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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.