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phi B3

# phi B3 - PHI 103 MWF 9:40 March 5 2008 Set B Paper Topic 3...

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PHI 103 MWF 9:40 March 5, 2008 Set B: Paper Topic 3 In this paper, I will be discussing the validity and soundness of the following argument: An argument has a true conclusion or it does not. An argument has a true conclusion only if it has a tautology as a conclusion. If it has a tautology as a conclusion, then it is both valid and sound. An argument is invalid, if it has a false conclusion. If an argument is invalid, then it has consistent premises. If the premises are consistent and the conclusion is a contradiction, then the argument is invalid. If an argument has a contradiction as a conclusion, then it is invalid. If an argument has a contradiction as a conclusion, then it is unsound. Thus, if an argument is valid, then it is sound. I will begin by putting the argument in standard logical form. To do this, I will provide a symbolization and a dictionary: A= an argument has a true conclusion T= an argument has a tautology as a conclusion V= an argument is valid S= an argument is sound P= an argument has consistent premises C= an argument has a contradiction as a conclusion Using this dictionary, the translation of the argument is as follows: Av~A A T T (V&S) ~A ~V

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~V P (P&C) ~V C ~V C ~S ______________ V S To prove that this argument is valid, I will use reverse truth tables. To do this, I must start with the conclusion. To prove the argument invalid, the conclusion would have to be false. V S is false only when V=t (true) and S=f (false). So far, the argument is as follows: Av~A A T T (t&f) ~A ~t ~t P (P&C) ~t C ~t C ~f ______________ t f (F) Next, we want the premises to be true, as an invalid argument must have true premises and a false conclusion. There are three ways for the first premise to be true, so I will skip over that one until we have better knowledge. I will skip to the fourth premise, because we know that V=t, so ~A ~t. “~t” symbolizes “not true.” The only way for this premise to be true with a false descendent is if the antecedent is false as well. Thus “A”
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phi B3 - PHI 103 MWF 9:40 March 5 2008 Set B Paper Topic 3...

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