Noah Webster
Unreconcilable
UNRECONCI'LABLE,
1. That cannot be reconciled; that cannot be made consistent with; as two unreconcilable propositions. [In this sense, irreconcilable is generally used.]
2. Not reconcilable; not capable of being appeased; implacable.
3. That cannot be persuaded to lay aside enmity or opposition, and to become friendly or favorable; as unreconcilable neighbors.
[Irreconcilable is generally used.]