Mad Father Endings
Lets talk about the main character, Aya. Aya is a very strange character to begin with; a child knowing about her fathers 'experiments' and yet said nothing. A child who in the face of danger can do terrible things barely reacting unless startled. Someone who had to choose between her father and the mother who had tried to save her from her fathers hand, she still chooses to save this man.
Mad Father has a total of three Main Endings, and two Bonus Endings. In the first bad ending. There are seven endings in the game Ib. Various choices and actions will affect which ending the player will receive. It is recommended that the player saves often in different slots so that the player can return to previous parts of the story in order to make different choices if other endings are desired. In all the endings in which either Ib or Garry is alive, both will forget the time.
Drawing even more question is the ending of the game. In the true ending you pick up a book and you get a cut scene, of Aya grown up, having become presumably the same person as her father. A killer.
Just what is wrong with Aya? Is she even sane? Does she have an illness? Here I will go over some options and then state my conclusion.
Alexithymia
Aya is an odd character, seemingly unaffected by many things. What if Aya had alexithymia? Alexithtmia is a disorder where one is unable to express their emotions, but how would this apply to Aya?
Aya through thick and thin barely expressed directly her emotions in her flash backs, or in the current time of the game. This would have been the prime choice if it wasn't for her lack of words period. Aya may indeed have Alexithymia (Lack of words for emotions) but it isn't the main problem for her behavior.
Schizophrenia
Aya could have Schizophrenia; a disconnection from reality, hallucinations and fantasies that could have been caused from seeing her fathers horrible experiments and the victims of it.
A way to cope with it, fantasies that sorta justify what she did. Her paranoia and the new knowledge of her finding her mother dead, and the patients gave her the idea she was next.
She was as we know and was chased and was aided by Maria. The possibility is still there that since she was hallucinating the corpses coming back to life; that she had set fire to the house herself .
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Anti Social Personality Disorder (Psychopath and Sociopath)
Is Aya a psychopath? Someone with no moral code, reckless, breaking laws? She has no moral compass seemingly in many times in the game, her use of the chain saw even when dangerous or the ability to harm her or someone else.
Burning the creature blocking her path, and even in the true ending taking on the route of her father and murdering and mutilating people. Even though she exhibits these moments there is simply not enough evidence to conclude this, she doesn't exhibit many grudges where they usually are shown which would also be odd for someone with this type of disorder.
Alas they don't have to be violent, in fact according to some sources they get calmer in this situation; which matches Aya's behavior as the game continues how she can calmly react to these situations.
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Conclusion
She doesn't have a mental disorder, and she is not insane.
This is a bold claim I know, after all we see she is the same as her father in the end. Well what gave me this thought is a real life case.
Carl von Cosel fell in love with a woman who came into his care at the hospital her worked. The woman suffered from an illness which he was unable to save her from. The mans obsession with the woman lead him to eventually keep the woman's corpse in his house with him, as she decomposed he replaced parts of her with materials like silk and porcelain, a wig made of hair that had fallen out. Making this woman into a human doll.
How does this have to do with Aya? Aya and her father both create dolls out of people for the love of their beauty. Same as the man had fallen in love with the beauty of his patient.
They both had no problem being around corpses even when it came to Aya it was with killing and dismembering the bodies, but when it came to Carl it was necrophilia and replacing rotting body parts with filler pieces. I draw parallels between them and their behaviors and decided if this man had a mental order then it'd be likely Aya had one as well. Well a test was taken with no result. This man was completely sane with no outstanding mental disorder. The man had done all of this completely sane with no medication but his own thoughts. I believe Aya is the same in this matter, inspired by her fathers work.
Anyways this is just a theory after all. I hope you enjoyed this post!