ETYM French incurable, Latin incurabilis. Related to In- not, and Curable.
1. Being such that a cure is impossible.
2. Unalterable in disposition or habits.
3. Without hope of cure.

ETYM Latin irremediabilis: cf. French irrémédiable. Related to In- not, and Remediable.
Impossible to remedy or correct or redress.

1. In a manner impossible to cure.
2. To an incurable degree.

In a manner, or to a degree, that precludes remedy, cure, or correction.