Unreconcilable

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

Source: wiktionary

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.

Source: wiktionary

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.

Source: wiktionary