On 21 Dec 2013, at 17:32, Craig Weinberg wrote:

On Thursday, December 19, 2013 10:13:25 AM UTC-5, Bruno Marchal wrote:

On 19 Dec 2013, at 15:07, Craig Weinberg wrote:

On Thursday, December 19, 2013 5:23:20 AM UTC-5, Bruno Marchal wrote:
Hello Craig,

That is the very well known attempt by Lucas to use Gödel's theorem to refute mechanism. He was not the only one.

Most people thinking about this have found the argument, and usually found the mistakes in it.

To my knowledge Emil Post is the first to develop both that argument, and to understand that not only that argument does not work, but that the machines can already refute that argument, due to the mechanizability of the diagonalization, made very general by Church thesis.

In fact either the argument is presented in an effective way, and then machine can refute it precisely, or the argument is based on some fuzziness, and then it proves nothing.

If 'proof' is an inappropriate concept for first person physics, then I would expect that fuzziness would be the only symptom we can expect. The criticism of Lucas seems to not really understand the spirit of Gödel's theorem, but only focus on the letter of its application...which in the case of Gödel's theorem is precisely the opposite of its meaning.

The link that Stathis provided demonstrates that Gödel himself understood this:

So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310).

To me it's clear that Gödel means that incompleteness reveals that mathematics is not completable

OK. Even arithmetic.

in the sense that it is not enough to contain the reality of human experience,


He says the 'human mind', but I say human experience.

Mathematics is not enough for the mind and experience of ... the machines.

not that it proves that mathematics or arithmetic truth is omniscient and omnipotent beyond our wildest dreams.

Arithmetical truth is by definition arithmetically omniscient, but certainly not omniscient in general. Indeed to get the whole arithmetical "Noùs", Arithmetical truth is still too much weak. All what Gödel showed is that arithmetical truth (or any richer notion of truth, like set theoretical, group theoretical, etc.) cannot be enumerated by machines or effective sound theories.

The issue though is whether that non-enumerablity is a symptom of the inadequacy of Noùs to contain Psyche, or a symptom of Noùs being so undefinable that it can easily contain Psyche as well as Physics.

The Noùs is the intelligible reality. It is not computable, but it is definable. Unlike truth and knowledge or first person experience.

I think that Gödel interpreted his own work in the former and you are interpreting it in the latter - doesn't mean you're wrong, but I agree with him if he thought the former, because Psyche doesn't make sense as a part of Noùs.

That is too much ambiguous. The psyche is not really a part of the Noùs, which is still purely 3p.

I see Psyche and Physics as the personal and impersonal presentations of sense,

Machine think the same, with "sense" replaced by arithmetical truth. Except that the machine has to be confused and for her that truth is beyond definability, like sense.

and Noùs is the re-presentation of physics (meaning physics is re- personalized as abstract digital concepts).

The Noùs has nothing to do with physics a priori. It is the world of the eternal platonic ideas, or God's ideas.

keep in mind the 8 hypostases:

- p (truth, not definable in arithmetic, but emulable in some trivial sense) - Bp (provable, believable, assumable, communicable). It splits into a communicable and non communicable part (some fact about communication are not communicable) - Bp & p (the soul, the knower, ... the psyche is here). It does not split.

- Bp & Dt (the intelligible matter, ... matter and physics is here). It splits in two. - Bp & Dt & p (the sensible matter. the physical experience, (pain, pleasure, qualia) are here. It splits also in two parts.

Physics is the commercialization of sense. Psyche is residential sense. Noùs is the hotel...commercialized residence.

An excellent book has been written on that subject by Judson Webb (mechanism, mentalism and metamathematics, reference in the bibliographies in my URL, or in any of my papers).

In "conscience and mechanism", I show all the details of why the argument of Lucas is already refuted by Löbian machines, and Lucas main error is reduced to a confusion between Bp and Bp & p. It is an implicit assumption, in the mind of Lucas and Penrose, of self- correctness, or self-consistency. To be sure, I found 49 errors of logic in Lucas' paper, but the main conceptual one is in that self- correctness assertion.

Penrose corrected his argument, and understood that it proves only that if we are machine, we cannot know which machine we are, and that gives the math of the 1-indeterminacy, exploited in the arithmetical hypostases. Unfortunately, Penrose did not take that correction into account.

Gödel's theorem and Quantum Mechanics could not have been more pleasing for the comp aficionado. Gödel's theorem (+UDA) shows that machine have a rich non trivial theology including physics, and QM confirms the most startling points of the comp physics.

As far as QM goes, it would not surprise me in the least that a formal system based on formal measurements is only able to consider itself and fails to locate the sensory experience or the motive 'power on' required to formalize them in the first place.

They don't address that question.
Formal systems are seen as mathematical object, even number, and they exist independently of us, if you still accept arithmetical realism.

I accept the realism of arithmetic representation, and that they exist independently of us humans, but not that they exist independently of all experience or possibility of aesthetic presentation. I say no to theoretical realism.

Realism is always defined with respect to some theory.
Arithmetical realism is not independent of experience, as arithmetic produces them necessarily. They are concomitant.

The consistency objections similarly fail to recognize the core capacity to discern consistency from inconsistency. It is not possible to doubt our own consistency without also doubting the consistency of our doubt.

On the contrary, we, and/or machines, cannot not doubt our consistency.

But we can't doubt the consistency of doubt.

Not sure what you mean. In fact we can doubt all assertion of consistency. We cannot doubt that we doubt, but we can doubt of the consistency of all the proposition. G does not contain any sentence beginning with a D, and G*, on the contrary is close from possibilitation (p ====> Dp).

We believe that it is within our power to disbelieve.

What we cannot doubt is our raw consciousness "here-and-now", which might be the first person view of consistency. Consistency (Dt) and consciousness have many things in common, but incorrigibility works only for consciousness. A good first person description of consciousness would be Dt v t, making it non doubtable and trivial (which it is from the 1p view). But that is still only a sort of approximation.

Eliminative physicalism is the embodiment of doubt of our raw consciousness.

OK. Nice.

Computationalism and emegentism is also used that way by many.

Yes. Alas. But I think that this is specifically and definitely refute with the UDA (and AUDA). Most people believe that comp is an ally to materialism, but in fact comp is incompatible with most reasonable form of materialism. of course primitve matter is a fuzzy notion, so you can adapt it to be compatible with anything, and that's why in step 8 we still need a bit of Occam, and that's normal as that has to be the case when we apply a theory to "reality".



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