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Soundness
 

Information About

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 ). Formally: a system is sound when if "X_1...X_n dash Y", then also "X_1...X_n \models 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.