Shutter Island

there is a  man who have psychosis,he want to find the man who killed his wife.unfortunately,the person who killed his wife is himself.The doctor want to treat him without surgery.he think he is teddy,with chuck,he is finding andrew,but he is daniels,all these three people is himself.at the end, he realize he killed his wife,and he choose to do the surgery,and says"Which would be worse? To live as a monster, or die as a good man?"