The Collaborative International Dictionary of English v.0.48:

Universality \U`ni*ver*sal"i*ty\, n.; pl. Universalties. [Cf.
   F. universalit['e].]
   The quality or state of being universal; unlimited extension
   or application; generality; -- distinguished from
   particularity; as, the unversality of a proposition; the
   unversality of sin; the unversality of the Deluge.
   [1913 Webster]

WordNet (r) 3.0 (2006):

universality
    n 1: the quality of being universal; existing everywhere [syn:
         universality, catholicity]