Unformatted text preview: LP L 2.22 R I K SENGUPTA The argument is not valid. So obviously it is not sound. The following is an informal counterexample to it. Let's consider this situation: There are 10,000 people in the world who know how to program a computer. Since anyone who knows how to program a computer is a computer scientist, these 10,000 people are all computer scientists. There are 5,000 other computer scientists, who do not know how to program a computer. Since each person in the world can either program a computer or not program one, so each computer scientist can also either program a computer or not program one, as computer scientists are people too; thus we have accounted for all computer scientists in the world, who number 15,000 (10,000 programmers + 5,000 non-programmers). These computer scientists are all r ich, but it is not necessary that all r ich people are computer scientists. Let Bill Gates be a r ich person who is not one of these 15,000; so he is for instance a r ich chartered accountant (we assume that if a person X is a chartered accountant, he is not a computer scientist, and if a person is a computer scientist, he is not a chartered accountant). So in this case, all the premises are t rue, as the arguments are based upon these very same premises. But the conclusion is clearly not t rue, as Bill Gates is not a computer scientist, so he obviously does not know how to program a computer (if he did know, then our assumption would lead to the logical conclusion that Bill Gates is a computer scientist, something which is not t rue, as we showed just now). This is a valid, informal counterexample to the argument. ...
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This note was uploaded on 05/03/2010 for the course PHI 201 at Princeton.