# Re: When will a computer pass the Turing Test?

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On 03 Sep 2013, at 18:23, John Clark wrote:```
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On Tue, Sep 3, 2013 at 12:01 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
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> indeed "free" does not add much to the will, except to emphasize a local freedom degrees spectrum.
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It doesn't even do that. "Will" is the set of things I want to do,
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It is a bit circular, but that's not a problem. OK.

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but some of those things may not be physically possible, and some of my wishes may not even be logically consistent with each other, but I want them all the same.
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? Well, in that case you have a problem to solve.

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> If you are imprisoned, you can keep the will, but have the free- will quite constrained
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I'm not imprisoned,
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How do you know that?

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however I very much want the cardinality of the Real Numbers to be the same as that of the integers, but my wish remains unfulfilled.
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Cardinality is a relative notion. All (first order) theories have an enumerable model.
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Your wish can be exhausted ... outside our universe.

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Assuming comp it is "absolutely undecidable if our "universe" (if it exists) is enumerable or not enumerable, but from inside it is definitely not enumerable, and all we can hope is that the "outside seen from inside" is constructively not enumerable, and this is the case for the ideally correct Turing (Post, Church, ...) Universal Machine.
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Comp associates consciousness to computation, and computation is an arithmetical concept (the proof of this is in all good textbook on computer science (the best one on that topic are Boolos and Jeffrey, Epstein & Carnielli, etc.). It follows also in an amazing way in Matiyasevitch work. The additive+multiplicative structure of the natural numbers does implement a universal dovetailer. (Probably just the way primes distributed I would bet).
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And this makes only possible to formulate the mind-body problem in term of the statistic on the computations, obtained through a limit based on the invariance of the first person for the computations below their substitution level. If comp is false, this would still provide tools to measure our degree of non-computability.
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My point is that comp makes this amenable to computer science, which is arithmetic, or take any base (universal system or language) you want.
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I don't assume there is a physical universe, and ontologically there is none, comp + arithmetic explain how to extract the beliefs in stable lawful universe from a sort of statistics on which converge ideally correct machines.
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A Turing machine cannot know which computations run her, but can bet that below her substitution level she is run by a sort of average on an infinity of computations.
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The mysteries are why unitary transformations?, why linearity?, etc. There are results and open problems.
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Of course, it is a different conception of "reality" than the usual (Aristotelian) one (since always, except for some antic greeks during a millenium, and Indian and mystic).
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Bruno

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John K Clark

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We might use free-will as just will + freedom. It presupposes some stable deterministic realities, at some level.
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Bruno

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

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