dxu comments on Infinite Certainty - Less Wrong
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(Note: This comment is not really directed at Paul himself, seeing as he's long gone, but at anyone who shares the sentiments he expresses in the above comment)
Note that there is almost certainly at least one person out there who is insane, drugged up, or otherwise cognitively impaired, who believes that the Law of Non-Contradiction is in fact false, is completely and intuitively convinced of this "fact", and who would sneer at any mathematician who tried to convince him/her otherwise, before walking away. Do you in fact assign 100% probability to the hypothesis that you are not that drugged-up person?