George,
I spent a while poring over Bruno's thesis, and borrowed
Boolos from a local university library to udnerstand more what it was
about. I didn't go into too great a length into the results and
structure of Modal logic, although I gained an appreciation, and an
understanding of the symbology.
However, my main problem with Bruno's work lay not in the technical
details of Model logic, rather with the phrases of the ilk "We
modelise knowledge by Bew(|p|)". I can appreciate its only a model,
but why should I believe that model of knowing has any connection with
reality? I'm afraid none of the Booloses, nor Bruno's posting helped
me with this.
Cheers
George Levy wrote:
>
> Hi Marchal,
>
> This is a reply to your last two posts. I hope other everythingers beside
> myself are attempting to follow this adventure in logic. It appears to be
> really worth the effort. Please feel free to contribute to this exchange.
>
> Marchal wrote:
>
> And we have as results (including the exercices!):
>
> > Any frame (W,R) respects K
> >A frame (W,R) respects T iff R is reflexive
> >A frame (W,R) respects 4 iff R is transitive
> >A frame (W,R) respects 5 iff R is euclidian
> > (where R is Euclidian means that if xRy and xRz then yRz, for x, y z
> in W).
> >A frame (W,R) respects D iff (W,R) is ideal
> >A frame (W,R) respects C iff (W,R) is realist.
>
> >We will talk on the semantics of L and Grz later.
>
> I do not think you defined euclidian.... There is obviously a connection
> to geometry but I dn't see it.
>
>
> > Actually we will need also
> >
> > -Predicate logic, and arithmetics
> > -weak logics (intuitionist logic, quantum logic)
> > -Algebraic semantics of weak logics
> > -Kripke semantics of weak logics
> >
>
> I guess we have to visit the whole Louvre to get to the Mona Lisa :-). Any
> short cut?
>
> > Then the interview itself will begin. We can follow the historical
> > progress of that interview:
> >
> > -Goedel's theorem;
> > -Loeb's theorem; (just this one makes the travel worth!)
> > -Solovay's theorem;
> > -Muravitski & Kusnetsov, Boolos, Goldblatt theorems;
> > -Other theorems by Goldblatt
> > -Still Other theorems by Goldblatt.
> > -Visser's theorem;
> >
> > It is the theorem by Solovay which will make clear the relation
> > between provability logic and some modal logics.
> > Boolos, Goldblatt, Visser has found result which will make part
> > of our the translation of the UDA argument almost transparent.
>
> Thank you for outlining a itinirary for our journey into logic.... I
> thought our destination was much closer.. Does it have to be that
> complicated? Thanks for the effort.
>
> George
>
>
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