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As others have pointed out, since you are in the main character's head, it's very hard to hide the fact that she feels no empathy. We are in her head, we know what she thinks and feels. That said,...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/47947 License name: CC BY-SA 4.0 License URL: https://creativecommons.org/licenses/by-sa/4.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/47947 License name: CC BY-SA 4.0 License URL: https://creativecommons.org/licenses/by-sa/4.0/
#2: Initial revision
As others have pointed out, since you are in the main character's head, it's very hard to hide the fact that she feels no empathy. We are in her head, we know what she thinks and feels. That said, if we agree with the character's goals, their actions might appear understandable, a bit cold but ultimately necessary, etc. At first, that is. You can make quite an interesting experience for the reader, if we start out agreeing with the character, and then gradually realise she's unhinged, we don't want to be her fans. Maybe we even still agree with her goals, but her means and the way she thinks about it all are too much. In that case, you initially hide the character's madness by the very fact that we agree with her, so she's "got" to be good. * * * If your character is not the main character, so you're not in fact in her head, the task becomes easier. You only show the character's actions, not what motivates those actions. I have recently read a book, I'm spoiler-tagging the title as everything I say is a major spoiler, and the English translation only came out this last WorldCon. > _The Heart of the Circle_, by Keren Landsman The antagonist of this story hides in plain sight, pretending to be the protagonist's friend. In fact, he's a sociopath, manipulating the protagonist and his friends. The novel was written by a medical doctor, so she knew exactly what she was about. You only know about the character what he says about himself, and what actions of his are observed by the MC. Sometimes his actions seem a bit off: behaviour that disregards social norms because "there will be no consequences, don't worry, it will be fun". Sometimes he's just a bit too calm. Sometimes he makes a weird request. There's always a perfectly reasonable explanation, but those bits of evidence mount up. Until it all hits you in the face. Even at this point, however, you are not handed a medical diagnosis. You are hit with the realisation that the character in question is a manipulative bastard who has no empathy for anyone and stops at nothing. Mind you, he thinks of himself as "doing what must be done", and his vision of the future is an extremely appealing one, if it weren't for the price. And that's all that's needed, really. We don't need a medical diagnosis to understand what kind of person that character is. If we do know about the existence of sociopathy and how it manifests, everything makes perfect sense. But that's a bonus, a diagnosis the reader does by himself (or gets the full understanding after reading the acknowledgements, where the author thanks a psychologist for helping her with information on sociopathy, among other things).