On 30 Jun 2012, at 18:44, Evgenii Rudnyi wrote:

On 30.06.2012 11:14 Bruno Marchal said the following:

On 29 Jun 2012, at 20:01, Evgenii Rudnyi wrote:

On 11.04.2012 11:11 Bruno Marchal said the following:

On 10 Apr 2012, at 21:21, Evgenii Rudnyi wrote:


...


Hence if you know something in Internet or in the written form,
I would appreciate your advice. The best about 20 pages, not
too little, and not to much.

OK I found the paper by Turing:
http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf



Of course, the language is old, and we prefer to talk today in
term of functions instead of real numbers.

You can try to read it. I will search other information, but
there are many, and of different type, and most still blinded by
the aristotelian preconception. So it is hard to find a paper
which would satisfy me. But you can get the intuition with
Turing's paper I think.

Bruno,

I have finally come to mechanism. Thank you for your suggestion. I
have browsed Turing's paper.

Do I understand correctly, that mechanism is something that could
be implemented by some Turing's machine?

You can say that. But you could take "fortran program" instead of
Turing machine. The choice of the initial formal system is not
important.

I think that you have mentioned that mechanism is incompatible with materialism. How this follows then?

Because concerning computation and emulation (exact simulation) all universal system are equivalent.

Turing machine and Fortran programs are completely equivalent, you can emulate any Turing machine by a fortran program, and you can emulate any fortran program by a Turing machine.

More, you can write a fortran program emulating a universal Turing machine, and you can find a Turing machine running a Fortran universal interpreter (or compiler). This means that not only those system compute the same functions from N to N, but also that they can compute those function in the same manner of the other machine.

Now, it happens that a tiny part of arithmetic is already Turing universal, and thus fortran universal, lisp universal, etc. So the arithmetical relations emulates already all computations, in Fortran, in Lisp, in all conceivable universal system (with Church thesis).

If you take the first person indeterminacy into account, and if you see that we cannot have both that consciousness supervenes on physical activity and that consciousness supervene on computations, you can see, with some work, that the laws of physics have to emerge from self-referential modalities put on the computations, and that this does not depend on the choice of the initial system. I use arithmetic only for illustrative purpose, and because it is easier to be realist on an arithmetical relations than on fortran programs, by lack of familiarity.

I hope this answer your question. The sequel and explicit derivation of measureble values is based on work by Gödel and Kleene, and others. I am using computer science to translate precisely the mind body problem, in the computationalist theory, into a mathematical problem of justifying physics by a statistics on dreams (computation as seen through a modality of self-reference). It extends the many- worlds of QM to a many-"dreams" in Arithmetic, in a sufficiently precise way as to be tested. I explain this in the sane04 paper. The main point, UDA, needs only a small amount of passive understanding of Church thesis and the basic of computer science. The explicit translation in the arithmetic (the part 2 of sane04) needs much more.

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

This provides also an arithmetical interpretation of Plotinus and many mystics' talks.

Bruno



Evgenii



Do you some paper about it that does not have equations but that
discusses this term philosophically?

Hmm... Not really. The start is simple, but without doing a minimum
of technical work, you can't get the correct intuition, for the field
is quickly counter-intuitive. I am currently explaining the whole
computability stuff on the FOAR list, where I have a very good
"candid" correspondent. You might try take the wagon. If not I would
suggest you to study a good book, like Cutland's book, or even the
first hundred pages of the Rogers' book. Many popular account on
computability are just invalid, or not precise enough to do serious
philosophy, I'm afraid.

Bruno


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




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



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