noun (n)

• the relation between propositions that cannot both be true at the same time(noun.linkdef)

  Synonym:
  incompatibility, mutual exclusiveness, repugnance
  

  source: wordnet30
• the quality of being inconsistent and lacking a harmonious uniformity among things or parts(noun.attribute)

  Antonym:
  consistence, consistency
  

  source: wordnet30
• The quality or state of being inconsistent; discordance in respect to sentiment or action; such contrariety between two things that both can not exist or be true together; disagreement; incompatibility.(noun)

  source: webster1913