Main Page | See live article | Alphabetical index An argument is sound if, and only if, (1) the argument is valid and (2) all of its premises are true. So suppose we have a sound argument: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. In this case we have an argument where, first, if the premises are all true, then the conclusion must be true (i.e., the argument is valid); and, second, it so happens that the premises are all true. It follows that the conclusion must be true. That is the nice thing about soundness: if you know an argument is sound, then you know that its conclusion is true. By definition, all sound arguments have true conclusions. So soundness is a very good quality for an argument to have. In mathematical logic, a formal deduction calculus is said to be sound with respect to a given logic (i.e. wrt its semantics) if every statement that can be derived within this calculus is a tautology of the logic. Stated differently, this says that everything that can be formally (syntactically) calculated is semantically true. The reverse condition is called completeness. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.