Source : Webster's Revised Unabridged Dictionary (1913)

Incurability \In*cur`a*bil"i*ty\, n. [Cf. F. incurabilit['e]
   incurability, LL. incurabilitas negligence.]
   The state of being uncurable; irremediableness. --Harvey.

Source : WordNet®

incurability
     n 1: incapability of being cured or healed [syn: {incurableness}]
          [ant: {curability}, {curability}]
     2: incapability of being altered in disposition or habits; "the
        incurability of his optimism"