jimrandomh comments on 0 And 1 Are Not Probabilities - Less Wrong
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Self-referential hypotheses do not always map to truth values, and "a rational mind will assign at least one hypothesis the status of absolute certainty" is self-referential. The contradiction you've encountered arises from using a statement isomorphic to "this statement is false" and requiring it to have a truth value, not to a problem with excluding 0 and 1 as probabilities.