Re: AUDA Page
Thanks, Günther. Bruno On 01 Mar 2009, at 23:34, Günther Greindl wrote: > > Hello, > > have incorporated most of Bruno's change wishes: > > http://groups.google.com/group/everything-list/web/auda > > Best Wishes, > Günther > > > > http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: AUDA Page
Hello, have incorporated most of Bruno's change wishes: http://groups.google.com/group/everything-list/web/auda Best Wishes, Günther --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: AUDA Page
Hi Günther, Le 22-févr.-09, à 23:16, Günther Greindl a écrit : > will incorporate your changes as soon as time permits :-) Take all your time. I am myself rather busy. But thanks for telling me. Actually I take this AUDA page as an opportunity for thinking about the best books on Gödel's incompleteness theorems. I could send a list of books with short comments, perhaps in April. All good books on incompleteness and "provability logic" can be helpful on the AUDA, given that the AUDA is entirely build on incompleteness. Right now I think about the book "inexhaustibility" by Torkel Franzen, which is very good, at least for the mathematically inclined reader. We have already talk about Franzen's little book on the abuse of Gödel's theorems. Quite useful too, especially for non-logicians. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: AUDA Page
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
Re: AUDA Page
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 understandin
