The Collaborative International Dictionary of English v.0.48:

Impossibility \Im*pos`si*bil"i*ty\, n.; pl. Impossibilities.
   [L. impossibilitas: cf. F. impossibilit['e].]
   1. The quality of being impossible; impracticability.
      [1913 Webster]

            They confound difficulty with impossibility.
                                                  --South.
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   2. An impossible thing; that which is not possible; that
      which can not be thought, done, or endured.
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            Impossibilities! O, no, there's none. --Cowley.
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   3. Inability; helplessness. [R.] --Latimer.
      [1913 Webster]

   Logical impossibility, a condition or statement involving
      contradiction or absurdity; as, that a thing can be and
      not be at the same time. See Principle of Contradiction,
      under Contradiction.
      [1913 Webster]

WordNet (r) 3.0 (2006):

impossibility
    n 1: incapability of existing or occurring [syn:
         impossibility, impossibleness] [ant: possibility,
         possibleness]
    2: an alternative that is not available [syn: impossibility,
       impossible action]

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

IMPOSSIBILITY. The character of that which. cannot be done agreeably to the
accustomed order of nature.
     2. It is a maxim that no one is bound to perform an impossibility. A
l'impossible nul n'est tenu. 1 Swift's Dig. 93; 6 Toull. n. 121, 481.
     3. As to impossible conditions in contracts, see Bac. Ab. Conditions,
M; Co. Litt. 206; Roll. Ab. 420; 6 Toull. n. 486, 686; Dig. 2, 14, 39; Id.
44, 7, 31; Id. 50, 17, 185; Id. 45, 1, 69. On the subject of impossible
conditions in wills, vide 1 Rop. Leg. 505; Swinb. pt. 4, s. 6; 6 Toull. 614.
Vide, generally, Dane's Ab. Index, h.t.; Clef des Lois Rom. par Fieffe
Lacroix, h.t.; Com. Dig. Conditions, D 1 & 2; Vin. Ab. Conditions, C a, D
a, E a.