The Collaborative International Dictionary of English v.0.48:

Infallibility \In*fal`li*bil"i*ty\, n. [Cf. F.
   infaillibilit['e].]
   The quality or state of being infallible, or exempt from
   error; inerrability.
   [1913 Webster]

         Infallibility is the highest perfection of the knowing
         faculty.                                 --Tillotson.
   [1913 Webster]

   Papal infallibility (R. C. Ch.), the dogma that the pope
      can not, when acting in his official character of supreme
      pontiff, err in defining a doctrine of Christian faith or
      rule of morals, to be held by the church. This was decreed
      by the Ecumenical Council at the Vatican, July 18, 1870.
      [1913 Webster]

WordNet (r) 3.0 (2006):

infallibility
    n 1: the quality of never making an error [ant: fallibility]

Moby Thesaurus II by Grady Ward, 1.0:

45 Moby Thesaurus words for "infallibility":
   absolute certainty, absoluteness, assurance, assuredness,
   certain knowledge, certainness, certainty, certitude, chastity,
   dead certainty, defectlessness, definiteness, determinacy,
   determinateness, faultlessness, finish, flawlessness,
   immaculateness, impeccability, ineluctability, inerrability,
   inerrancy, inevitability, infallibilism, necessity, nonambiguity,
   noncontingency, perfection, positiveness, predestination,
   predetermination, probatum, proved fact, purity, sinlessness,
   spotlessness, stainlessness, sureness, surety, taintlessness,
   truth, unambiguity, unequivocalness, univocity, unmistakableness