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thomblake comments on Controlling your inner control circuits - Less Wrong
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If by "almost certainly false" you mean that say, 1 out of every 10,000 such sentences will be true, then no, that does not entail a higher order of infinity.
I meant, as in the math case, that the probability of selecting a true statement by choosing one at random out of the space of all possible statements is 0 (there are true statements, but as a literal infinitesimal).
It's possible that both infinities are countable, as I am not sure how one would prove it either way, but that detail doesn't really matter for the broader argument.
See the note by JGWeissman--this is only true when considering constructively true statements (those that carry non-negligible informational content, i.e. not the negation of an arbitrary false statement).