The Collaborative International Dictionary of English v.0.48:

Purposeless \Pur"pose*less\, a.
   Having no purpose or result; objectless. --Bp. Hall. --
   Pur"pose*less*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

purposelessness
    n 1: the quality of lacking any definite purpose [syn:
         purposelessness, aimlessness] [ant: purposefulness,
         sense of purpose]