# soundness

## English

### Etymology

From Middle English soundenes, soundnes, from Old English *sundnes, *ġesundnes (attested in onsundnes), from Proto-West Germanic *sundnassī (soundness, health); equivalent to sound +‎ -ness. Cognate with West Frisian sûnens (soundness, health), Middle Low German suntnisse (soundness, health), Middle High German suntnisse (soundness, health), German Gesundnis (health).

### Noun

soundness (countable and uncountable, plural soundnesses)

1. (uncountable) The state or quality of being sound.
2. (countable) The result or product of being sound.
3. (logic) The property (of an argument) of not only being valid, but also of having true premises.
4. (logic) The property of a logical theory that whenever a wff is a theorem then it must also be valid. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever ${\displaystyle T\vdash \phi }$ is true, then ${\displaystyle T\vDash \phi }$ must also be true, for any wff φ of logic L.