Source : Webster's Revised Unabridged Dictionary (1913)

Inconsequent \In*con"se*quent\, a. [L. inconsequens: cf. F.
   incons['e]quent. See {In-} not, and {Consequent}.]
   Not following from the premises; not regularly inferred;
   invalid; not characterized by logical method; illogical;
   arbitrary; inconsistent; of no consequence.

         Loose and inconsequent conjectures.      --Sir T.
                                                  Browne.

Source : WordNet®

inconsequent
     adj : lacking worth or importance; "his work seems trivial and
           inconsequential"; "the quite inconsequent fellow was
           managed like a puppet" [syn: {inconsequential}]