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Illicit Substitution of Identicals

(also known as: hooded man fallacy, masked man fallacy, intensional fallacy)

Description: A formal fallacy due to confusing the knowing of a thing (extension) with the knowing of it under all its various names or descriptions (intension).

We need to define two terms here to understand this fallacy fully: intensional and extensional.  In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.  In contrast, an extensional definition is defined by its listing everything that falls under that definition.  Confused?  You should be, but relax because I am not done.

Imagine Superman, who is also Clark Kent, flew to Italy for a slice of pizza.  If we said, “Clark Kent flew to Italy for pizza” we would be right, because of the extensional context of that statement.  Conversely, if we said, “Lois Lane thinks Superman flew to Italy for pizza”, we would still be making a true claim, although the context is now intensional as indicated by the term, “thinks”.  Now if we said, “Lois Lane thinks Clark Kent flew to Italy for pizza”, we would be wrong and would have committed this fallacy because Lois does not believe that, even though extensionally it is the case (this is after the kiss that wiped her memory of Clark being Superman).

Example #1:

The lady in the pink dress is Julia Roberts.

The reporter thinks the lady in the pink dress drives a Prius.

Therefore, the reporter thinks Julia Roberts drives a Prius.

Example #2:

The reporter thinks the lady in the pink dress drives a Prius.

Julia Roberts does not drive a Prius.

Therefore, the reporter does not think that Julia Roberts is the lady in the pink dress.

Explanation: The examples used are just two different logical forms of the same fallacy.  Because the reporter, “thinks” the statement is made in an intensional context, we cannot switch the terms.  However, if we were to keep the premises in an extensional context, we could get away with switching the terms.  This would be a valid logical argument form known as Leibniz’ Law.

Exception: Technically, none, but here is the above example #1 using Leibniz’ Law, with no fallacy:

The lady in the pink dress is Julia Roberts.

The lady in the pink dress drives a Prius.

Therefore, Julia Roberts drives a Prius.

References:

Neil, S. (1853). The Art of Reasoning: A Popular Exposition of the Principles of Logic. Walton & Maberly.

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