Philosophy Index

Soundness

The term sound is most frequently used to describe whether or not an argument is valid and has true premises, thereby guaranteeing the truth of its conclusion. In meta-logic, it is also used to describe a feature of a logical system.

Soundness of arguments

An argument that is sound is one that is both valid, and has all true premises. Therefore, by definition, a sound argument has a true conclusion.

Soundness of logical systems

A logical system, or simply a “logic” is said to be sound when anything that can be proven in the system actually follows. That is, if we assume a set of formulas (Γ) and some conclusion (φ), then in a sound system any relationship of provability is accompanied by a relationship of implication.

Formally, a logic is sound if, and only if, when Γ ⊢ φ, then it is also the case that Γ ⊨ φ.

Soundness is an important property of a logical system, because in a system that is not sound, one can prove things that do not actually follow. For example, one could potentially prove a logical fallacy to be valid in that system.