Hi Bruno,

will incorporate your changes as soon as time permits :-)

Best Wishes,

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

Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/

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