A valid argument has a good link, but its premises may be false. For an argument to prove its conclusion, it needs both a good link and true starting points.
Key idea
An argument is sound when it is valid and all its premises are true. A sound argument's conclusion must be true.
Why it works
Validity says: if the premises are true, the conclusion is true. Soundness adds: and the premises are true. Put the two together and the conclusion cannot escape being true. That is why a sound argument settles a question.
| Valid? | All premises true? | Verdict |
|---|---|---|
| Yes | Yes | Sound |
| Yes | No | Valid, not sound |
| No | Yes or no | Not sound |
Worked example: Sound
"All squares are rectangles. All rectangles have four sides. So all squares have four sides."
- Valid: if both premises are true, the conclusion must be.
- Both premises are true.
Answer: Sound.
Worked example: Valid but not sound
"All birds can fly. Penguins are birds. So penguins can fly."
- Valid: the form "All B are C; A is B; so A is C" never fails.
- But "All birds can fly" is false (penguins and ostriches can't).
Answer: Valid, but not sound.
Common mistake
Thinking a true conclusion makes an argument sound. "All dogs are mammals. Rex the dog is a mammal. So Rex is a dog" has a true conclusion, but its form is invalid, so it is not sound. Check validity first, then the premises; the conclusion's truth is not a test.