Fact: the car peeling away from the robbed bank has Alice's license plate

Conclusion 1: suggests Alice might be involved in the bank robbery.

Conclusion 2: if Alice was involved in the robbery, she wouldn't be so stupid to use her own car. So this evidence actually suggests she was not involved in the robbery.

It strikes me that Conclusion 2 is some kind of fallacy, or maybe both put together are a fallacy, because the Fact cannot suggest both involvement and no involvement.

Help on the name of this fallacy?

(Maybe it is related to the economist who does not pick up the dollar bill because if it was real, someone would have already picked it up.)

  • Conclusions 1 and 2 use different implicit premises, namely, assumptions about Alice's level of intelligence, and there is nothing surprising that the same fact combined with them leads to different conclusions. However, "people are not that dumb" argument is, in general, fallacious, because first, some people are that dumb, and second, even generally smart people act that dumb at times. Some call excessive rationalism in judging human decisions rational fallacy.
    – Conifold
    Commented Feb 3 at 18:03
  • This seems similar to the Latin 'cut bono?'. 'Who profits (from this)' was used to convince a jury that someone should be suspected of some act, though it was accepted by itself as evidence. It is more a rule of thumb, and it can defeat itself by self-reference. Example: father is killed. The first son should inherit, unless he murdered his father, in which case the second son inherits... Commented Feb 3 at 18:42
  • Conclude informally while sitting on your couch watching the news on tv? Or conclude legally as a member of the jury? Seeing someone drive away from a crime is not evidence that they committed the crime. It doesn't matter what the public thinks. It matters what the law says.
    – user4894
    Commented Mar 5 at 1:01
  • 1
    @RichardKirk It's "cui bono" :)
    – haxor789
    Commented Apr 4 at 9:09

3 Answers 3


If there are two facts: "Alice's car was used in the bank robbery" and "Alice would not be so stupid", then 1 and 2 don't contradict one another at all. The evidence suggests (if we grant both premises) that Alice might be involved in the bank robbery, but she probably wasn't. Very well, Alice is a suspect but we shall focus the investigation elsewhere.

If there is really only the one fact, and it's not "Alice would not be so stupid", then 2 has a spurious conclusion by valid induction from a false premise.


All logical fallacies are non sequitur (does not follow). And with regards to fallacies we usually consider deductive reasoning and distinguish by properties of being valid/invalid and sound/not sound. So an argument is valid if true premises always lead to a true conclusion and it is sound if it is valid and if the premises are actually true. So idk "All Orcs have nose rings", "Brian is an Orc" therefore "Brian has a nose ring", is valid (if the premises were true you could follow the conclusion being also true), though as Orcs don't exist it's not sound (the premises aren't actually true so no conclusion can be followed from that).

Now if you look at C1 in terms of deductive reasoning then it's invalid because it doesn't follow that Alice is part of the crime, there are actually a lot of possible alternatives to that:

  • Alice's car could have been stolen
  • Alice's license plate could have been stolen
  • Someone might have borrowed Alice's car
  • Alice's car might been at the wrong time and place by accident

Sure if you find out that Alice's license plate is connected to a robbery it's reasonable to look deeper into Alice, as it's likely that she or someone in her environment (social and/or spacial) was involved in the crime. Though as said Alice's involvement with the crime might be totally accidental, for example she might have borrowed her car to someone in another city, who parked it close to the bank and then the car got stolen because it was in an ideal get away parking spot. So Alice and her social or spacial background would be completely irrelevant to the crime as her car was just at the wrong place at the wrong time.

So there might be good reasons for the ad hoc assumption to check Alice's background if her license plate was involved in a crime, but it's an assumption, it's not conclusive to argue that Alice actually had anything to do with the crime.

So as long as you keep it that vague (like in C1), in the sense of "suggests", "might be", "involved", that is a fairly reasonable assumption. There is some evidence to support your assumption of "involvement", in fact in a very technical sense her property being used in the crime already IS an involvement, though it leaves a lot of room for the criminal culpability of the nature of the involvement and even whether she was involved in the first place in the sense of whether it actually was her property at the time.

In other words there's a difference between saying "something could be" or saying "something IS". If you said explicitly or insinuate as much, that it IS, then this would be a fallacy, because the evidence are, as said, not conclusive, there are various other options that could also have happened, so it's not a given that this MUST follow from the premises. But if you keep below the threshold of certainty that's a reasonable assumption to be made. But that would be inductive reasoning.

Now the legal context makes this a little tricky. Because from a practical point of view all these statements are inductive reasoning trying to construct a general rule from empiric observation of different cases. That being said at the end of the day someone actually ends up passing judgement, so they decide that the evidence IS conclusive (enough), which is technically a fallacy, as outside of pure logic, it's hardly possible to prove anything to the degree of certainty. Which means they don't go to certainty but just go for "beyond reasonable doubt", which is somewhat of a more or less arbitrary line that is drawn somewhere in between certain knowledge and complete uncertainty.

Now the second "conclusion" is a little more tricky. Essentially it's arguing:

Only stupid people use their own license plate in a robbery
Alice is not stupid
Hence Alice didn't use her own license plate in a robbery

now that argument is valid, if the premises were true then the conclusion would also be true. Though while presumably the second premise is true (benefit of the doubt), the first is likely to be wrong or at least not certain. That is if you'd be able to predict the logic of law enforcement ruling out smart people doing something stupid, you could just do something stupid to get away with the crime, hence it is not only possible for smart people to do something stupid, it might actually be smart to ACT stupid. Hence the premise is not true and so the argument is valid but not sound.

Also again vague language that leaves room for alternatives, shields it from being an outright fallacy in the first place. (But at the same time also takes away from the commanding nature of the conclusion. So if the law mandates that criminals be locked up and Alice IS a criminal, Alice ought to be locked up. However if Alice just could be a criminal, that is not enough to lock her up, as anybody "could" theoretically be a criminal. So you'd need a more quantitative analysis of the evidence whether that is warranted enough)

  • 1
    If you're really smart, no one would suspect you of doing something stupid, so then you can get away with it, unless the judge is even smarter... It's the 'stupid' arms race! But if you're really smart and no one knows, you will be suspected of doing stupid things, which is just galling...
    – Scott Rowe
    Commented Apr 4 at 10:56

Logical fallacy: no one would be so dumb to

Sounds like an argument from incredulity.


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