Hi Gabriel,
On 06 Jan 2014, at 02:48, Gabriel Bodeen wrote:
Hi Bruno (& all),
I was trying to read through your paper "The Origin of Physical Laws
and Sensations", which I saw linked to in a conversation earlier. I
started to get lost about page 13 of the PDF,
Waw! Good. No problem with the UDA?
What is it that you don't understand page 13? You might need to study
a good book in logic, like Mendelson, or Boolos and Jeffrey (+
Burgess in late editions).
You might also benefits from the study of Smullyan's Forever
Undecided, although he is quite quick (and too abstract) in his
chapter "The Heart of the Matter".
MENDELSON E., 1987, Introduction to Mathematical Logic, 3ème édition,
Wadsworth &
brooks/Cole.
BOOLOS G. S. et JEFFREY R. C., 1974, Computability and Logic,
Cambridge University
Press, 3ème éd. : 1989, Cambridge. (+ BURGESS for late editions)
The book by Epstein & Carnielli is very good too. The original edition
is out of stock, but I found a paperback in stock on Amazon. You will
find it easily.
and by page 17 I was too lost to profitably continue.
I explain the diagonal lemma there, which is "the heart of the matter"
indeed. Smullyan dropped its use to explain the logic G, by using the
trick of the Island of Knaves and Knight instead. This works well
logically, but make people believe that the diagonal conclusion is due
to a fairy tale. But for formal theories or (ideally consistent or
sound) machines, the effect of the Island of Knight and Knaves is
obtained by that diagonalization lemma, due initially to Gödel. It is
rather standard in logic, as Gödel proved that lemma in 1931.
Can you (or anyone) suggest, based on the topics on those pages,
some resources that I might find helpful for understanding the paper?
-Gabe
The books above can help, but you can also copy and past the first
paragraph that you don't understand, and I can explain more online,
although you might need to make more solid your basic knowledge in
mathematical logic.
If you understand the eight steps of the UDA, that is already a lot.
The second part of the paper is not needed to get the reversal, only
to make it constructive and to actually derive a bit of physics from
arithmetic.
Bruno
http://iridia.ulb.ac.be/~marchal/
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