Valid argument

A valid argument, in formal logic, one in which the conclusion is correctly derived from the premises. That is, a valid argument is one in which, if the premises are true, the conclusion must also be true. A valid argument whose premises are true is called a sound argument, and its conclusion must be true.

A valid argument whose premises are not all true is called a valid but unsound argument, and its conclusion is not necessarily true. The following is an example of a valid but unsound argument, in which one of the premises is untrue, so that the conclusion cannot be relied upon (and is wrong):

• Grass is green.
• All green things taste like limes. (untrue premise)
• Therefore, grass tastes like limes.

A deductive argument is said to be valid when the inference from premises to conclusion is perfect. Arguments and Inference: truth and validity