The Collaborative International Dictionary of English v.0.48:

Singleness \Sin"gle*ness\, n.
   1. The quality or state of being single, or separate from all
      others; the opposite of doubleness, complication, or
      multiplicity.
      [1913 Webster]

   2. Freedom from duplicity, or secondary and selfish ends;
      purity of mind or purpose; simplicity; sincerity; as,
      singleness of purpose; singleness of heart.
      [1913 Webster]

WordNet (r) 3.0 (2006):

singleness
    n 1: without hypocrisy; "the singleness of his motives could not
         be questioned" [syn: singleness, straightforwardness]
    2: the quality of concentrating on one central objective; "his
       singleness of purpose"

Moby Thesaurus II by Grady Ward, 1.0:

63 Moby Thesaurus words for "singleness":
   aloneness, bachelordom, bachelorhood, bachelorism, bachelorship,
   celibacy, combination, continence, elementarity, fundamentality,
   fusion, homogeneity, identity, individuality, indivisibility,
   intactness, integrality, integration, integrity, inviolability,
   irreducibility, loneliness, loneness, lonesomeness, maidenhead,
   maidenhood, misogamy, misogyny, monachism, monasticism, monism,
   oneness, organic unity, particularity, plainness, purity,
   selfsameness, severity, simpleness, simplicity, single blessedness,
   single state, singularity, solidarity, solidification, solidity,
   solitariness, solitude, spinsterhood, starkness, unadulteration,
   undividedness, unification, uniformity, uniqueness, unity,
   univocity, unmixedness, unsophistication, unwed state,
   virgin state, virginity, wholeness