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.
Sounds 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.
> 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.
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.