The Collaborative International Dictionary of English v.0.48:

Antinomy \An*tin"o*my\ (?; 277), n.; pl. Antinomies. [L.
   antinomia, Gr. ?; 'anti` against + ? law.]
   1. Opposition of one law or rule to another law or rule.
      [1913 Webster]

            Different commentators have deduced from it the very
            opposite doctrines. In some instances this apparent
            antinomy is doubtful.                 --De Quincey.
      [1913 Webster]

   2. An opposing law or rule of any kind.
      [1913 Webster]

            As it were by his own antinomy, or counterstatute.
                                                  --Milton.
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   3. (Metaph.) A contradiction or incompatibility of thought or
      language; -- in the Kantian philosophy, such a
      contradiction as arises from the attempt to apply to the
      ideas of the reason, relations or attributes which are
      appropriate only to the facts or the concepts of
      experience.
      [1913 Webster]

WordNet (r) 3.0 (2006):

antinomy
    n 1: a contradiction between two statements that seem equally
         reasonable

Moby Thesaurus II by Grady Ward, 1.0:

26 Moby Thesaurus words for "antinomy":
   ambiguity, ambivalence, asymmetry, disproportion,
   disproportionateness, equivocality, equivocation, heresy,
   heterodoxy, heterogeneity, incoherence, incommensurability,
   incompatibility, incongruity, inconsistency, inconsonance, irony,
   irreconcilability, nonconformability, nonconformity, oxymoron,
   paradox, self-contradiction, unconformability, unconformity,
   unorthodoxy