In classical two-valued logic, an argument is said to have validity or to be valid if, and only if, it is the case that, if the premises of the argument are true, then the conclusion must be true. In other words, a valid argument is one where the premises make the conclusion true. There are many other ways to formulate this basic definition: the premises entail the conclusion; it cannot be the case both that the premises are true and the conclusion false; the falsehood of the conclusion entails the falsehood of at least one premise; etc.
A close examination of the definition of 'valid' should make a few things clear about validity. The definition says neither that the premises have to be true nor that that the conclusion has to be true. Validity is a conditional notion: what it says is that if the premises happen to be true, then the conclusion has to be true. As far as validity is concerned the premises might be completely and obviously false. Consider an example of a valid argument:
- All dogs have eight legs.
- The President is a dog.
- Therefore, the President has eight legs.
Validity is not to be confused with soundness; a sound argument is not only valid, its premises are true as well. Not all valid arguments are valid in the loose and popular sense of this word, meaning 'good': not all valid arguments (valid, as this term is used in logic) are good, or successful, as the above example should show.
Argument form is what makes an argument valid. But a valid argument is one where, if the premises are true, then the conclusion must be true (and here is a way to put it more briefly: the premises make the conclusion necessary). Now put these two propositions together and draw a conclusion:
- Form makes an argument valid.
- If an argument is valid, then the premises make the conclusion necessary.
- Form makes an argument such that the premises make the conclusion necessary.
- All S is P.
- a is S.
- Therefore, a is P.
- All dogs are canines.
- Fido is a dog.
- Therefore, Fido is a canine.
In psychometrics, a valid measure is one that measures what it is supposed to measure. For example, a valid measure of mathematical problem-solving measures mathematical ability rather than the verbal ability necessary to understand complicated statements of mathematical problems. See Validity (psychometric).