Source : Webster's Revised Unabridged Dictionary (1913)

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.

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

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

            How can these contrarieties agree?    --Shak.

   Syn: Inconsistency; discrepancy; repugnance.

Source : WordNet®

contrariety
     n : the relation between contraries