Monday, July 13, 2009

Catch 22 - silent cages

1. $(E \Rightarrow (I \land R))$ (Premise: If a person is excused from flying (E), that must be because they are both insane (I), and request an evaluation (R));
2. $(I \Rightarrow \neg R)$ (Premise: If a person is insane (I), they should not realize that they are, and would have no reason to request an evaluation)
3. $(\neg I \lor \neg R)$ (2, Definition of implication: since an insane person would not request an evaluation, it follows that all persons must either not be insane, or not request an evaluation)
4. $(\neg (I \land R))$ (3, De Morgan: since all persons must either not be insane, or not request an evaluation, it follows that no person can be both insane and request an evaluation)
5. $(\neg E)$ (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)
"Catch 22 (logic)." Wikipedia, The Free Encyclopedia. 21 June 2009, 13:31 UTC. Wikimedia Foundation, Inc. 10 Aug. 2004.< http://en.wikipedia.org/wiki/Catch-22_(logic) >.

In short: you don't have to fly if you are insane, but to be proven insane you must request an evaluation. The very act of requesting an evaluation demonstrates your sanity so therefore you must fly!