irreconcilable

adj

1. Unable to be reconciled; opposed; uncompromising.

   “[T]he fact that the peccant doctor [Sir James Clark, 1st Baronet] continued in the Queen's service made the Hastings family irreconcilable and produced an unpleasant impression of unrepentant error upon the public mind.”

2. Incompatible, discrepant, contradictory.

   “I amused myself by thinking that in his choice of books he showed pleasantly the irreconcilable sides of his fantastic nature.”

noun

1. Something that cannot be reconciled.
2. (US, dated, slang)A Confederate who moved to another country following the American Civil War, rather than live in a reunited United States.
3. (US, dated, slang)A vociferous opponent of the Treaty of Versailles.