Masked-man fallacy

In philosophical logic, the masked-man fallacy is the false assumption that knowledge or a belief about an object can be used to correctly tell it apart from another object. 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. 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.

Examples

The name of the fallacy comes from the example:

Premise 1: I know who Claus is.
Premise 2: I do not know who the masked man is.
Conclusion: Therefore, Claus is not the masked man.

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:

Premise 1: I know who X is.
Premise 2: I do not know who Y is.
Conclusion: Therefore, X is not Y.

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: The speaker believes they know who X is.
Premise 2: The speaker believes they do not know who Y is.
Conclusion: Therefore, the speaker believes X is not Y.

Premise 1 is a very strong one, as it is logically equivalent to. It is very likely that this is a false belief: is likely a false proposition, as the ignorance on the proposition does not imply the negation of it is true.
Another example:

Premise 1: Lois Lane thinks Superman can fly.
Premise 2: Lois Lane thinks Clark Kent cannot fly.
Conclusion: Therefore, Superman and Clark Kent are not the same person.

Expressed in doxastic logic, the above syllogism is:

Premise 1:
Premise 2:
Conclusion:

The above reasoning is inconsistent. The consistent conclusion should be.
The following similar argument is valid:

X is Z
Y is not Z
Therefore, X is not Y

This is valid because being something is different from knowing something. The valid and invalid inferences can be compared when looking at the invalid formal inference:

X is Z
Y is Z, or Y is not Z.
Therefore, X is not Y.

Intension is the connotation of a word or phrase—in contrast with its extension, the things to which it applies. Intensional sentences are often intentional, that is they involve a relation, unique to the mental, that is directed from concepts, sensations, etc., toward objects.