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inconsistency (n.)

1640s, "something which is inconsistent;" 1650s as "quality of being inconsistent," from in- (1) "not, opposite of" + consistency. Related: Inconsistencies. Inconsistence (1630s) is marked "Now rare or Obs." in OED.

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Definitions of inconsistency from WordNet

inconsistency (n.)
the relation between propositions that cannot both be true at the same time;
Synonyms: incompatibility / mutual exclusiveness / repugnance
inconsistency (n.)
the quality of being inconsistent and lacking a harmonious uniformity among things or parts;
From wordnet.princeton.edu