Logic

Is self-contradiction still the prima facie sign of a faulty argument? How do we tell an apparent contradiction from a real contradiction if the argument is in words? (Most of us don't know how to translate arguments in words into symbolic logic.)

Comments

Most logicians would regard self-contradiction as a flaw, yes. Thereason is that a good argument is supposed to be one whose conclusionmust be true if its premises are true. If at some point in the argumenta contradiction appears, then either (i) the reasoning was bad or (ii)the premises cannot all be true. That said, however, one can usepossibilty (ii) to argue for something by what is called reductio ad absurdum:If you want to show that not-p, show that p (possibly together withother things that are agreed to be true) leads, via good reasoning, to contradiction. Then not all of the premises can be true. So if the ones other than p are, it isn't.

Now,how do you tell if you have a contradiction when the argument in words?There's no magic bullet, I'm afraid. Being able to translate intosymbolic logic only helps so much, and in the really hard cases it'llbe controversial how to do the translation, anyway. So, to a firstapproximation, you have reached a contradiction if you have reached aconclusion that cannot be true. There is more to say, to be sure, but most of it involves trying to explain what "cannot" means here.

It is perhaps worth adding that self-contradiction is not the only sign of a faulty argument. An argument can be faulty but not lead to a contradiction. For example, suppose that you know that some number x has the property that x2 = 4. If you claim that x must be 2, you have engaged in faulty reasoning. The conclusion x = 2 does not contradict the hypothesis that x2 = 4; the two statements are perfectly consistent. But your reasoning is faulty because you haven't taken into account the possibility that x might be -2.

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