At this stage we can draw a distinction between sound and unsound arguments. An argument is called sound if and only if it is valid and all its premises are true. Otherwise, the argument is called unsound. The following is an example of a sound argument.

All mammals have lungs.

All rabbits are mammals.

Therefore, all rabbits have lungs.


Here all the premises are true and the argument is valid. Hence, it is a sound argument, the other hand, an argument is unsound if it is either invalid or some of its premises are false.

For example,

No mammals have lungs.

No whales are mammals.


Therefore, no whales have lungs.

Here the argument is invalid and the premises are also false. Hence it is unsound. Further, even if an argument is valid but some or all of its premises are false then also the argument is sound. Consider the following example:

No insects have six legs.

All spiders are insects.


Therefore, no spiders have six legs.

Here both the premises are false but the argument is valid. Hence, it is also an unsound argument. Thus mere validity of an argument does not make the argument sound, because there ire valid arguments those are not sound. To say that an argument is unsound amounts to the claim that the argument is either invalid or some of its premises are false.

Thus the soundness of an argument implies validity as well as the truth of all its premises. But the unsoundness of an argument does not imply invalidity, because there are unsound arguments that are valid.

At this stage the following question may be asked. Why logicians should not confine their attention only to sound arguments? The answer is, we cannot study only sound arguments though it is interesting. Because, to know an argument to be sound we must know that all its premises are true. But knowing the truth of the premises is not always possible.


Further, we are often intercoted in arguments whose premises are not known to be true. For example, when a scientist verifies a scientific hypothesis or even a theory, he or she very often deduces consequences from the hypothesis or the theory in question and compares these consequences with the data and if the result tallies then the hypothesis or the theory is verified to be true.

Here the investigator can not know the truth of the hypothesis or the theory prior to the process of testing. If the truth of theory or the hypothesis was known to the scientist prior to the verification, the verification would be pointless. This is in fact not the case.

So, to confine our attention to sound arguments only would be self-defeating. But this does not make sound arguments logically uninteresting because, if by some means, we know that an argument is sound then we may infer the truth of its conclusion.