: How to make the reader think that the *character's* logic is flawed instead of the author's? Following up on my previous question, "How to make the villain's motives understandable if his logic

My answer to this is quite simple: Show proof that they're wrong in-story. Doesn't have to be blatant, doesn't have to be screamed, but if you have a reader who is detail-oriented enough to pick up the flaws in a character's logic, they'll be detail-oriented enough to pick up on the tiny consequences that foreshadow the big one.

---

(0)

Use Bad Logic as the Villain's Character Flaw

Logic is an abstract concept. Bad logic is a character flaw.

In most characters, character flaws lead to conflict and growth. They influence the outcomes of that character's actions, and a character might reflect on them or change because of them. They help readers empathise as characters struggle.

This matters because a reader won't put up with an egregious character flaw no matter what kind of flaw it is. You don't read many books with characters as racist as H.P. Lovecraft's any more. Flawed logic that's so bad a reader can't put up with it isn't just bad logic: it's bad characterisation.

The Villain is Committed to Bad Logic

You've mentioned this is specifically about a villain, which introduces one complexity. To quote an article by Stephen Pressfield, "the villain never changes". If they changed, they'd be the hero. That means we spend a lot of time with the villain's logic.

Normally, a character with a flaw like bad logic would cause some problems for themselves. Their assumptions would cause conflict, such as having a plan go awry because what actually happened didn't match their assumptions. One might even be able to say that heroes survive mostly because the villain failed to think of everything. :)

But, since this character is a villain, no matter what the results of their flawed logic are, they should not see the problem as being with their logic.

Basically, villains don't change, they double down. Jafar's plan in Aladdin to make Jasmine fall in love with him failed not because it was impossible in the first place, but because he didn't have ultimate cosmic power. We as an audience know that his logic is wrong, but there's nothing trite about the way his logic appears.

So how do you present bad logic as something a character can be committed to?

How is this Flaw Reasonable?

Bad logic is just like any other flaw: a character is the way they are because being that way makes sense to them. The character should see their flaw as reasonable or even necessary. This is what internal consistency means, and it's absolutely required for us as readers to empathise with the villain.

In particular with logic, even if we as readers can see that the villain isn't thinking correctly, we should be able to say "I wouldn't do that" and not "Nobody would do that." For logic, that means agreeing with his premises and disagreeing with his conclusion (see examples below), as well as appreciating the thought that went into arriving at his conclusion.

In fact, you rarely want a character to come off only as illogical. Illogical characters are ones that readers don't understand and don't empathise with, and are more commonly comedic. Find something that's close but more emotionally charged: When Billy in Shazam goes to find his mother and expects to be a family again, we don't think he's illogical, we think he's naive (and it warms our hearts).

Flaws should help us as readers empathise with the character, not isolate us from them.

Tying it Back to Motives

Logic and motives are completely separate. Jafar is illogical because he believes he can accomplish something that's impossible; he's evil because he's motivated by conquest of Jasmine instead of love. The best villains want something universal but reason about it in abhorrent ways, such as how Thanos from the Avengers movies wants sustainability at all costs.

Evil isn't dumb, it's corrupt.

Examples

Bad logic that the reader can see is bad logic can be used for comedy or villainy, but only if the character with bad logic is completely unaware of how bad his logic really is, he refuses to change even when his bad logic is pointed out, and we as readers can believe it even if we don't agree with it.

The Tragic Approach

A villain railing at the limits of their understanding is a powerfully moving thing. Yet, he cannot succeed.

See the first two and a half minutes of this video from Fullmetal Alchemist (Brotherhood): "What more could I have done?"

Note that it isn't even necessary for us to agree with the author's idea of logic - it's possible to view this exchange as cruel, for example, even if we don't agree with the villain either. The important part is how the world itself works, and the statement the author wants to make with their view of what's logical.

The Comedic Approach

With comedy, the result of bad logic has to be relatively benign. Otherwise, a character who is unaware of their affects on others is calloused, not funny.

See this scene from the Big Bang Theory: "I accept your premise, I reject your conclusion."

