Unformatted text preview: EXTRA CRED I T R I K SENGUPTA There is no way that the addition of an extra premise will validate an argument if one of the original premises actually contradicts the conclusion, i.e. if a premise negates the t ruth of the conclusion, then the addition of any number of extra premises will not make the argument valid. In general, the premises have to be such that P1, P2, ..., Pn, and S (the conclusion we are t rying to reach) can be t rue together, but P1, P2, ..., Pn do not necessarily guarantee the t ruth of S. This is usually achieved by a premise of the "OR" type, i.e. either A \/B, or (A/ \ B), and another premise C, with a conclusion of an "AND" type, such as "C/ \A" or "C/ \ A" and so on. In all these cases, there are possibilities that P1 and P2 are t rue together, but C does not follow from them. So in these cases, the addition of an extra premise P3 that determines the t ruth value of one of the elements in the premise containing the "OR" term WITHOUT conflicting with the conclusion usually renders the argument valid as well. So for instance: P1: Men or Gods are mortal. P2: Animals other than men are also mortal. C: Men and other animals are mortal. This is an example of an invalid argument, because for all we know, Gods can be immortal, and men can be mortal; the premises will still be t rue but the conclusion will be false. But the addition of an extra premise P3 renders i t valid. P1: Men or Gods are mortal. P2: Animals other than men are also mortal. P3: Men are mortal. C: Men and other animals are mortal. Note that P3 could also have been "Gods are not mortal". ...
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This note was uploaded on 05/03/2010 for the course PHI 201 at Princeton.