# Re: COMP, Quantum Logic and Gleason's Theorem

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Mon, 26 Jan 2009 18:30:36 +0100

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

Give me time to think on the best book for the technical understanding
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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Received on Mon Jan 26 2009 - 12:30:51 PST

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