This article discusses the soundness notion of informal logic. For soundness in mathematical logic see the entry on the soundness theorem.

A logical argument is sound if and only if

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 "$X\_1...X\_n\; \backslash vdash\; Y$", then also "$X\_1...X\_n\; \backslash models\; Y$".

Sound arguments

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Suppose we have a sound argument (in this case a syllogism):

All Greeks are men.

Socrates is Greek.

Therefore, Socrates is a man.

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.

Logic

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