Masked-Man Fallacy: Why What You Know Cannot Tell Two People Apart

The argument borrows the authority of a sound rule and applies it where the rule does not reach. The rule is Leibniz's law, the indiscernibility of identicals: if two things are one and the same, everything true of one is true of the other, so a property that holds of one and fails of the other proves they are two. It is how people tell things apart every day. The brother is six foot two and the masked man is five foot four, therefore two people. The fallacy runs the same inference with a premise that is not about the man at all but about the speaker's mind: I know who my brother is, I do not know who the masked man is, therefore two people. The form looks identical, and the conclusion does not follow.

What breaks it is the nature of knowing, believing, recognizing, wanting and the other verbs that take a mind's perspective. A sentence such as "I know who that is" depends on how the person is presented to me, under which name or appearance, and not only on which person it is. Philosophers call such contexts intensional, from the Latin for stretching toward, and contrast them with extensional contexts such as height or location, where only the thing itself matters. Inside an intensional context, replacing a name by another name for the same thing can turn a truth into a falsehood, so the substitution that Leibniz's law licenses elsewhere is not available. Quine's example is that Giorgione was so called because of his size and Barbarelli was not, although Giorgione was Barbarelli; the sentence is about the name, not the man.

Frege had made the same point in 1892 with the morning star and the evening star. The ancients knew that Hesperus was Hesperus; they did not know that Hesperus was Phosphorus, although both names pick out Venus. If knowing were a property of the planet, the planet would both have and lack it. Frege's resolution was that names carry a sense as well as a reference, and that in contexts of knowledge and belief it is the sense that does the work. The masked-man argument ignores this and treats "known to me" as if it were a size or a color.

Psychologically, the pull of the argument has not been studied under this name. The nearest evidence is on syllogistic reasoning generally, where people accept invalid arguments far more readily when the conclusion is believable, and on children's developing grasp that what someone knows about an object depends on how it was presented to them. The fallacy is less a bias with a mechanism than a trap in the surface grammar of English, and it is worth knowing because its modern forms are everywhere.

There is no experiment; there is a puzzle with a long history, and the psychology meaning of the term is the only one in use. Diogenes Laertius, in the second book of his Lives of Eminent Philosophers, lists Eubulides of Miletus, a member of the Megarian school in the fourth century BC, as the author of many dialectical arguments in interrogatory form and names seven: the Liar, the Disguised, Electra, the Veiled Figure, the Sorites, the Horned One and the Bald Head. The Disguised and the Veiled Figure are the masked man, and Electra is a version of it from the myth: Electra knows her brother Orestes, and does not know that the stranger in front of her is Orestes, so she both knows and does not know her brother.

The modern analysis comes from two sources. Gottfried Leibniz stated the law that bears his name, that things which are identical share all their properties, in his work on metaphysics, and the law is now treated as the defining feature of identity. Gottlob Frege, in "On Sense and Reference" in 1892, identified the contexts in which the law seems to fail and explained them: inside reports of knowledge and belief, a name contributes its sense, the way it presents its object, and not merely its reference, so that two names for one object are not interchangeable there. The English translation appeared in the Philosophical Review in 1948.

Willard Van Orman Quine sharpened the diagnosis in the 1950s. In "Reference and modality" he called the positions where substitution fails referentially opaque and gave the Giorgione example; in "Quantifiers and propositional attitudes" he turned to belief, with the case of Ralph, who believes that the man in the brown hat is a spy and does not believe it of the man he knows as Ortcutt, although they are one man. Quine's conclusion was that in such positions the name is not functioning purely to pick out its object, so the inference that treats it as if it were is unlicensed. The Stanford Encyclopedia of Philosophy's entries on identity and on propositional attitude reports carry the current state of the discussion, including the view that substitution fails in these contexts for different reasons in different cases.

The demo on this page therefore has no study figure of its own. It borrows one from the nearest psychological literature, the belief bias in syllogistic reasoning, where Evans, Barston and Pollard found in 1983 that students accepted two thirds of invalid arguments with believable conclusions and almost none with unbelievable ones, as the measure of how readily a conclusion that sounds right is let through.

The modern masked man rarely wears a mask. He appears whenever what people know or think about something is treated as a fact about the thing.

The counter is a habit of checking which kind of premise an argument is using before applying the rule that tells things apart.

• Sort the predicate. Ask whether the property in each premise belongs to the thing itself, like height, weight, location or date, or to someone's mind directed at the thing, like known, believed, recognized, trusted, wanted or doubted. Leibniz's law applies to the first kind only.
• Try the unmasking test. Imagine the two descriptions turn out to name one thing. If both premises could still be true, the argument did not prove they are two things.
• Rewrite with the name. Replace the description with the name of the thing and see whether the premise still holds. "I do not know who the masked man is" becomes "I do not know who my brother is," which is false; the premise was about the mask, not the man.
• Watch the verbs. Know, think, believe, want, agree, recognize, trust and seek all open an intensional context. An argument that passes through one of them and comes out with a conclusion about identity or difference deserves a second look.
• Separate the panel's information from the panel's verdict. In hiring, diagnosis and politics, the practical form of the fallacy is treating a judgment made with partial information as a fact about the candidate, the disease or the bill.

The masked-man fallacy is a formal error about identity, and it is easy to confuse with nearby mistakes about arguments and minds.

• It is not belief bias, the tendency to accept an argument because its conclusion is believable. Belief bias is about what makes a bad argument persuasive; the masked-man fallacy is a specific bad argument, and it can persuade whether or not its conclusion is believable.
• It is not the argument from fallacy, which concludes that a claim is false because an argument for it was bad. The masked-man conclusion can be true, as when the masked man really is a stranger; the argument still fails to establish it.
• It is not naive realism, the conviction that one's own view of the world is simply how things are. The masked man is a cousin, since both treat the contents of a mind as if they were features of the world, but naive realism is a stance and the fallacy is an inference.