soundness

noun

1. The condition of being free from defects or flaws: durability, firmness, integrity, solidity, stability, strength, wholeness. See better/worse.
2. The condition of being physically and mentally sound: haleness, health, healthiness, heartiness, wholeness. See health/sickness.
3. A healthy mental state: lucidity, lucidness, mind, reason, saneness, sanity, sense (often used in plural), wit (used in plural). Slang marble (used in plural). See sane/insane.
4. Reliability in withstanding pressure, force, or stress: fastness, firmness, hardness, security, stability, stableness, steadiness, strength, sturdiness, sureness. See better/worse, change/persist, continue/stop/pause.

Of an argument, the property of being valid and having all true premises. Logical systems are sound if every theorem is valid, that is, true in all interpretations.

The noun has 3 meanings:

Meaning #1: a state or condition free from damage or decay
  Antonym: unsoundness (meaning #1)

Meaning #2: the quality of being prudent and sensible
  Synonyms: wisdom, wiseness

Meaning #3: the firmness and tone of healthy tissue
  Synonym: firmness