inconsistency

1. The state or quality of being inconsistent.
2. Something inconsistent: many inconsistencies in your proposal.

noun

A marked lack of correspondence or agreement: difference, disagreement, discrepance, discrepancy, disparity, gap, incompatibility, incongruity. See agree/disagree.

The noun has 2 meanings:

Meaning #1: the relation between propositions that cannot both be true at the same time
  Synonyms: incompatibility, mutual exclusiveness, repugnance

Meaning #2: the quality of being inconsistent and lacking a harmonious uniformity among things or parts
  Antonym: consistency (meaning #2)

Quotes:

"Mutability of temper and inconsistency with ourselves is the greatest weakness of human nature." - Joseph Addison

"No author ever drew a character consistent to human nature, but he was forced to ascribe to it many inconsistencies." - Edward G. Bulwer-Lytton