Masked-man fallacy

In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is the false assumption that knowledge or a belief about an object (an intension) can be used to correctly tell it apart from another object (as opposed to facts, that can be used to correctly tell two objects apart). It 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, yet the conclusion is false if Claus is the masked man and the speaker does not know that. Though the speaker is aware of a large part of Claus's identity, it would not logically follow that Claus is not the masked man, seeing as the speaker cannot account for those parts of Claus's identity that are not known to them. Thus, the argument is a fallacious one. The fallacy results from the speaker's confusion of their own knowledge with complete factuality.

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 would be:

Premise 1 ${\displaystyle {\mathcal {B_{s}}}\forall t(t=X\rightarrow K_{s}(t=X))}$ is a very strong one, as it is logically equivalent to ${\displaystyle {\mathcal {B_{s}}}\forall t(\neg K_{s}(t=X)\rightarrow t\not =X)}$. It is very likely that this is a false belief: ${\displaystyle \forall t(\neg K_{s}(t=X)\rightarrow t\not =X)}$ is likely a false proposition, as the ignorance on the proposition ${\displaystyle t=X}$ does not imply the negation of it is true.

Another example:

Expressed in doxastic logic, the above syllogism is: