Definition moves up from a species to its genus. Logical division moves down: it splits a genus into its species. Done well, it gives a clean map of a subject; done badly, it causes the confusion you see in messy categories.
Key idea
A good division uses one principle, so its parts are exclusive (nothing falls in two parts) and together exhaustive (everything falls in some part).
Why it works
A principle is one question that sorts every member: "What is the largest angle of this triangle?" Because each triangle has exactly one answer, it lands in exactly one part, so no overlaps; and because every triangle has some answer, none are left out. Mixing two questions, such as kind of writing and type of binding for books, breaks both: a hardcover novel lands in two parts, and some books may land in none.
| Division | Principle | Verdict |
|---|---|---|
| triangles: acute, right, obtuse | largest angle | good |
| books: novels, hardcovers, library books | three at once | overlaps |
| vehicles: cars, trucks | kind of vehicle | leaves out bicycles and buses |
Worked examples
Worked example: Finding the fault
Is "dogs: puppies, beagles and pets" a good division?
- Look for the principle. "Puppies" sorts by age, "beagles" by breed, "pets" by whether someone owns the dog.
- Three principles at once means overlap: a pet beagle puppy fits all three parts.
- And a stray adult collie fits none.
Answer: not good: it mixes principles
Worked example: Parts, not kinds
Is "a bicycle: frame, wheels, chain and handlebars" a logical division?
- In a logical division each part is itself a kind of the whole: every acute triangle is a triangle.
- A wheel is not a kind of bicycle. These are the physical pieces of one thing.
Answer: no: it is a partition into parts, not a division into kinds
Common mistake
Mixing principles ("books: novels, hardcovers, library books"). The parts overlap, and some books fit nowhere or in two places. Check: name the single question that sorts every member. If you need two questions, the division is mixed.