I think you can be a peaceful nut-case though. I am the living proof ;-)
No seriously though, "peace of mind" and "madness" or insanity are not necessarily contrary to one another.
Peace of mind can just as easily be interpreted as "comfort within one's madness."
"The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."
Niels Bohr
Austrian physicist Wolfgang Pauli once dismissed a muddled analysis of a physics problem saying, "It's not right. It's not even wrong."