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Make the insanity questionable. Think of Macbeth, he falls into madness as the play goes on but he might not be diagnosable. "Insanity" can be brought upon by something other than a mental illness....
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/31567 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Make the insanity questionable. Think of Macbeth, he falls into madness as the play goes on but he might not be diagnosable. "Insanity" can be brought upon by something other than a mental illness. The villain can be tormented by his past and hell-bent on some other goal which he's just using to try and deal with the old trauma. The villain can become a nihilist and expressing how nothing matters good or bad everything is relative and it doesn't matter if he kills a woman or loves her. (Ex. Hamlet: "Nothing is good or bad but thinking makes it so.") The villain could be a fanatic of some sort of ideology or ideals, even if the ideology is well intentioned, the villain followed it to its natural conclusion and brought great suffering. (Ex. Government/Socialism/Communism) Try to make the villain's insanity somewhat logical so the audience can understand them and see the villain in themselves.