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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]