Category
Formal fallacies
A formal fallacy is a mistake in the shape of an argument. The premises, even if every one of them is true, don’t guarantee the conclusion, and the reason is visible without knowing what the argument is about. Replace the subject matter with letters (P, Q) and the flaw is still there.
Formal fallacies are the most clear-cut errors on this site. There’s no “it depends on context”: an argument form is either valid or it isn’t.
Entries (11)
- Affirming a disjunctConcluding that one option is false because the other is true, when the “or” allowed both to be true.
- Affirming the consequentConcluding that the “if” part is true because the “then” part turned out to be true.
- Denying a conjunctConcluding that one of two things is true because they can’t both be true and the other one isn’t.
- Denying the antecedentConcluding that the “then” part is false because the “if” part turned out to be false.
- Existential fallacyConcluding that something of a kind exists from “all” or “no” statements, which can be true even when nothing of that kind exists.
- Fallacy of four termsA syllogism that seems to link two groups through a shared term, when the “shared” term is really two different things.
- Illicit majorA syllogism whose conclusion covers all of its predicate group, when the premise naming that group covered only part of it.
- Illicit minorA syllogism whose conclusion covers all of its subject group, when the premise naming that group covered only part of it.
- Masked man fallacyConcluding that two things are different because you know or believe something about one that you don’t about the other.
- Prosecutor's fallacyTreating the chance that an innocent person would match the evidence as if it were the chance that a person who matches is innocent.
- Undistributed middleConcluding two groups are linked because both belong to a third group, when neither premise says anything about all of that third group.
How to spot one
Look for a counterexample: a case with the same shape where the premises are obviously true and the conclusion is obviously false. If you can find one, the form doesn’t work.
If it’s a dog, it’s a mammal. It’s a mammal. So it’s a dog.
Swap in “cat” and both premises stay true while the conclusion fails. Any argument with that shape is unreliable, including ones where the conclusion happens to be right.
A true conclusion doesn’t rescue it
A formally fallacious argument can reach a true conclusion by luck. The fallacy is that the argument doesn’t show it. Equally, spotting a formal fallacy doesn’t show the conclusion is false. It shows only that this argument gives you no reason to believe it.
Valid is not the same as true
The opposite of a formal fallacy is a valid form, where true premises guarantee a true conclusion. Modus ponens (affirming the antecedent) is the standard example. Validity says nothing about whether the premises are true; an argument that is valid and also has true premises is called sound.
Formal and informal
A formal fallacy is wrong because of its structure. An Informal fallacy can have a perfectly valid structure and still be a bad argument, because of what it’s about, what it assumes, or how it’s being used.
Other categories: Informal fallacies · Cognitive biases · Research biases