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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