Conclusion

Bad logic is an excellent flaw that can be used to emphasise willing blindness of consequences. Bad logic contrasts the evil things a villain values with the good things that the protagonist values, rather than separating the villain from reality (and the reader). Bad logic is logic we disagree with rather than logic that misses a few steps.

Show us what your character values by what they're willing to ignore.

---

(0)

So this would be where we would want to use dramatic Irony. Set up a scene where the hero is presented with a similar yet distinct logic question and takes the opposite answer. One of the best examples of this I've recently seen occurred in the recent Avengers: Infinity War Movie. As this is still in theaters, I'm going to be very vague as there are spoilers but suffice to say, that in order for the villain to complete his plans, he must make a sacrifice and it must be a living person. Naturally he accepts this because Villain.

But earlier in the movie, the heroes are presented with a solution to stopping the villain. All they have to do is make a similar sacrifice of a living person and the villain can't complete his plan. They refuse, pointing out that "We do not trade lives" which will stand in contrast to a similar statement that is uttered with respect to the villain's similar actions. The fact that neither party knows the other's thoughts or logic does not matter as they are given a goal that can be near impossible to win without making a sacrifice of a person they are close with. The similarity of the two phrases cement the two answers to the ethical conundrum presented.

---

(0)

Have someone else reject the logic

Even if they don't have access to the character's train of thought, they may decide to try to figure out what's going on, based on their actions; simply have them concoct the very same reasoning that the character uses and then have them reject that reasoning for being absurd.

That way, nobody knows what the character is thinking but the author can still reveal to the reader that it's not their reasoning that's the problem -- merely the character's.

---

(0)

Making it a flaw in logic is difficult. A common approach is to have the character trying to work something out, and they notice an object which gives them an (obvious) solution. e.g. they want to get on the roof, they see a ladder. But then, after they leave, we zoom in on the ladder to reveal some detail not visible to them e.g. a splintered rung or loose nail. Dramatic chord!

But that's ignorance, a flaw in knowledge, not in reasoning. The problem becomes "how to show a splinter in logic, not in a ladder?" How do you show logic, at all? In the below, I suggest ways of showing general lack of logic, and how to show a specific lack of logic.

Note that general or specific irrationality does not necessarily mean stupid (just as clever does not necessarily mean wise). Cue mad scientist.

Related is suspension of disbelief: in accepting the conceit of a story, readers willingly accept the illogical, counterfactual, improbable, implausible, impossible. Talking animals, superman, ghosts, eerie supernatural guidance and justice. Even readers who notice a plot hole or inconsistency will often allow it, in order to enjoy the story..

General
So, apart from very specific reasoning, you just need to make it more plausible that the character has flawed logic - that that explanation is primed to be the first thing to enter the reader's mind, by showing the character to be illogical, neurotic, irrational in general.

Some blunt examples: have the character do cliche neurotic things to establish their illogical nature: like OCD checking everything twice, unnecessary rituals, paranoia. So, now when their plot-significant actions come up, the reader will be ready to suspect it's a bit crazy. But here's the danger: there's a common trope where setup is used to show their neutroticism was justified all along! (Because readers willingly suspend belief). However, maybe that's OK for your question, as they're not seeing it as an authorial error.

You could also establish the background history of their erroneous thinking: an experience making them irrationally fear something ordinary... and when it comes up in their plans, they make irrational allowances for it,

Specific
Similarly, you could show their specific error in a minor scenario, perhaps one presaging the main plot. But this I think is really tricky: if they make this error, and they fail because of it, why don't they learn from it? I suppose you could just show them making the same error time and again, and that would be enough to prime the reader for it to happen again (and the "why" is just secondary background).

Alternatively, if they make this error, and it does work out but clearly for some other reason (so they don't learn), the reader might take the message that they are magically lucky, and it's something they can and do legitimately rely on. But again, for your question, this again might be OK, because it's not interpreted as authorial error.

---

(0)

You don't need an omniscient narrator or POV character to point out that something seems illogical. If it is obviously illogical to your reader then it is obviously illogical to your characters as well and they will likely respond to that fact.

