Composition goes from the parts to the whole. Division goes the other way.
Key idea
Division reasons that because the whole has a property, each part must have it too.
Why it works
A whole can have properties that come from how its parts work together or add up. An orchestra can be famous while its players are not; a class can raise a lot of money from many small gifts. The property belongs to the whole, not to each part.
Worked example: Does it pass down?
"The cake is sweet, so the flour in it is sweet."
- The cake is sweet because of the sugar.
- Sweetness of the whole does not pass to every ingredient.
Answer: Division.
Worked example: It passes down
"The whole fence is painted white, so each board of the fence is painted white."
- If all of the fence is white, each board is white.
- Color spread over the whole passes to each part.
Answer: Not a fallacy.
| Composition | Division |
|---|---|
| parts → whole | whole → parts |
| Every player is great, so the team is great. | The team is great, so every player is great. |
Common mistake
Mixing up composition and division. Composition goes from the parts up to the whole; division goes from the whole down to the parts. Find which one the premise is about and which one the conclusion is about.