Logical Division
How ideas are explained by dividing them: the doctrine of Logical Division (its three elements — Principle, Totality, Dividing Members) and the four rules that govern a correct division.
Logical Division explains an idea by analysing its Extension — distributing the idea into its inferior ideas according to a governing Principle of Division. Every division has three elements: the Whole to be divided (the divident), the Principle of Division (the characteristic used to divide it), and the Dividing Members (the resulting classes). Four rules govern valid division: it must be exhaustive (the members jointly equal the whole), exclusive (the members do not overlap), immediate (members are taken at the same level of generality rather than skipping levels), and consistent (the same principle is used throughout — cross-division, mixing principles, is the principal error to avoid). Logical Division is carefully distinguished from physical partition (dividing a whole into its parts) and from mere Classification.
a) Doctrine of Logical Division
Logical Division is the orderly and systematic grouping or classification of the inferiors of a Universal. To divide the inferiors of the Universal man into white men, red men, yellow men, black men, is a Logical Division. Logical Division explains ideas by exemplifying them in classes.
Logical vs. Real Division
Logical Division differs from Real Division, which is the division of a reality into its component parts. Real Division is:
- Physical: distinguishing actual objective parts of a reality (man divided into body and soul; a tree into trunk, roots, and branches).
- Metaphysical: distinguishing essential notes in an idea (man divided into rational and animal).
Definition depends upon metaphysical division, for an idea must be analysed into its essential notes before those notes can be summed up in an essential definition. Real Division looks to content; Logical Division looks to Extension or application of an idea.
Three Elements of Logical Division
Every Logical Division has three elements:
1. The Principle of Division — the base, aspect, or point of view from which the division is made. If I divide Books into Books on Theology, Philosophy, and History, the Principle is “Nature of Contents.” If I divide Books into red, blue, and green books, the Principle is “Colour of Binding.”
2. The Totality Divided — a universal idea considered as applied in Extension. In the examples above, the Totality Divided is the Universal book taken in extension.
3. The Dividing Members — the groups effected by the Logical Division. If I divide the Universal man (taken in extension as all human beings) into white, black, yellow, and red men, each of those classifications is a Dividing Member.
To illustrate all three together:
| Element | Value |
|---|---|
| Totality Divided | man |
| Principle of Division | race |
| Dividing Members | men of the white race, men of the black race, men of the yellow race, men of the red race |
b) Rules of Logical Division
Logical Division, like Definition, is a means of clarifying ideas. If not regular, consistent, systematic, and complete, it will muddle and obscure rather than clarify. The following rules must be carefully learned.
Rule I: In each Logical Division there must be only one Principle of Division
A shift in base makes the Division confused rather than clarifying. The following offends against this rule:
Totality Divided: Americans Principle of Division: Religion Dividing Members: Catholics, Protestants, Democrats, Quakers, etc.
Democrats is a political, not a religious, classification — the principle has shifted.
Rule II: The sum of the Dividing Members must equal the Totality Divided
The Division must be complete — no Dividing Members omitted. An incomplete Division lacks the definiteness needed to clarify. The following offends:
Totality Divided: chairs Principle of Division: service Dividing Members: useful chairs, ornamental chairs.
Incomplete — there are chairs which serve neither use nor ornament.
Rule III: Let no single Dividing Member be coextensive with the Totality Divided
To propose as a Dividing Member what is equal in Extension with the Totality Divided is to fail to divide at all. The following offends:
Totality Divided: Animals Principle of Division: Cognitive capacity Dividing Members: sentient animals, rational animals.
“Sentient animals” is not a proper subclass of animals — all animals are sentient. No real division has been made.
Rule IV: The Dividing Members must be properly arranged
Failure in proper arrangement — coordination and subordination — makes the Division a confusing jumble. The following offends:
Totality Divided: Americans Principle of Division: Place of Residence Dividing Members: North Americans, South Americans, Central Americans, Mexicans.
Mexicans (a national group) should not be co-ordinated with continental groups; its proper place is one of subordination to “North Americans.”
A correct Division under this same Principle would look like:
Americans
├── North Americans
│ ├── Canadians
│ ├── Inhabitants of U.S.A.
│ │ ├── (by State) Pennsylvanians, Ohioans, New Yorkers…
│ │ └── (by County, Town, Ward…)
│ ├── Mexicans
│ └── Alaskans
├── Central Americans
└── South AmericansThe Rules of Logical Division are summed up in the following mnemonic:
One principle; all members call; And let no member equal all; Arrange — with due deliberation — Coordinate subordination.
Summary of the Article
We have learned what is meant by Logical Division and have contrasted it with Real Division (physical and metaphysical). We have learned the three essential elements of Logical Division — the Principle of Division, the Totality Divided, and the Dividing Members — and have exemplified the four rules which must be observed in order to make Logical Division serve its purpose of clarifying ideas.