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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