Source : Webster's Revised Unabridged Dictionary (1913)

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

         Infallibility is the highest perfection of the knowing
         faculty.                                 --Tillotson.

   {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.

Source : WordNet®

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