Hi Bruno, will incorporate your changes as soon as time permits :-)
Best Wishes, Günther Bruno Marchal wrote: > Hi Günther, > > Nice work Günther. Now my comment is longer than I wish. I really would > insist on one change. See (**) below. > > On 16 Feb 2009, at 22:54, Günther Greindl wrote: > >> >> Hi guys, >> >> I finally got around to writing the AUDA references page: >> >> http://groups.google.com/group/everything-list/web/auda >> >> Comments welcome. > > > I would separate better the introduction to (general) mathematical logic ... > > Enderton (you mention it) > Mendelson (one of the best introduction to mathematical logic) > Perhaps the Podniek web page > The book by Boolos and Jeffrey (and Burgess for the last edition), and > the book by Epstein and Carnielli > Kleene's 1952 book on Metamathematics. > > ...from the general book on computability (but those books are really > needed already for the UDA, actually for the seventh step of UDA): so I > would put them there: I am thinking about > > Cutland > Rogers > > And then come the most fundamental books on the logic of self-reference > and/or provability logic per se (those are books on G and G*). This is > part of AUDA: > > First the main initial original papers : Davis 1965 (contain Gödel 1931, > Church, Post, Kleene, Rosser). Then the textbook on self-reference > (provability) logic: > > Boolos 1979 > Boolos 1993 > Smorynski 1985 > Smullyan's Forever undecided (a recreative introduction to the modal > logic G). > > And then you can add some books on (general) modal logic (but they are > not needed because the book on provability logic reintroduces the modal > logic). You did already mentioned : > > Chellas (excellent) > But the new edition of Hugues and Creswel is an easier one, and is very > good too imo. > > The relation between modal logic and provability is a bit like tensor > calculus and general relativity. Modal logic is but a tool, provabilty > logic (sometimes called self-reference logics) is the object of study. > It is part of AUDA. "AUDA" really begins with Gödel's famous 1931 paper, > and the very special modal logic G and G*, found by Solovay, is a > machinery encapsulating all the incompleteness phenomenon. > > > (**) If you want make just one little change in the page: in your > sentence "For modal logic these are further guides:" I would make clear > you are referring to the modal logic G and G*, that is the logic of > self-reference. Or just put "provability" or "self-reference" instead of > modal. > > I would not put the Solovay paper in "guide on modal logic". It is > really the seminal paper on the self-reference logics. > > The modal logic G and G* are really the logic of provability or > self-reference on which AUDA is based. > > I am aware we touch "advanced matter", which presupposes a good > understanding of mathematical logic, or metamathematics, something which > is usually well known only by professional mathematical logicians. Even > a genius like Penrose got Gödel's wrong. By the way, Hofstadter got > Gödel's right in his book "Gödel, Escher, Back". He is correct on > computationalism too, but he missed the "matter problem", and even the > universal machine, the first person indetermincay and its "reversal" > consequences. > > I have realized that some of my students have still a problem with > completeness and incompleteness. In part due to the bad choice in the > vocabulary (yet standard). > For example the theory PA (Peano Arithmetic) is complete in the sense of > Gödel 1930, and incomplete in the sense of Gödel 1931. > > Completeness: (PA proves A) is equivalent with (A is true in all models > of PA). This makes "Dt" equivalent with "there is a reality": the basic > theological bet. > Incompleteness: there are true arithmetical statement (= true in the > standard model of PA) which are not provable by PA. > > Don't hesitate to ask any question. Of course UDA is *the* argument. > AUDA is far more difficult and is needed to pursue the concrete > derivation of the physical laws (among all hypostases). UDA shows that > physics is a branch of computationalist self-reference logic. AUDA > begins the concrete derivation of physics from the existing > self-reference logic (thanks to Gödel, Löb, Solovay). > > Note that for a time i have believed that the hypostases were all > collapsing. If this would have been the case, the comp-physics would > have been reduced to classical logic, and what we call physics would > have been a sort of comp-geography. The SWE would have been a local truth. > > Ask any question, we are in deep water. People like Tegmark and > Schmidhuber are on the right track concerning the ontology. The > intersection of Tegmark work and Schmidhuber's work gives the "correct" > minimal ontology: the mathematical elementary truth (on numbers or > mathematical digital machine). My (older) work derives this from comp > and the imperative of the mind body problem, which both Schmidhuber and > Tegmark seems not willing to take into account: they presuppose some > mind:machine identity which the UDA shows impossible to maintain. > > I cpntinue to think that for a non mathematician, a thorough > understanding of the UDA is needed before AUDA. UDA is really the > question, including the consequences that the solution has to be given > by the self-introspective universal machine; and AUDA is that beginning > of the universal machine's answer. For a logician AUDA is far simpler > than UDA, but only for them. My work, like the work by Penrose > illustrates that mathematical logicians are not well understood by non > logicians. Mathematical logicians lives in a ivory tower. > > Best, > > Bruno > http://iridia.ulb.ac.be/~marchal/ > > > > > > -- Günther Greindl Department of Philosophy of Science University of Vienna guenther.grei...@univie.ac.at Blog: http://www.complexitystudies.org/ Thesis: http://www.complexitystudies.org/proposal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
