Valid Argument Analysis - Superman and Evil Prevention
Explore a logical argument on the existence of Superman based on statements about his ability and willingness to prevent evil. By applying rules of inference and contradiction, the conclusion is drawn that Superman does not exist.
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Discrete Math: Rules of Inference Exercise 22
Exercise Determine whether this argument, taken from Kalish and Montague [KaMo64], is valid. If Superman were able and willing to prevent evil, he would do so. If Superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. Superman does not prevent evil. If Superman exists, he is neither impotent nor malevolent. Therefore, Superman does not exist.
Solution This argument is valid. We argue by contradiction. Assume that Superman does exist. Then he is not impotent, and he is not malevolent (this follows from the fourth sentence). Therefore by (the contrapositives of) the two parts of the second sentence, we conclude that he is able to prevent evil, and he is willing to prevent evil. By the first sentence, we therefore know that Superman does prevent evil. This contradicts the third sentence. Since we have arrived at a contradiction, our original assumption must have been false, so we conclude finally that Superman does not exist.
References Discrete Mathematics and Its Applications, McGraw-Hill; 7th edition (June 26, 2006). Kenneth Rosen Discrete Mathematics An Open Introduction, 2nd edition. Oscar Le in A Short Course in Discrete Mathematics, 01 Dec 2004, Edward Bender & S. Gill Williamson
