Re: COMP, Quantum Logic and Gleason's Theorem

2009-01-26 Thread Bruno Marchal
I will think about it. Somehow, the best layman intro to UDA and  
AUDA are in this list. The first 15-step version of UDA was a reply to  
Russell Standish a long time ago. UDA is the logical guide to AUDA,  
which is just a deeper second pass on UDA.

AUDA *is* UDA explained to the dummy, with the dummy played by the  
machine.

Can we still access the everything list posts individually through web  
address?

Give me time to think on the best book for the technical understanding  
of AUDA, I have already made some advertising on some books like the  
one by Boolos, or (better for the layman) Smullyan, especially Forever  
Undecided, for a recreative introduction to the modal logic G. Any  
good textbook in mathematical logic is a necessary companion. AUDA  
uses the most standard notion and results there. Probably a key book  
(even for just the seventh step of UDA) is the book by Webb. See the  
reference of the paper linked below).

For UDA, good popular training are SIMULACRON 3, MATRIX, but also  
Plato, and many other up to the book Minds'I edited by Dennett and  
Hofstadter. The original paper on the UD and UDA (and MGA) is my 1991  
paper. It contains the seeds of AUDA.
It contains a shorter bibliography, which could help...

Marchal B., 1991, Mechanism and Personal Identity, proceedings of  
WOCFAI 91, M. De Glas  D. Gabbay (Eds), Angkor, Paris.

Except that for understanding the UD itself, and thus the seventh  
step, and to comprehend its generality, you have to know a bit of  
theoretical computer science and mathematical logic. Rereading  
Conscience et Mécanisme I realize Russell Standish was right, and  
that book should be translated in english because it contains an  
almost complete (self-contained) explanation of logic (for the  
physicists), including the historical foundations which are genuine,  
and a detailed explanation of the measurement problem in quantum  
physics, for the logicians. (beyong the most detailed account of the  
UD). It renders also justice to all the contributors in the debate on  
Gödel (like Benacerraf, Reinhardt, Webb, Wang, and many others). There  
are many misunderstandings, which reminds me the book by Torkel  
Franzen ...


Also, it is hard to *believe* in the plausibility of the conclusion of  
UDA without having a good understanding of Everett's Quantum  
Mechanics. What could be a good introduction to Everett? ... Deutch'  
FOR book, but also Albert's one, D'Espagnat, .

There are many good books, working at different levels. Let me think a  
bit,

Best,

Bruno


On 25 Jan 2009, at 18:45, Günther Greindl wrote:


 Hi Bruno,

 Goldblatt, Mathematics of Modality
 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.

 I would like to add a guide to AUDA section on the resources page.
 Maybe you could specify the core references necessary for  
 understanding
 the AUDA (if you like and have the time)?

 Here a first suggestion of what I am thinking of:

 Boolos Et Al. Computability and Logic. 2002. 4th Edition

 Chellas. Modal Logic. 1980.

 Goldblatt,  Semantic Analysis of Orthologic and
 Arithmetical Necessity, Provability and Intuitionistic Logic
 to be found in Goldblatt, Mathematics of Modality. 1993.



 What do you think?

 Best Wishes,
 Günther

 

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




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Re: COMP, Quantum Logic and Gleason's Theorem

2009-01-26 Thread Mirek Dobsicek


Goldblatt 1993, Mathematics of Modality
this book is available online:
http://standish.stanford.edu/bin/detail?fileID=458253745

mirek

 Goldblatt, Mathematics of Modality

 http://www.amazon.com/Mathematics-Modality-Center-Language-Information/dp/1881526240/ref=sr_1_1?ie=UTF8s=booksqid=1232402154sr=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).

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