Inphilosophical logic, themasked-man fallacy (also known as theintensional fallacy orepistemic fallacy)^[1] is the false assumption that knowledge or a belief about an object (anintension) 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 ofLeibniz'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). Bymodus 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 isepistemic 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:

• 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.

Thepremises 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 thissyllogism happens in the reasoning by the speaker "I"; Therefore, in the formalmodal logic form, it would be:

• Premise 1: The speakerbelieves theyknow 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${\displaystyle {\mathcal{B}}_{\mathcal{s}}\mathrm{\forall }t(t=X\to K_s(t=X))}$ is a very strong one, as it islogically equivalent to${\displaystyle {\mathcal{B}}_{\mathcal{s}}\mathrm{\forall }t(\mathrm{\neg }{K}_s(t=X)\to t\ne X)}$. It is very likely that this is afalse belief:${\displaystyle \mathrm{\forall }t(\mathrm{\neg }{K}_s(t=X)\to t\ne X)}$ 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:

• 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 indoxastic logic, the above syllogism is:

• Premise 1:${\displaystyle {\mathcal{B}}_{Lois}Fl{y}_{(Superman)}}$
• Premise 2:${\displaystyle {\mathcal{B}}_{Lois}\mathrm{\neg }Fl{y}_{(Clark)}}$
• Conclusion:${\displaystyle Superman\ne Clark}$

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

The following similar argumentisvalid:

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

This is valid becausebeing something is different fromknowing (or believing, etc.) 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 (with an 's') is the connotation of a word or phrase—in contrast with itsextension, 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.

• Black box
• Eubulides' second paradox
• Identity of indiscernibles
• List of fallacies
• Opaque context
• Transitivity of identity
• Use–mention distinction
• Metonymy

• Informal fallacies
• Epistemic logic

• Articles with short description
• Short description is different from Wikidata