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Kawoomba comments on Infinite Certainty - Less Wrong
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So by that logic I should assign a nonzero probability to ¬(A→A). And if something has nonzero probability, you should bet on it if the payout is sufficiently high. Would you bet any amount of money or utilons at any odds on this proposition? If not, then I don't believe you truly believe 100% certainty is impossible. Also, 100% certainty can't be impossible, because impossibility implies that it is 0% likely, which would be a self-defeating argument. You may find it highly improbable that I can truly be 100% certain. What probability do you assign to me being able to assign 100% probability?
If any agent within a system were able to assign a 1 or 0 probability to any belief about that system being true, that would mean that the map-territory divide would have been broken.
However, since that agent can never rule out being mistaken about its own ontology, its reasoning mechanism, following an invisible (if vanishingly unlikely) internal failure, it can never gain final certainty about any feature of territory, although it can get arbitrarily close.