------------------------------------------------------------------------ Subject: MORE ABOUT VALIDITY ------------------------------------------------------------------------ A student writes: | Consider an argument where some premises may be true and some may be | false, but the conclusion is false. From my understanding that would | be a valid argument because some of the premises are false and the | conclusion is false, therefore the argument is valid. Is this approach | correct? An argument is valid if and only if it is *necessarily* "truth-preserving", i.e., if & only if it's *impossible* for all premises to be true but the conclusion false. Note that this has nothing at all to do with whether any of the premises actually *are* true or false; it's a "what if" kind of situation. So you can have an argument with false premises and a false conclusion that's valid, and you can have one like that that's invalid. Here's a valid one: All cats are fish. All fish can fly. .'. All cats can fly. Here, everything's false, but the argument is valid. It's valid because it has the form: All Ps are Qs. All Qs are Rs. .'. All Ps are Rs. and there's no way for a P to be a Q, and a Q to be an R, without having the P be an R. I.e., it's impossible for the premises to be true and the conclusion to be false. Here's an invalid one: All cats are fish. All cats can fly. .'. All fish can fly. Again, everything's false; moreover, the argument is invalid. It's invalid, because it has the form: All Ps are Qs. All Ps are Rs. .'. All Qs are Rs. and an example of an argument with this form that has true premises and a false conclusion is this one: All cats are mammals. All cats purr. .'. All mammals purr. So, it's *possible* for this argument (form) to have true premises and a false conclusion; hence, it's not valid. Missing premises can *sometimes* make an invalid argument valid, as we saw in PP1. In other cases of invalid arguments, no missing premises will help; for an example, look at the invalid argument above. One more point: An argument with *inconsistent* premises (i.e., premises that contradict each other) is always valid(!), because it's impossible for it to have all true premises with a false conclusion, and that's because it's impossible for it to have all true premises, period. Of course, such an argument cannot be sound.