Deductive Logic: Validity and Soundness
Deductive arguments are evaluated in terms of their validity and soundness. It is possible to have a deductive argument that is logically valid but is not sound.
An argument is valid if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises, whatever they may be, are true. An argument can be valid even though the premises are false.
An argument is sound if it is valid and the premises are true.
The following is an example of an argument that is valid, but not sound:
- Everyone who eats steak is a quarterback.
- John eats steak.
- Therefore, John is a quarterback.
The example's first premise is false – there are people who eat steak and are not quarterbacks – but the conclusion must be true, so long as the premises are true (i.e. it is impossible for the premises to be true and the conclusion false). Therefore the argument is valid, but not sound.
In this example, the first statement uses categorical reasoning, saying that all steak-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.
Deductive reasoning can be contrasted with inductive reasoning, in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is "valid", it is possible for the conclusion to be false (determined to be false with a counterexample or other means).
Read more about this topic: Deductive Reasoning
Famous quotes containing the words validity and/or soundness:
“The hardiest skeptic who has seen a horse broken, a pointer trained, or has visited a menagerie or the exhibition of the Industrious Fleas, will not deny the validity of education. “A boy,” says Plato, “is the most vicious of all beasts;” and in the same spirit the old English poet Gascoigne says, “A boy is better unborn than untaught.””
—Ralph Waldo Emerson (1803–1882)
“Men are qualified for civil liberty in exact proportion to their disposition to put moral chains upon their own appetites; in proportion as their love to justice is above their rapacity; in proportion as their soundness and sobriety of understanding is above their vanity and presumption; in proportion as they are more disposed to listen to the counsels of the wise and good, in preference to the flattery of knaves.”
—Edmund Burke (1729–1797)