Steelman
Undistributed middle
Also called fallacy of the undistributed middle, maldistributed middle.
Two things share a trait, so one must belong to the other.
What it is
A categorical syllogism in which the middle term (the one shared by both premises but absent from the conclusion) is not distributed in either premise, so the premises never link the other two terms together.
The pattern
All P are M. All S are M. Therefore, all S are P. (invalid) Valid look-alike (Barbara): All M are P. All S are M. Therefore, all S are P.
An example
“All Olympic swimmers are strong swimmers. My brother is a strong swimmer. So my brother is an Olympic swimmer.”
Middle term: “strong swimmers”, undistributed in both premises. Olympic swimmers are only some of the strong swimmers.
Why it fails
Both premises say S and P fall somewhere inside M, but not where. They could overlap or be completely separate: cats and dogs are both mammals without cats being dogs. The middle term has to cover all of its class at least once to connect S to P.
When it’s not a fallacy
Most lists skip this part. Calling a fair point a fallacy is a mistake too.
It can be fair when
- The middle term is distributed at least once, for example when “All M are P” puts M in subject position. That is the valid form Barbara.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Reddit thread. A: “Esports aren’t sports. They’re video games with prize money.”
B: “Every sport has coaches, sponsors and packed finals. Esports have all three: the League of Legends final filled a stadium in Seoul, so don’t tell me nobody shows up. So esports are sports. You don’t have to like them, but that’s what they are.”
What’s the flaw?
Sports have coaches, sponsors and packed finals, and so do esports. Sharing those traits doesn’t put esports inside “sports,” since lots of things that aren’t sports have them too. The premises never link the two groups.
A fair reply
“Singing contests have coaches, sponsors and packed finals too, and nobody calls them a sport.”
Often confused with
- Guilt by association
Guilt by association is often an undistributed middle in everyday dress: “Bad people do X; you do X; so you’re bad.”
- Affirming the consequent
Affirming the consequent is the propositional cousin: “If P then Q; Q; so P”.
Where the name comes from
The middle term is the group that shows up in both premises (the two starting statements) but not in the conclusion. Its job is to link the other two groups. A term is distributed when a statement covers every member of it. “All chefs are cooks” covers every chef but only some cooks. An undistributed middle never covers all its members, so it can’t link anything. Fallacy of the undistributed middle is the full name, and maldistributed middle means the same: mal- means “badly.”
Sources
- Undistributed Middle Term, The Fallacy Files
- Syllogistic Fallacy (terminology and distribution), The Fallacy Files
- Fallacies, Bradley Dowden, Internet Encyclopedia of Philosophy
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of undistributed middle, how to answer it in a real conversation, and practice rounds that mix it with its look-alikes, so you learn the difference, not just the name. Coming soon to iPhone and Android.
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