Most dementedly is a descriptor that refers to extreme madness or insanity. Its antonyms, therefore, would be words that describe the absence of madness or insanity. Words like sanely, rationally, wisely, sensibly, and prudently could be used in place of most dementedly. These words reflect a degree of soundness of mind, which is the opposite of the mental instability and irrationality that the term most dementedly connotes. By choosing these antonyms, we are explicitly stating that the behavior or thought patterns in question are not insane, but rather are grounded in logic and reason, making them more acceptable and common.