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Well, no. That is the same kind of error as Zeno's paradox. One assigns a prior to a class of hypotheses, and the cardinality of that set does not change the t
by inimino 7y ago
Well, no. That is the same kind of error as Zeno's paradox.
One assigns a prior to a class of hypotheses, and the cardinality of that set does not change the total probability you assign to the entire hypothesis class.
If one instead assigns a constant non-zero prior to each individual hypothesis of an infinite class, a grievous error has been committed and inconsistent and paradoxical beliefs can be the only result.
- yters 7y agoSounds like then you can just arbitrarily divide up your classes to benefit whatever hypothesis you want, leading to special pleading. I think to remain objective one has to integrate over the entire space of hypothesis instances, using an infinitesimal weighting in the case of infinite spaces.
- inimino 7y ago> integrate over the entire space of hypothesis instances, using an infinitesimal weighting in the case of infinite spaces. Agreed. However, when you write: > the evidence makes the uncomputable partial Oracle the most likely hypothesis, since the space of uncomputable partial oracles is much much larger you seem to argue that a hypothesis is more likely because it represents a larger (indeed infinite) space of sub-hypotheses. Reasoning from the cardinality of a set of hypotheses to a degree of belief in the set would in general seem to be unsound.