NOUN (3)

1. a condition of damage or decay;

2. a misconception that is fallacious and not true or valid;
- Example: "the unsoundness of his conclusion was obvious"

3. not mentally or physically healthy;
- Example: "no one can be a poet without a certain unsoundness of mind"

The Collaborative International Dictionary of English v.0.48:

Unsound \Un*sound"\, a.
   Not sound; not whole; not solid; defective; infirm; diseased.
   [1913 Webster] -- Un*sound"ly, adv. -- Un*sound"ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unsoundness
    n 1: a condition of damage or decay [ant: soundness]
    2: a misconception that is fallacious and not true or valid;
       "the unsoundness of his conclusion was obvious"
    3: not mentally or physically healthy; "no one can be a poet
       without a certain unsoundness of mind" [ant: firmness,
       soundness, wisdom, wiseness]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

UNSOUNDNESS. Vide Crib-biting; Roaring; Soundness.