Source : Webster's Revised Unabridged Dictionary (1913)

Purposeless \Pur"pose*less\, a.
   Having no purpose or result; objectless. --Bp. Hall. --
   {Pur"pose*less*ness}, n.

Source : WordNet®

purposelessness
     n : the quality of lacking any definite purpose [syn: {aimlessness}]
         [ant: {purposefulness}]