On Wed, May 30, 2012  Bruno Marchal <marc...@ulb.ac.be> wrote:

> The axiom of choice just asserts that an arbitrary product of a family of
> non empty set is non empty.

True, but my dictionary says "arbitrary" means "based on a random choice or
personal whim".

> There is no clue of direct relationship with physics

If modern physics said randomness does not exist then there would be a
conflict with the Axiom of Choice, they could not both be true; but physics
says randomness DOES exist so they are compatible.

> It has a priori nothing to do with free will

Of course it doesn't, nothing real can have anything to do with "free will"
because "free will" is gibberish. But the Axiom of Choice does have
something to do with cause and effect and randomness because those things
are not gibberish, it even has something to do with intelligence. When Alan
Turing designed the first stored program electronic digital computer, the
Manchester Mark 1, he insisted it have a hardware random number generator
incorporated in it because he felt that pseudo-random numbers being
produced by a numerical process could not be truly random. He thought that
if a machine could sometimes make purely random guesses and then use logic
to examine the validity of those guesses it might be able to overcome some
of the limitations he himself had found in pure Turing Machines (although
he never used that name for them), and then you could make what he called a
"Learning Machine. He thought that in this way the limitations all
deterministic processes have that he and Godel had found might be overcome,
at least in part.

  John K Clark

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