On 17 Dec 2012, at 22:55, Stephen P. King wrote:

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 have always insisted on that non computability of the relative measure. Anyway, I start from comp and I deduce only (with some definitions). It is not like if we had any choice in the matter.



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.

I don't do set theory. the axiom of choice is not needed.





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!

Indeed. Maudlin already, in psyche, shows that comp entails some conclusion by Penrose. Too bad Penrose derived then from non-comp.





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.

At first sight this is wrong for me, but you can try an argument. Comp assume arithmetic which can be seen as a pre-established harmony, but of course that term can get many other interpretations.

Bruno




--
Onward!

Stephen


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



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