In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible (that is, they have all the same properties). By modus tollens, this means that if one object has a certain property, while another object does not have the same property, the two objects cannot be identical. The fallacy is "epistemic" because it posits an immediate identity between a subject's knowledge of an object with the object itself, failing to recognize that Leibniz's Law is not capable of accounting for intensional contexts.
The name of the fallacy comes from the example:
The premises may be true and the conclusion false if Lucas is the masked man and the speaker does not know that. Thus the argument is a fallacious one.[clarification needed]
In symbolic form, the above arguments are
Note, however, that this syllogism happens in the reasoning by the speaker "I"; Therefore, in the formal modal logic form, it'll be
Premise 1 is a very strong one, as it's logically equivalent to . It's very likely that this is a false belief: is likely a false proposition, as the ignorance on the proposition doesn't imply the negation of it is true.
Expressed in doxastic logic, the above syllogism is:
The above reasoning is inconsistent (not truth-preserving). The consistent conclusion should be .
The following similar argument is valid:
This is valid because being something is different from knowing (or believing, etc.) something. The valid and invalid inferences can be compared when looking at the invalid formal inference:
Intension (with an 's') is the connotation of a word or phrase—in contrast with its extension, the things to which it applies. Intensional sentences are often intentional (with a 't'), that is they involve a relation, unique to the mental, that is directed from concepts, sensations, etc., toward objects.