(This article discusses the soundess notion of informal logic. For soundess in mathematical logic see the entry on the soundness theorem.) Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... The soundness theorem is a theorem in mathematical logic stating for a given system of inference rules and system of axioms satisfying certain conditions, any first-order formula that is provable is universally valid. ...

A logical argument is sound if and only if An argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ...

1. the argument is valid
2. all of its premises are true.

A proof procedure (e.g. natural deduction) for a logic is sound if it proves only valid formulas (also tautologies). Formally: a system is sound when if "X₁...X_n ⊢ Y", then also "X₁...X_n ⊨ Y" In logic, an argument is said to be valid if the truth of the conclusion follows from the truth of the premises. ... This article is primarily concerned with truth as it is used in the evaluation of propositions, sentences, and similar items. ... In mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. ... In logic, an argument is said to be valid if the truth of the conclusion follows from the truth of the premises. ... In logic, a tautology is a statement which is true by its own definition. ...

Sound arguments

Suppose we have a sound argument (in this case a syllogism): In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ...

All men are mortal.

Isaac Newton is a man.

Therefore, Isaac Newton is mortal.

The argument is valid and since the premises are in fact true, the argument is sound.

The following argument is valid but not sound:

All animals can fly.

Pigs are animals.

Therefore, pigs can fly.

Since the first premise is actually false, the argument, though valid, is not sound.