noun (n)

• having no important effects or influence(noun.attribute)

  Antonym:
  consequence, import, moment
  

  source: wordnet30
• invalid or incorrect reasoning(noun.attribute)

  Synonym:
  illogic, illogicality, illogicalness
  Antonym:
  logicality, logicalness
  

  source: wordnet30
• The quality or state of being inconsequent; want of just or logical inference or argument; inconclusiveness.(noun)

  source: webster1913