Composition / Division Fallacy
The composition/division fallacy is two mirror-image errors that confuse properties of parts with properties of wholes.
Why don't parts and wholes share properties?
Some properties are structural or emergent: they belong to the arrangement, not the constituents (and vice versa). The fallacy collapses the distinction between aggregate and individual.
Composition: inferring that what is true of the parts must be true of the whole.
Example
Each brick in this wall weighs 2 kg, so the wall weighs 2 kg.
Every player on the team is excellent, so the team is excellent (ignores chemistry, coaching, opposition).
Division: the reverse, inferring that what is true of the whole must be true of each part.
Example
The team is the best in the league, so each player is the best in the league at their position.
Water is wet, so each Hâ‚‚O molecule is wet.
Redressing the fallacy
Ask whether the property in question is the kind that could plausibly transfer between parts and whole. If you can construct a counter-example where the parts have the property but the whole doesn’t (or vice versa), the inference is unsafe.