Masked-man fallacy

The name of the fallacy comes from the example:

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

The premises may be true and the conclusion false if Flint is the masked man and the speaker does not know that. Thus the argument is a fallacious one.

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'll 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 ${\displaystyle {\mathcal {B_{s}}}\forall t(t=X\rightarrow K_{s}(t=X))}$ is a very strong one, as it's logically equivalent to ${\displaystyle {\mathcal {B_{s}}}\forall t(\neg K_{s}(t=X)\rightarrow t\not =X)}$. It's 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 ${\displaystyle t=X}$ doesn't 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: ${\displaystyle {\mathcal {B}}_{Lois}Fly_{(Superman)}}$
• Premise 2: ${\displaystyle {\mathcal {B}}_{Lois}\neg Fly_{(Clark)}}$
• Conclusion: ${\displaystyle Superman\neq Clark}$

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

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 (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 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.

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