The Collaborative International Dictionary of English v.0.48:

Contrariety \Con`tra*ri"e*ty\n.; pl. Contrarieties. [L.
   contrarietas: cf. F. contrari['e]t['e].]
   1. The state or quality of being contrary; opposition;
      repugnance; disagreement; antagonism.
      [1913 Webster]

            There is a contrariety between those things that
            conscience inclines to, and those that entertain the
            senses.                               --South.
      [1913 Webster]

   2. Something which is contrary to, or inconsistent with,
      something else; an inconsistency.
      [1913 Webster]

            How can these contrarieties agree?    --Shak.

   Syn: Inconsistency; discrepancy; repugnance.
        [1913 Webster]

WordNet (r) 3.0 (2006):

contrariety
    n 1: the relation between contraries