The Collaborative International Dictionary of English v.0.48:

Aloneness \A*lone"ness\, n.
   A state of being alone, or without company; solitariness.
   [R.] --Bp. Montagu.
   [1913 Webster]

WordNet (r) 3.0 (2006):

aloneness
    n 1: a disposition toward being alone [syn: aloneness,
         loneliness, lonesomeness, solitariness]