Intensional

The mistake of treating different descriptions or names of the same object as equivalent even in those contexts in which the differences between them matter. Reporting someone's beliefs or assertions or making claims about necessity or possibility can be such contexts. In these contexts, replacing a description with another that refers: the same object is not valid and may turn a true sentence into a false one.

Example:

Michelle said she wants to meet her new neighbor Stalnaker tonight. But I happen to know Stalnaker is a spy for North Korea, so Michelle said she wants to meet a spy for North Korea tonight.

Michelle said no such thing. The faulty reasoner illegitimately assumed that what is true of a person under one description will remain true when said of that person under a second description even in this context of indirect quotation. What was true of the person when described as “her new neighbor Stalnaker” is that Michelle said she wants to meet him, but it wasn’t legitimate for me to assume this is true of the same person when he is described as “a spy for North Korea.” Extensional contexts are those in which it is legitimate to substitute equals for equals with no worry. But any context in which this substitution of co-referring terms is illegitimate is called an intensional context. Intensional contexts are produced by quotation, modality, and intentionality (propositional attitudes). Intensionality is failure of extensionality, thus the name “intensional fallacy”.