Frank couldn't believe the sign on the door. Did Dick really expect him to leave the door closed simply because the sign asked? It must be a trap. After searching fruitlessly for some kind of mechanism for 30 minutes Frank tentatively turned the knob, eyes shut tight in anticipation of some kind of doom. Nothing happened and later that evening Frank found himself still wondering about the note as he cradled his newly acquired chest of gold bars.

---

(0)

Seems to me the basic options are:

Make his logic so insane that the reader will just take it for granted that anyone capable of writing a coherent book couldn't really believe this. Possible, but this may force you to make the character so crazy that he ceases to be interesting. He's no longer a reasonably intelligent person who makes a big mistake, but a certifiable lunatic.
Have the narrator point out the flaw in the logic. But you say that doesn't work with the kind of narrator you want.
Have the character discuss his thoughts with other people, and then those people say that his logic is flawed, either to the character or to each other. But I think you ruled that out, too.
Have the character consider objections to his logic, and dismiss them. "I suppose people will say that this won't work because ... but they don't know that ..."

Have the character's logic appear valid and don't reveal the flaw until later. This may or may not work depending on the details of the story. You may be able to leave out crucial details until the right time, for example. Like, "And then he discovered that it would require driving 500 miles across the desert, and his car could only carry enough gas to travel 400 miles." Or whatever obviously.

---

(0)

In my experience with writing, I've come to see huge dramatic potential in the distance between a character's actions and a character's dialogue. Put some distance between what he says he will do and what he does, have him do something against his proclaimed goals that demonstrates the conflict in his nature. Simplistic example: villain who claims to be pure evil but can't quite outright kill the hero. Sure, he can leave them in a burning building... but shoot them between the eyes when they're unarmed after giving a whole speech about being the worst bad guy in the whole universe...?

If you don't have access to their thoughts, their actions are the next best thing, specifically in contrast to what they say.

P.s. I also think @cloudchaser 's solution is brilliant. However, I have a personal issue with humanised villains that has been getting worse the more jaded I get; I sometimes want the bad guys to get away with it. Ocean's Eleven syndrome. Accepted wisdom is that the criminals can never win, but I've had some experiences with "wrong" logic being so relatable that I've ended up feeling just as cheated when the bad guy ended up in jail as if the author had ended with "ta da, and it was all a dream."

---

(0)

Show the character's motives involves a fact the character believes to be true, but which the reader has earlier seen is false.

Example from David Weber's Honor Harrington SF series: the Grand Alliance believes the resumption of the war between Manticore and Haven (which they eventually settled) was the result of the Mesan Alignment manipulating the situation and then later killing the man responsible for altering diplomatic messages in a traffic accident. From their point of view, the logic is completely plausible; the Alignment has been manipulating things behind the scenes for centuries, a resumption of the war was in their interest, and killing patsies is a standard operating procedure for them.

The Alignment leadership, however, is surprised to hear this accusation because they had nothing to do with it, as the readers (at least those who read about the incident in question in an earlier book), already knew. The man responsible did it for his own selfish goals, but it spun out of his control and he was killed in a legitimate traffic accident before he could be arrested and the truth found out.

In this case, what the protagonists believe about the incident flows from what they perceive to be the truth, which the reader knows is incorrect because they've seen how the belief the characters are acting on is wrong.

Another example, from television, and perhaps closer to what you're looking for. On Agents of SHIELD, the Superior, Anton Ivanov, starts his vendetta against Coulson because he's connected Coulson to all sorts of incidents involving aliens and other potential threats to humanity, and has come to the conclusion that Coulson is therefore somehow involved or responsible for these incidents. His facts are right; Coulson is connected to those incidents, but Ivanov has mixed up cause and effect. Coulson was responding to the incidents, not instigating. From the audience point of view, Ivanov is nutty because they know the truth.

---

(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.

---

(0)

Here's another idea.
Turn the bug into a feature, and promise it in the opening to your novel.

Strong Hero knew that every argument had its flaws. More to the point, whoever made the argument usually didn't even see the error in
their thinking. And that was critical. Finding the flaw, seeing the crucial mistake, the weak link - was a skill she had honed.
Their mistakes became her personal weapons.

