The Collaborative International Dictionary of English v.0.48:

Singularity \Sin`gu*lar"i*ty\
   (s[i^][ng]`g[-u]*l[a^]r"[i^]*t[y^]), n.; pl. Singularities
   (s[i^][ng]`g[-u]*l[a^]r"[i^]*t[i^]z). [L. singularitas: cf.
   F. singularit['e].]
   1. The quality or state of being singular; some character or
      quality of a thing by which it is distinguished from all,
      or from most, others; peculiarity.
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            Pliny addeth this singularity to that soil, that the
            second year the very falling down of the seeds
            yieldeth corn.                        --Sir. W.
                                                  Raleigh.
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            I took notice of this little figure for the
            singularity of the instrument.        --Addison.
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   2. Anything singular, rare, or curious.
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            Your gallery
            Have we passed through, not without much content
            In many singularities.                --Shak.
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   3. Possession of a particular or exclusive privilege,
      prerogative, or distinction.
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            No bishop of Rome ever took upon him this name of
            singularity [universal bishop].       --Hooker.
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            Catholicism . . . must be understood in opposition
            to the legal singularity of the Jewish nation. --Bp.
                                                  Pearson.
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   4. Celibacy. [Obs.] --Jer. Taylor.
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WordNet (r) 3.0 (2006):

singularity
    n 1: the quality of being one of a kind; "that singularity
         distinguished him from all his companions" [syn:
         singularity, uniqueness]
    2: strangeness by virtue of being remarkable or unusual

Moby Thesaurus II by Grady Ward, 1.0:

145 Moby Thesaurus words for "singularity":
   aberration, abnormality, absurdity, anomaly, anticness, aroma,
   attribute, badge, bizarreness, bizarrerie, black hole, brand,
   cachet, cast, character, characteristic, combination, conceit,
   configuration, crackpotism, crank, crankiness, crankism, crotchet,
   crotchetiness, curiousness, cut, deformity, deviancy, deviation,
   differentia, differential, differentiation, differentness,
   distinctive feature, distinctiveness, divergence, dottiness,
   earmark, eccentricity, egohood, erraticism, erraticness,
   fantasticality, feature, figure, flavor, freakiness, freakishness,
   fusion, grotesqueness, grotesquerie, gust, hallmark, human factor,
   identity, idiocrasy, idiosyncrasy, impress, impression, index,
   individualism, individuality, indivisibility, intactness,
   integrality, integration, integrity, inviolability, irreducibility,
   irregularity, keynote, kink, lineaments, maggot, malformation,
   mannerism, mark, marking, mold, monstrosity, monstrousness, nature,
   nominalism, nonconformity, oddity, oddness, odor, oneness,
   organic unity, outlandishness, particularism, particularity,
   peculiarity, personal equation, personal identity, personality,
   personship, property, purity, quaintness, quality, queerness, quip,
   quirk, quirkiness, savor, seal, self-identity, selfhood, selfness,
   selfsameness, shape, simplicity, singleness, smack, solidarity,
   solidification, solidity, soul, specialty, stamp, strangeness,
   taint, tang, taste, teratism, token, trait, trick, twist,
   uncommonness, unconventionality, undividedness, unification,
   uniformity, uniqueness, unity, univocity, unnaturalness, weirdness,
   whim, whimsicality, whimsy, wholeness