1) Characteristic 2) Incurableness 1) Incurableness 
• (n.) The state of being uncurable; irremediableness.
In·cur`a·bil'i·ty noun [ Confer French incurabilité incurability, Late Latin incurabilitas negligence.] The state of being incurable; irremediableness. Harvey. 
[n] - incapability of being cured or healed 2. [n] - incapability of being altered in disposition or habits
incurability 1. The condition in which a cure is impossible; not curable: an incurable disease. 2. Incapable of being altered, as in disposition or habits.
noun incapability of being cured or healed