Ambiguous middle

Core claim: The middle term of a syllogism – the one that should connect the two premises – is used in two different meanings, so no valid link between them exists and no conclusion can be drawn.

• A categorical syllogism uses its middle term with two distinct senses (different extensions) across the premises.
• The argument otherwise has the appearance of a valid three-term syllogism, but the equivocation hides a fourth meaning.

• This is the most common form of the four-term fallacy: the ambiguity specifically concerns an equivocation if connecting middle term rather than any other term.
• Because the two senses refer to different things, they are effectively two different terms that only “coincidentally” look identical.

• The middle term has a single, consistent meaning throughout (even if the syllogism fails for another reason, e.g., undistributed middle).
• Two terms denote the same object but differ in intension (e.g., “morning star” vs. “evening star” both = Venus) – that is an intensional fallacy, not an ambiguous middle.

• Four-term fallacy (MD) – the general category; ask: is any term ambiguous (→ four-term), or specifically the middle term that connects the premises (→ ambiguous middle)?
• Intensional fallacy (MD) – same referent, different mode of presentation; ask: do the terms point to different things (→ ambiguous middle) or to the same thing described differently (→ intensional)?
• Undistributed middle (MD) – the middle term has one meaning but fails to cover all instances; ask: is the problem about meaning (→ ambiguous middle) or about scope/distribution (→ undistributed middle)?

Input: “Nothing light can ever be dark. All feathers are light. Therefore, no feather can ever be dark.”
Output: The middle term “light” shifts meaning: in the first premise it means “bright” (presence of photons), in the second “low in weight”. Since the premises talk about different properties, they do not connect – no conclusion follows.

Input: “All man are mortal. No man is a woman. Therefore, no woman is mortal.” Output: The middle term “man” shifts meaning: in the first premise it stands for humans in general (the species), in the second for male humans only. Since the premises talk about different groups, they do not connect – no conclusion follows.

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