Soundness in Logic { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies, and introductions to philosophers, and explanations on a number of topics. Accredited homeschooling online at Northgate Academy and Philosophy online tutoring.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WTI offers immigration law course online - fully accredited. ACE credits online at EES.



Philosophy Topics





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.