Deductive Reasoning - Deductive Logic: Validity and Soundness

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:

1. Everyone who eats steak is a quarterback.
2. John eats steak.
3. 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 This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.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).