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.
