

In arithmetic there is no potential existence. Either a number, verifying some property, exists, or it does not exists. On the contrary, comp rehabilitates Pythagore and Quine on this issue.



It is how you answer these questions that I need to understand.

In the whole theory, properties are derived directly from the laws of + and *. "potentiality" and other modalities comes the abilities of some cognitively rich numbers to lokk at themselves and to discover many possibilities.





So to refute comp you need to find a non recoverable, by the first person indeterminacy, physical processes. If there were evidences that the wave function collapse, that might be considered as a refutation of comp. But after a century of the collapse speculation, we can only say that this evidences is meagre.

OK, so we have to show a counter-example to the recoverability of physical process by first person indeterminancy (IPI)? Could you elaborate a bit more on how IPI covers all possible physical processes

The result is that we have to do that job. AUDA shows the most direct way to do it, in a way which keeps the distinction between quanta and qualia. But to do it is a job which maight take centuries, or more. I just show that we have to do it. You should not take comp as an answer, but as a tool to make the questions and problems mathematically precise.



without assuming AR?

If I can't assume AR, I can't even define digital, Church thesis, universal numbers.



I ask this because it seems to me that AR is what allows your entire thesis to run.

Yes. But I have never find someone doubting AR. I can see philosophers faking that they doubt AR for the purpose of blocking a reasoning, on the internet (to talk like John Clark). But someone doubting AR? I have never seen that. I have taught to highly mentally disabled persons, and none of them shows doubt in AR. Without the help of a computer, I might have been able to conclude that some miss it, because they could neither talk, nor count, but by using some game- trick with the computer I realize that they understood and believe in AR like anybody else.



My problem with AR is that it prevents us from finding any solutions to many problems including the concurrency problem as it assumes property definiteness absent specifiably.

Prove this, or at least formulate this in the comp theory. If you show that the concurrency is not solvable in comp, then you refute comp, and that would be a progress. But that task might be premature. Comp- physics is not yet at that stage.

Stephen, we are probably 200 years in advance, on this list. Not 500 years!

:)



You are tacitly assuming that all possible computations can inspect each other simultaneously and act upon each other without any occurrence of a conflict or contradiction.

?




This tells me that you do not understand the concurrency problem!
This is an aspect of the problem of time that many thinkers have not considered. This problem is seen in the statement: "Time exists because not everything can occur all at once". Simultaneity is not a simple and unproblematic concept in ontology.

This is true for all theories negating the possibility of "block realities", that is theories which presuppose a primary time. But comp, by MGA, is incompatible with such theories. You can forget comp if you don't like that, or you can try to find a flaw in the argument.

But this contradicts your repeated claim that you don't assume mind or matter (in which I include time) at the start, so I am not sure what to think.

Bruno


http://iridia.ulb.ac.be/~marchal/



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