Soundness

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 "X₁...X_n ⊢ Y", then also "X₁...X_n ⊨ Y"

Sound arguments

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

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.

See also: Soundness, Logical argument, Natural deduction, Syllogism, Tautology, Truth, Validity