Four-term fallacy

Core claim: A syllogism is presented as valid while containing four terms instead of the required three – typically because one term shifts meaning between premises – which breaks the formal conditions for syllogistic inference.

• The argument has the form of a categorical syllogism (two premises, one conclusion) but contains four distinct terms rather than exactly three.
• A term is used in two different senses across the premises (equivocation), especially the middle term that should connect them.

• The fallacy often hides behind an apparent three-term structure where one of the terms is used in an equivocation; count meanings, not words.
• When the ambiguity lies specifically in the middle term, this becomes the ambiguous middle term variant – the most common form of the four-term fallacy.
• Beware of equivocations that hide in different levels of abstraction, shifting meanings because of variations in the grammatical structure (amphiboly), intensional ambiguities that derive from how a term references the subject, and how meanings can change historically (etymological fallacy).

• The argument is an enthymeme: a premise has been omitted but can be supplied, restoring a valid three-term syllogism (e.g., “All humans are mortal; Socrates is a man” implicitly relies on “All men are humans”).
• All terms are unambiguous and the syllogism follows proper distribution rules.

• Ambiguous middle term (MD) – the specific variant where the middle term shifts meaning. Ask: is any term ambiguous (→ four-term fallacy), or specifically the connecting middle term (→ ambiguous middle)?
• Fallacies of distribution (MD) – In a syllogistic form, a term is used in a way that breaks distribution rules. Ask: does the middle term keep one consistent meaning throughout and merely refer to too little of its class (→ fallacy of distribution), or does it change meaning between premises (→ ambiguous middle)?

Input: “Nothing light can ever be dark. All feathers are light. Therefore, no feather can ever be dark.”
Output: The term “light” shifts meaning between premises: in the first it means “bright” (opposite of dark), in the second “low in weight” (opposite of heavy). With four terms instead of three, no conclusion follows.

Input: “Humans are a species. Socrates is a human. Therefore, Socrates is a species.”
Output: “Human” is used generically in the first premise (the genus as a whole) and specifically in the second (an individual member). The middle term does not refer to the same thing in both premises, so the syllogism fails.

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