In Latin, it turns out that “amens” means a person without reason or mind, someone who does things for no reason, or an idiot in the classical sense. We still have a related word, “dementia,” which is the condition of a “demens,” a person who acts against reason and the mind while sure that he is still acting reasonably, much like an insane person. (Although “insanus” is yet another concept.)
This may be why so many authors in the Roman Empire who wrote against Christians would emphasize how they were not acting reasonably — purposeful punning on important concepts.
Anyway, there are lots of interesting things in The Handbook of Latin Synonymes by Doederlein, translated by H.H. Arnold. And yes, he did spell it “synonymes.”