Source : Webster's Revised Unabridged Dictionary (1913)

Inconsequence \In*con"se*quence\, n. [L. inconsequentia: cf. F.
   incons['e]quence.]
   The quality or state of being inconsequent; want of just or
   logical inference or argument; inconclusiveness. --Bp.
   Stillingfleet.

         Strange, that you should not see the inconsequence of
         your own reasoning!                      --Bp. Hurd.

Source : WordNet®

inconsequence
     n : having no important effects or influence [ant: {consequence}]