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.greindl.domain.name.hidden
Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/
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Received on Sun Feb 22 2009 - 17:15:39 PST