# Validity

In logic, an argument is said to be*valid*(noun:

**validity**) 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.

Bear in mind that 'valid' is a technical term in logic: this is a perfectly valid argument. What does that mean, in this example? Something like this: suppose it were *true* that all dogs had eight legs; and suppose, just suppose, that the President really were a dog; well, in that absurd imaginary world, the President would have to have eight legs. The conclusion *has* to be true, if the premises are true. So the argument is valid, even though it has false premises, not to mention a false conclusion.

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.

*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*.

One can see whether the premises make the conclusion necessary *just* *by* *looking* *at* *the* *form* *of* *the* *argument*. That is why argument form is so important. Look, for example, at the following argument form. In fact, *any* argument that follows this form is valid. You can see that just by reading it:

- All S is P.
*a*is S.*Therefore*,*a*is P.

Now examine the following argument. It fits that form and is (therefore) valid:

- All dogs are canines.
- Fido is a dog.
*Therefore*, Fido is a canine.

Validity is a basic, essential notion in logic, since it is a basic requirement for an argument to be good. But validity by itself is not enough to make an argument good. True premises are needed in addition. So suppose we have a valid argument with true premises. Then, we will say, we have a *sound* argument.

*See also:* validity (psychometric).