Soundness Soundness

Soundness - Definition and Overview

Related Words: Authenticity, Authority, Balance, Benevolence, Body, Canonicity, Class, Cogency, Cool

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).

Sound Arguments

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

All men are mortal.
Socrates is a man.
Therefore, Socrates 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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