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Source: https://writers.stackexchange.com/a/35987
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

Source: https://writers.stackexchange.com/a/35987
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

The OP (now) specifies the narrator cannot know the thoughts of any character, including the villain (see question comments).

Human logic, both formal and informal, is grounded in **self-evident truths** , meaning things we believe to be true and require no evidence for that but common sense. e.g. Euclidean geometry claims the shortest distance between two points in space is a straight line; no non-straight line can be shorter than the straight line. There is no proof for that, it is self-evident.

The same goes for "parallel lines never meet." There is no formal proof. However, we can discard this and come up with new geometrical systems; and in mathematics we call these "non-Euclidean" geometries. For example, Einstein's space-time unification uses a non-Euclidean geometry.

But those are examples from mathematics; we work with many similar self-evident truths in our daily lives. A person cannot be in two places at one time. The past is fixed and cannot be changed. If a person is dead, they are not walking around.

So you must begin with the presumption that all people are always thinking logically **_from their self-evident truths._** If I think my brother is **not** thinking logically, that is because he holds different truths than me as self-evident. What he thinks, about God, about politics, about women, about war, are logical conclusions given what he believes is _obviously_ true and needs no proof.

For your villain to act illogically in the eyes of the reader, you need an internally consistent villain. They are not just "crazy" they just do not believe something nearly all readers will believe, or vice versa: They believe something is self-evident that nearly all readers will refute as self-evidently false. For example, the villain believes in some kind of magic or protective talisman or curse. Or the villain believes drinking the blood of a virgin every day will extend his life indefinitely. Or the villain believes they are the second coming of Christ, and protected from harm by God.

You want your illogicality to be consistent, even if it doesn't work. Then your villain can still be reasonably intelligent, but they are using the good part of their logic and intelligence to pursue an insane goal, due to something they truly believe is a self-evident fact, but virtually nobody else believes is a fact.

To complete this answer, since the narrator cannot know what the villain is thinking, you should try to limit the difference from normal logic to ONE specific thing they believe that nobody else believes. That way, both the reader and other characters might discern this discrepancy, the villain is being insane in **one particular way** , time after time. Then the actions of the cops, detectives, etc (or the reader) may figure this out. Even if the reader does not figure it out, by the time the villain is defeated, make sure somebody has figured it out and used that insight to trap and defeat the villain, and says so explicitly. Mystery solved, and retrospectively, the reader will realize it all makes sense; the villain believes X and that explains everything.

Original score: 12