Bruno:
It will take quite a while for Mendelson, so I may ask again when I
am "finished" or want to start something new.
Ronald
On Sep 29, 12:47 pm, Bruno Marchal wrote:
> On 28 Sep 2009, at 21:51, ronaldheld wrote:
>
>
>
> > My book has arrived. Perhaps in several months, I will be able to
> > follow the symbolic arguments better?
>
> Nice. Now I feel some guild because for all books in logic, there
> exists always a better book :)
>
> The books by Torkel Fraenkel are very good. Too, like Carnielli and
> Epstein and the Boolos and Jeffrey series.
>
> As a unique book for a serious study, some remains the best, like
> Mendelson for an introduction to mathematical logic (a branch of math
> which study the formal or symbolical systems) and Hartley Rogers for a
> serious introduction to recursion theory (alias theoretical computer
> science; computability theory, uncomputability theory, ...).
>
> And the book by Boolos (1979, 1993) are basically the best
> introduction to the G and G* logics of self-reference. (The AUDA main
> tools).
>
> Smullyan wrote many chef-d'oeuvre.
>
> The deepest bible of the field is Davis 1965,
>
> DAVIS M. (ed.), 1965, The Undecidable, Raven Press, Hewlett, New York.
>
> with the original papers by Gödel, Turing, Kleene, Church, and the
> most incredible Paper which anticipated everything up to now and
> beyond ... (I could argue).
> It exists in DOVER now!
>
> My october month is a bit charged, and I am slow down. I will come
> back on the diagonalization, and the "mathematical
> definition or approach to the notion of computation, and the relation
> between physics and the (mathematically shaped) border of the
> uncomputable, asap.
>
> Best,
>
> Bruno
>
>
>
>
>
> > Ronald
>
> > On Sep 19, 5:38 pm, ronaldheld wrote:
> >> Thanks, Bruno. Mendelson is on its way to me.
> >> Ronald
>
> >> On Sep 18, 10:10 am, Bruno Marchal wrote:
>
> >>> Hi Ronald,
>
> >>> Mendelson' book is an excellent book.
>
> >>> The many editions of Boolos and Jeffrey are very good, but the
> >>> mathematical logic part is not really self-contained. I like very
> >>> much
> >>> also the book by Epstein and Carnielli, and Epstein alone wrote nice
> >>> big books on both classical and non classical logics, but I do think
> >>> that Mendelson is one of the best introduction to classical
> >>> mathematical logic. It gives the standard detailed account on
> >>> computability, and on Gödel and Löb theorems.
>
> >>> Note that the understanding of UDA does not rely on mathematical
> >>> logic, just on the notion of universal machine, and Church thesis
> >>> (which I am explaining currently). But the "formal theory" and the
> >>> notion of Löbian Machine, relies on mathematical logic. Those matter
> >>> are not well known beyond the circle of mathematical logicians.
> >>> Gödel's theorem is frequently abused (that does not help).
>
> >>> This makes me think about the book by Torkel Franzèn, which are very
> >>> nice. Excellent complement to Mendelson.
>
> >>> Google on "Torkel Franzèn inexhaustibility" and "Torkel Franzèn
> >>> abuse
> >>> Gödel". You can't miss them.
>
> >>> If and when I try to explain AUDA, I can say more. Mendelson does
> >>> not
> >>> introduce to modal logic, but the little book by Bools 1979 does it
> >>> very well, before using it for the formal self-reference.
>
> >>> So for AUDA, ma suggestion, for serious studies, is:
>
> >>> 1) Mendelson
> >>> 2) Boolos 1979
>
> >>> Bruno
>
> >>> On 18 Sep 2009, at 15:14, ronaldheld wrote:
>
> Bruno:
> It sounds as if the way to begin is with the latest Mendelson
> book.
> Ronald
>
> On Sep 18, 2:55 am, Bruno Marchal wrote:
> > Hi Ronald,
>
> > You may ask Günther Greindl, who asked me references for the UDA
> > and
> > AUDA, and he put them on the list archive.
>
> > guenther.grei...@gmail.com
>
> > You can take a look on the references in my
> > theses.http://iridia.ulb.ac.be/~marchal/lillethesis/these/node79.html#SECTIO
> > ...
> > ://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/7%20biblio
> > %20gen...
>
> > An excellent introduction to mathematical logic is the book by
> > Eliot
> > Mendelson. Classical treatises on the self-reference logic are the
> > book by Boolos 1979 (recently reedited), or the later version:
> > Boolos
> > 1993. The book by Smorynski is very good too, but those books
> > presuppose knowledge of logic (Like explained in Mendelson).
>
> > Then all books, technical or recreative by Raymond Smullyan, are
> > introduction to diagonalization, self-reference, Gödel and Tarski
> > theorem, and they are quite excellent. Notably his little
> > recreative
> > (but not so easy apparently) introduction to the modal G system;
> >
