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8/31/2009

Catch-22

  1. (Premise: If a person is excused from flying (E), that must be because they are both insane (I), and request an evaluation (R));
  2. (I⇒¬R) (Premise: If a person is insane (I), they should not realize that they are, and would have no reason to request an evaluation)
  3. (2, Definition of implication: since an insane person would not request an evaluation, it follows that all people must either not be insane, or not request an evaluation)
  4. (3, De Morgan: since all people must either not be insane, or not request an evaluation, it follows that no person is both insane and request an evaluation)
  5. (¬E) (4, 1, Modus Tollens: since a person may be excused from flying only if they are both insane and request an evaluation, but no person can be both insane and request an evaluation, it follows that no person can be excused from flying)
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