An argument is valid when it is impossible for its premises to be true and its conclusion to be false, or, to put it another way, if the premises were true the conclusion would have to be true, or again, the conclusion follows necessarily from the premises.
An argument can be valid even though the premises are false. Note, for example, that the conclusion of the following argument would have to be true if the premises were true, (even though they are, in fact, false):
- →All fire-breathing rabbits live on Earth
- →All humans are fire-breathing rabbits
- →(Therefore,) all humans live on Earth
The argument, however, is not sound. In order for a deductive argument to be sound, it must not only be valid, the premises must be true as well.