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Beehaw decides: what is the set of all genders?
(strawpoll.com)
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The universe might be discrete.
If mental states are finite, then the space of all possible human minds is finite and includes the one that believes they have knowledge of the computation's result. It is possible for mental states of 2 minds to be different but extensionally behave like the same person. We would exclude human minds whose models don't map well onto the physics of our universe though. You might not be willing to pick the opposite if we are talking about morality also @askbeehaw
It's possible that brains act stochastically such that two discrete identical brains produce a range of outputs under identical conditions. In that case, mental states would be confined by the space of outputs of minds, and if that's the real numbers then it would be uncountably many.