the world > relative properties > order > disorder > disharmony or incongruity > [adjective] > irreconcilable (4)
Not reconcilable; = irreconcilable, adj. 1 2.
Incapable of being conciliated or reconciled; irreconcilable.
Of statements, ideas, etc.: That cannot be brought into harmony or made consistent; incompatible. Const. to, with.