Having to pick a metric is comparable to having an epistemological frame. Some metrics might have a different “double convergence” than other metrics. If the metrics do not agree then its not really objective.
If probablity of a statement doesn’t make sense is treated as 0 it would seem to me that “I can’t derive that” should also be assigned 0 by the same basis. So the logical uncertainty is defined but just clunky and not particularly inspiring. I would have also thought that the analog would be to have different axiom sets to be the things metrics are defined over.
Or if one wants to insist that logical probabloities are undefined it should also be extended so that the Trump probabilities start to become undefined once the ϵ-sphere starts to include sufficiently alien worlds. That could also be a natural boundary, the largest radius for which the statement is still defined.
One interesting metric to use would be to pick an agent in the world and use the difference in qualia / experience for the distance. That would be “worlds that feel almost like this”. But if these sort of “exotic” metrics are “too partial” there is still work to be done in defining what sort of metrics are “well-behaved”.
A deterministic system has good basis to be time reversible and in the case that it is then past events do have butterfly probabilities. There is analog with quantum probablities, there is no fact of the matter which slit the particle went throught in the double slit experiement. Thus starting moving away from the screen even if the particle is classical only a small velocity vector shift would be required that the ball had been coming from the other slit (both slits having appriciable butterfly amplitude).
Having to pick a metric is comparable to having an epistemological frame. Some metrics might have a different “double convergence” than other metrics. If the metrics do not agree then its not really objective.
If probablity of a statement doesn’t make sense is treated as 0 it would seem to me that “I can’t derive that” should also be assigned 0 by the same basis. So the logical uncertainty is defined but just clunky and not particularly inspiring. I would have also thought that the analog would be to have different axiom sets to be the things metrics are defined over.
Or if one wants to insist that logical probabloities are undefined it should also be extended so that the Trump probabilities start to become undefined once the ϵ-sphere starts to include sufficiently alien worlds. That could also be a natural boundary, the largest radius for which the statement is still defined.
One interesting metric to use would be to pick an agent in the world and use the difference in qualia / experience for the distance. That would be “worlds that feel almost like this”. But if these sort of “exotic” metrics are “too partial” there is still work to be done in defining what sort of metrics are “well-behaved”.
A deterministic system has good basis to be time reversible and in the case that it is then past events do have butterfly probabilities. There is analog with quantum probablities, there is no fact of the matter which slit the particle went throught in the double slit experiement. Thus starting moving away from the screen even if the particle is classical only a small velocity vector shift would be required that the ball had been coming from the other slit (both slits having appriciable butterfly amplitude).