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.

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. WOLI offers immigration law course online - fully accredited. ACE credits online at EES.

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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.