On 12/17/2012 2:15 PM, Bruno Marchal wrote:
Is it possible to define a "relative probability" in the case where it is not possible to count or otherwise partition the members of the ensemble?

Yes. "relative probability" is not necessarily a constructive notion.
Dear Bruno,

Is this not a confession that there is something fundamentally non-computable in the notion of a relative measure? I know about this from my study of the problem of the axiom of choice, but I would like to see your opinion on this.



Not that I know of! If you know how, please explain this to me!

Normally if you follow the UDA you might understand intuitively why the relative probability are a priori not constructive. So you can't use them in practice, but you still can use them to derive physics, notably because the case "P = 1" can be handled at the proposition level through the logic of self-references (Bp & Dt, p sigma_1).

Was it not Penrose that was roundly criticized to claiming that there had to be something non-computable in physics? It seems that you might have proven his case! I go much further (faster!) and claim that this non-constructable aspect is the main reason why there cannot exist a pre-established harmony in the Laplacean sense of the universe.

--
Onward!

Stephen


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