unreconcilable

adj

1. Irreconcilable.

   “But yet let me lament […] that our stars, / Unreconcilable, should divide / Our equalness to this.”

   “Kant's embrace of an unreconcilable contradiction at the foundation of human experience is not a turn to irrationalism; indeed, it is hard to imagine a more rigorous and rational thinker than Kant.”

noun

1. A person or thing that cannot be reconciled.

   “Rather than the beginning of a new era of calm and prosperity for Afghans, a peace deal with the Taliban will split the movement, divide the reconcilable elements of the insurgency with the unreconcilables who see compromise as capitulation, and provide a small Islamic State faction in the country with the men and support they need to grow.”