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. > > > > 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. 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. I see Psyche and Physics as the personal and impersonal presentations of sense, and Noùs is the re-presentation of physics (meaning physics is re-personalized as abstract digital concepts). 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. > > > > 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. 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. Computationalism and emegentism is also used that way by many. Thanks, Craig > > Bruno > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
