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Therefore, no human is an animal.
That is the purported conclusion, but it is unacceptable. The qualification on “rational” shifts the respect under which the middle term is considered. A word can look the same while failing to serve as one logically identical middle term throughout the proof.
Classical classification holds that every human is an animal. Examining rationality as an abstract differentia does not abolish this generic relation. The mistake confuses a conceptual abstraction with a judgment about the complete subject.