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Kawoomba comments on How to offend a rationalist (who hasn't thought about it yet): a life lesson - Less Wrong Discussion
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In theory, yes. In practice, ... maybe. Like saying "a human can implement a bounded TM and can in principle, without tools other than paper&pencil, compute a prime number with a million digits".
It depends on how inconsistent the axioms are in practice. If the contradictions are minor, before leveraging that contradiction to derive arbitrary results, the hu-man may die of old age.
Of course, if the belief system in questions becomes popular, one of his disciples may wind up doing this.