Then you provide a few minor examples through action in real time or maybe through flashback. Now the audience knows they're in good hands.
The flaw in logic of the villain should be satisfying in some way, not an obvious 'he's so stupid' thing but a clever twist.

---

(0)

One way is to have the character's plans that were based on that logic to fall apart later. Also, if you show other examples of the character having flawed logic, then the reader is more likely to put it into that pattern. Another tactic is to have the flaw be over the top. While you can't guarantee that some readers will fall prey to Poe's law, the more flawed the character's logic is, the more likely it will be perceived as intended to be flawed.

What exactly are your motives? Do yo think the story works better if the reader knows the author knows the logic is flawed? Or is it just an ego thing, wanting the reader to know that you don't think the logic is valid?

It sounds like you want the reader to attribute an in-universe explanation (the character's logic is flawed) rather that out-of-universe (the author couldn't come up with a better motivation). So make a valid in-universe explanation. Show what character-specific reason there are for believing in this logic. If the character believes the logic and you don't, why is that? What differences are there between you and the character? Is the character stressed? Limited worldview? Had previous experiences they're improperly generalizing? Less intelligent?

---

(0)

Show subtle inconsistencies from outside sources. If the character's logic was based on some historical fact, have some minor, easy to miss, detail or conversation piece that refutes that fact.

Character believes his wife died at the hospital. A week later when he got home there is a hospital bill. Still in grief, only glances at it and notices a couple of lines but while the reader sees those lines, the character largely ignores it. "They charged me for two days stay but she was only there for one before the doctor killed her. How cruel is it that they are trying to stiff me now?" he said. That sort of thing.

Though my first thought to answer this question was the TV/movie trope, 'no one is dead until we see the body.' Yet the characters in universe assume that body goes over cliff equals dead the end.

---

(0)

The narrator knows about the thoughts. And the narrator will know that the thoughts are illogical, and can distance himself/herself from the thoughts. Of course that only works if the narrator isn't the villain in first-person.

For example, you might write something like:

Dick thought about his problem. How on earth could he lock a door that did not even have a lock? Sure, he could block it from the inside, but that would mean he would have to be inside, and that was not possible. He could order someone else to stay inside, but his people were unreliable, so that was not really an option either. So what to do?

Finally he had what he considered the perfect idea: Just put a sign on the door: “This door is locked. Any attempt to get inside is futile.” Dick was sure: Yes, that would definitely work. He was absolutely convinced that nobody would ever even try to open that door. After all, it was written there plainly that trying was futile, so why should they waste their time? They couldn't know that it was a lie.

Dick was happy about that solution he thought he had found, and immediately went to ordering such a sign.

Note how the narrator always explicitly attributes the logic to Dick. The formulations should make it clear that the narrator doesn't think it is a reasonable strategy, and since the narrator knows that it is stupid, it is clear that the author knows it, too.

Edit:

The question was edited to state that the narrator only knows the actions, but not the thoughts of the characters.

For that case, notice that even if the narrator does not know the thoughts, he/she can speculate about them, or draw conclusions from previous behaviour. Or the thoughts might be uttered by the character, and then the narrator can directly comment on them.

For example, with the new restriction, the door sign “solution” might be introduced like this:

Dick was wandering around, constantly murmuring: “How on earth can I lock that door?” It apparently was a hard problem for him, given the time he spent on it. And granted, locking a door that had no lock is not an obvious problem to solve.

Then suddenly his face brightened. He called out for his personal assistant: ”Order a sign, saying ‘This door is locked. Any attempt to get inside is futile.’ And make sure that sign is put on the door to the chamber.”

The servant momentarily looked confused. But that passed quickly; after all, it wasn't the first time he had been given orders of questionable utility. And he was smart enough not to contradict. Just to be sure he didn't misunderstand, he asked: “You mean the special chamber behind the storage room?“

“Sure,“ Dick replied angry, “what else should I mean?”

“It's as good as done,” the assistant said, as he hastened away. Probably not so much due to solicitude, as due to self-protection. When Dick was angry, it was not a good idea to be close.

---

(0)