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.
      [1913 Webster]

   2. An impossible thing; that which is not possible; that
      which can not be thought, done, or endured.
      [1913 Webster]

            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]