Re: COMP, Quantum Logic and Gleason's Theorem

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Wed, 21 Jan 2009 18:17:49 +0100

Hi GŁnther,



> The paper is not online, but I found it in this book which is at our
> University Library, maybe interesting also for other people:
>
> Goldblatt, Mathematics of Modality
>
> http://www.amazon.com/Mathematics-Modality-Center-Language-Information/dp/1881526240/ref=sr_1_1?ie=UTF8&s=books&qid=1232402154&sr=8-1
>
>
> (the book contains the full paper)


Not only that! It contains also his paper on the arithmetical
intuitionist, alias the arithmetical knower, alias the universal first
person, alias the arithmetical interpretation of Plotinus' third
hypostase (the universal soul), alias the epistemical temporal
arithmetical modal logic S4Grz (pronounce: S four Grzegorczyk). A key
paper for the AUDA, except that Boolos found those results, on SAGrz
about the same time, see the reference to Boolos in any of my theses.
Or see the S4 chapters in the Boolos 1993, book or in the recent
paperback reedition of Boolos 1979.

It is the logic of provable and true. It leads to a notion of person
which the machine cannot named or define. The "arithmetical knower" is
not arithmetical!


The book contains also a very interesting study of the Diodorean
modality in the Minkowski Space-time, and a logical approach to
Groethendieck topology.
Note that it is advanced stuff for people familiarized with
mathematical logic (it presupposes Mendelson's book, or Boolos &
Jeffrey).

Two papers in that book are "part" of AUDA: the UDA explain to the
universal machine, and her opinion on the matter.

Bruno


http://iridia.ulb.ac.be/~marchal/




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Received on Wed Jan 21 2009 - 12:18:10 PST

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