An intelligence with the power to form analogies, which maps a description of a logic onto a simpler subsystem, can form paradox because it does not perform recursion on the logic — instead, higher-order assessments simply fail to settle upon a single answer, generating contradiction in every circumstance. Paradox isn’t the rejection of opposites, it is the contradiction inevitable when accepting the truth of each statement.
Look at Russel’s paradox: “Let R be a set of all sets which are not members of themselves.” If R contains itself, then it must be removed from R. If R is removed from R, then it must be placed back in. There is never a moment of truth. A computer, consequently, cannot manage paradox. It stalls. We don’t.
We accept the first premise, and find that it yields a contradiction. Then, we accept the alternate premise as true, and find that it also forms a contradiction. Because both possible states generate a contradiction, we call this a paradox — without needing to settle on a singular truth. We never ‘hold’ the paradox entirely; we accept one or the other premise as true. This lack of recursion is what allows us to contemplate Godelian logic-enumeration. If we truly recursed upon paradoxical logics, we would be unable to utilize them.