Masked-man fallacy

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.

Examples
The name of the fallacy comes from the example: The premises may be true and the conclusion false if Claus is the masked man and the speaker does not know that. Thus the argument is a fallacious one.
 * 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.

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 will be
 * Premise 1: The speaker believes he knows who X is.
 * Premise 2: The speaker believes he does not know who Y is.
 * Conclusion: Therefore, the speaker believes X is not Y.

Premise 1 $$\mathcal{B_s}\forall t (t=X\rightarrow K_s(t=X))$$ is a very strong one, as it is logically equivalent to $$\mathcal{B_s}\forall t (\neg K_s(t=X)\rightarrow t\not=X)$$. It is very likely that this is a false belief: $$\forall t (\neg K_s(t=X)\rightarrow t\not=X)$$ is likely a false proposition, as the ignorance on the proposition $$t=X$$ 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: $$\mathcal{B}_{Lois}Fly_{(Superman)}$$
 * Premise 2: $$\mathcal{B}_{Lois}\neg Fly_{(Clark)}$$
 * Conclusion: $$Superman\neq Clark$$

The above reasoning is inconsistent (not truth-preserving). The consistent conclusion should be $$\mathcal{B}_{Lois}(Superman\neq Clark)$$.

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

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.