Soundness
A logical argument is sound if and only if - the argument is valid
- 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).
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.
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