Actually it does. While it's logically possible, evidence for a hypothesis A is still provided by any data that is more likely under hypothesis A than under hypothesis B.
The hypothesis that the mind is computable but is using heuristics, of various levels of sophistication, explains the data better and is more parsimonious than your hypothesis, because we already have reason to believe that the mind uses heuristics extensively.
Where you see uncomputable oracular insights, others see computable combinations of heuristics. If you introspect deeply enough while problem-solving, you may be able to sense the heuristics working prior to the flash of intuition.
In that setup the evidence makes the uncomputable partial Oracle the most likely hypothesis, since the space of uncomputable partial oracles is much much larger (infinitely so) than either computable minds or perfect halting oracles.
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.
The hypothesis that the mind is computable but is using heuristics, of various levels of sophistication, explains the data better and is more parsimonious than your hypothesis, because we already have reason to believe that the mind uses heuristics extensively.
Where you see uncomputable oracular insights, others see computable combinations of heuristics. If you introspect deeply enough while problem-solving, you may be able to sense the heuristics working prior to the flash of intuition.