The term "Valid" refers to arguments, not to statements. Validity concerns the relationship between the premises and the conclusion, and not the actual truth values of the component statements at all. That is, it has to do with what combinations of truth values for premises and conclusion an argument will permit, not with what combinations actually do occur. So the fact that an argument has true premises plus a true conclusion does not tell us whether it is valid or not, since it does not answer the question of whether true premises plus false conclusion is a possibility for this argument (for some arguments it is, for others not.) The combination of false premises and false conclusion likewise does not give us a verdict about the validity of the argument- since it doesn't tell us whether the combination of true premises and false conclusion is a possibility. The combination of true premises and a false conclusion does tell us about the validity of the argument, since it does answer the relevant question. And since the answer is "Yes, this argument permits the combination of true premises and a false conclusion," the verdict is "No, this argument is not valid, since a valid argument would not permit that combination."
"Valid", then, is not a synonym for "Good"-- some valid arguments don't have a bit of truth in them, and some valid arguments composed totally of true statements are nevertheless worthless. All that its being valid tells us is that when and if the premises of this argument are ever all true, the conclusion is guaranteed to be true too. A valid argument is like a strong yet portable bridge: if you make sure that the premises are firmly planted on the truth, you can be sure that it will carry you over to a conclusion that is true too. If you proceed from false premises, however, there's no telling where the argument may take you.
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Last modified: 03/02/04