On 31 May 2012, at 17:03, John Clark wrote:

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On Wed, May 30, 2012 Bruno Marchal <marc...@ulb.ac.be> wrote:> The axiom of choice just asserts that an arbitrary product of afamily of non empty set is non empty.True, but my dictionary says "arbitrary" means "based on a randomchoice or personal whim".

`It math, if P(x) is true for arbitrary x, it just means that P(x) is`

`true for all x.`

> There is no clue of direct relationship with physicsIf modern physics said randomness does not exist then there would bea conflict with the Axiom of Choice,

`The axiom of choice has nothing to with randomness, a priori. I can`

`imagine the existence of theories bringing relation, for divine (non`

`turing emulable) entities. But then you have to present those theories.`

they could not both be true; but physics says randomness DOES existso they are compatible.

`Comp says randomness does exist, and physics confirms that, OK. But`

`again, this has nothing to do directly with the axiom of choice which`

`concerns set theory.`

`There are evidence that 'mathematical" physics can live in little`

`constructive toposes, and if I remember well the reading of papers`

`some time ago, I think that the axiom of choice makes those toposes,`

`or topoi, boolean, that is still obeying classical logic, which is not`

`so much liked by the constructive people. Physics lives in very short`

`initial segment of ZF, it is not clear if the axiom of choice says`

`anything about the physical reality, nor even of the math, except by`

`making true some nice completing property, like having *all* Hilbet`

`space having orthonormal base, in physics, or like all consistent set`

`of sentences having unique consistent extensions. But, with comp, this`

`concerns the epistemology, and things are very difficult.`

`Consciousness surfs on coherent dreams, and it is just an open`

`question if that converges to a unique physical universe, or a unique`

`multiverse, or a unique multi-multiverse, or and this on all ordinals`

`(in which theory? With AC?.`

> It has a priori nothing to do with free willOf course it doesn't, nothing real can have anything to do with"free will" because "free will" is gibberish.

`That is *your* theory, and to be honest, I don't find it so much`

`interesting. I do agree that some definition of free will are`

`"gibberish", that is either inconsistent, or empty, but some are not.`

`I suggest that free-will is the machine awareness of the possibility`

`of hesitating in front of a spectrum of possibilities.`

`Butterflies are close to free will, imo, because of the spectrum of`

`flowers and nectars, but I have no evidence that butterfly have free`

`will because I have no evidence that butterfly can infer and reflect.`

`They might be mainly attracted. But I gave evidence that jumping`

`spiders and octopi have free will in the sense that they do infer the`

`possibilities, and reflect on it.`

`Relatively to their cognitive abilities, they have as much free will`

`than you, me and PA (with the definition above).`

But the Axiom of Choice does have something to do with cause andeffect and randomness because those things are not gibberish,

`We could make that true if we would formalize physics in set theory.`

`But there are conceptual reason why such an enterprise is doomed at`

`the start.`

`ZF is the "fortran" of the mathematical theories. Just an altar for`

`category theory and "natural transformations" (Eilenberg and MacLane).`

I love ZF, but as a very imaginative LĂ¶bian machine.

`To say that the axiom of choice has something to do with the notion of`

`cause and effect, without saying in which theory you work is confusing.`

it even has something to do with intelligence. When Alan Turingdesigned the first stored program electronic digital computer, theManchester Mark 1, he insisted it have a hardware random numbergenerator incorporated in it because he felt that pseudo-randomnumbers being produced by a numerical process could not be trulyrandom. He thought that if a machine could sometimes make purelyrandom guesses and then use logic to examine the validity of thoseguesses it might be able to overcome some of the limitations hehimself had found in pure Turing Machines (although he never usedthat name for them), and then you could make what he called a"Learning Machine. He thought that in this way the limitations alldeterministic processes have that he and Godel had found might beovercome, at least in part.

`For problem solving this in vindicated by the result that Random`

`Oracle can enlarged classes of problem solving. Those are given by`

`necessary non constructive proofs. This does not overcome`

`Incompleteness or insolubility, but can reduce complexities in`

`relative way. That might play a role in the first person indeterminacy`

`comp measure problem, as it gives freely a first person "random`

`Oracle" a priori, relativized by their many computational extensions.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.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.