Logical Division and Its Rules

Rule three: the division must be exhaustive.

The subclasses taken together must equal the genus: everything in the totum divisum must fall into one of the membra dividentia. Dividing courts into civil and criminal leaves out the tribunals and the revenue courts.

Rule four: the division must proceed by gradual steps.

Each division must produce the species immediately below the genus, not a species several levels down. Dividing "legal proceedings" straight into "appeals to the Supreme Court" and "everything else" skips every intermediate level and tells you nothing about the structure of the class.

Rule five: the division must be appropriate to the purpose.

Dividing decrees by the colour of the paper they are typed on satisfies rules one to four perfectly and is useless. This rule is the one sequence 540 supplies: a division, like a definition, is good only in relation to a purpose.

Why rules two and three matter most

Because between them they express the whole point of a division, and there is a name for it.

A division that satisfies rules two and three is exhaustive and exclusive, which means every member of the class falls into exactly one subclass, no more and no less. Applied to a case, such a division always gives one answer, which is why a statute that divides its subject properly can be applied without argument.

Rule three failing produces a gap, and a gap in a statutory division is a case the Act does not reach.

Rule two failing produces an overlap, and an overlap in a statutory division is a case to which two inconsistent provisions apply at once.

Both defects are litigated constantly, and both are visible on the face of the division to a reader who applies the rules.

Logical, physical and metaphysical division

Added after the past-paper check, since MU asks for metaphysical division by name.

Traditional logic recognises three operations that all get called division, and only the first is logical division.

Logical division separates a class into subclasses, on a fundamentum divisionis. Contracts into written and oral. The members of a subclass are members of the class: a written contract is a contract.

Physical division, which is partition, separates a whole into its parts. An Act into its sections, a car into its wheels and body, a trial into its stages. The parts are not members of the whole: a section is not an Act.

Metaphysical division separates a thing into its constituent attributes, the qualities that together make it what it is. Man into animality and rationality. A contract into agreement, competent parties, free consent, lawful consideration and lawful object. The attributes are not members of the class and are not parts of the thing in the physical sense; they are what the definition of it consists of.

The three are told apart by one question: what is being separated, a class, a thing, or the connotation of a term?

And the third is the one worth noticing, because it is the mirror of definition. A metaphysical division sets out exactly the attributes a definition per genus et differentiam states, which is why section 10 of the Indian Contract Act 1872, read as a list of four requirements, is at once a definition of a contract and a metaphysical division of it.

The rules of this chapter apply to logical division only. Asking whether a metaphysical division is exhaustive of its class, or whether an Act's sections are mutually exclusive as subclasses, is asking a question about nothing.

Division and partition

The two are often confused and the distinction is examinable.

Division separates a class into subclasses. The members of a subclass are members of the class: a written contract is a contract.

Partition separates a whole into parts. The parts are not members of the whole: a chapter of an Act is not an Act, and a wheel is not a car.

The test. Ask whether the name of the genus can be predicated of what you have produced. "A written contract is a contract" is true, so that was a division. "A section is an Act" is false, so that was a partition.

Why it matters. Because the rules above apply to division and not to partition, and because the fallacy of arguing from a whole to its parts, or from parts to the whole, is a distinct error which sequence 640 has to keep separate from the fallacies of division proper.

A worked example

An Act is to divide "documents" for the purpose of prescribing which must be registered.

Attempt one. Documents are divided into wills, sale deeds, leases, mortgages and others.

Rule one. What is the fundamentum? There is none: this is a list, not a division. "Others" is doing the whole work.

Rule three. It is exhaustive only because of "others", which is a way of pretending to be exhaustive without being informative.

Attempt two. Documents are divided into those which create or extinguish an interest in immoveable property and those which do not.

Rule one. One fundamentum: whether an interest in immoveable property is created or extinguished. Satisfied.

Rule two. No document can both create such an interest and not create it. Satisfied.

Rule three. Every document falls on one side or the other. Satisfied.

Rule four. The step is a single one from the genus. Satisfied.

Rule five. Is it appropriate to the purpose of a registration statute? Yes: registration exists to give notice of dealings with land. Satisfied.

Attempt three, and the trap. Documents are divided into those creating an interest in immoveable property, those creating an interest in moveable property, and those in writing.

Rule one fails. Two principles are in play, subject matter and form, and once that happens rules two and three fail with it: a written sale deed falls into two classes, and an oral transaction affecting neither kind of property falls into none.

What the exercise shows. The rules are not decoration. Attempt three is exactly the shape a badly drafted definition clause takes, and applying five short tests to it exposes both defects in a line.

Distinctions that carry marks

What this does not mean

A list is not a division. A list with "and others" at the end is exhaustive and has no principle, so it tells you nothing about anything not named.

A division is not a definition. It sorts the things a term denotes; a definition states the attributes the term connotes. Each can be used to check the other and neither replaces it.

More subclasses is not better. A division is judged by its rules and its purpose, and a division into twenty classes that fails rule two is worse than a division into two that satisfies it.

Quick revision

Logical division sorts a denotation, where a definition states a connotation.

Vocabulary: totum divisum, the class divided; membra dividentia, the subclasses; fundamentum divisionis, the principle.

One class, many divisions, according to the fundamentum chosen, and none of them the true one.

Five rules: one fundamentum at a time; mutually exclusive subclasses; exhaustive subclasses; gradual steps; appropriateness to the purpose.

Rules two and three together make a division exhaustive and exclusive, so that every member falls into exactly one class. A gap in a statutory division is a case the Act misses; an overlap is a case two provisions govern at once.

Division against partition: a written contract is a contract, so that was a division; a section is not an Act, so that was a partition.

Three operations called division: LOGICAL, a class into subclasses; PHYSICAL or partition, a whole into parts; METAPHYSICAL, a thing into its constituent attributes, as man into animality and rationality. Only the first is governed by the five rules.

Test yourself

1. Define logical division and name its three elements.

Logical division is the process of dividing a genus into its constituent species on a single principle. Its elements are the totum divisum, the class being divided; the membra dividentia, the subclasses produced; and the fundamentum divisionis, the principle on which the division is made, being the attribute whose presence or absence sorts the members of the class.

2. How does division relate to definition?

They are mirror images operating on the two sides of one relation. A definition states the connotation of a term, listing the attributes a thing must have to fall under it; a division sorts the denotation, taking the things that have those attributes and grouping them. Each can check the other: a subclass with no members shows that the definition and the fundamentum are inconsistent, and a fundamentum that cannot sort a case shows that the definition was not made definite enough.

3. State the five rules of division.

There must be one fundamentum divisionis, and only one at a time. The membra dividentia must be mutually exclusive, so that nothing falls into two of them. The division must be exhaustive, the subclasses together equalling the genus. It must proceed by gradual steps, producing the species immediately below the genus rather than one several levels down. And it must be appropriate to the purpose for which it is made.

4. Why are rules two and three said to matter most?

Because together they make the division exhaustive and exclusive, so that every member of the class falls into exactly one subclass and applying the division to a case always yields one answer. A breach of rule three leaves a gap, which in a statute is a case the Act fails to reach; a breach of rule two leaves an overlap, which is a case to which two provisions apply at once. Both are visible on the face of the division and both are litigated constantly.

5. Distinguish division from partition, and give the test.

Division separates a class into subclasses whose members are members of the class; partition separates a whole into parts which are not members of the whole. The test is whether the name of the genus can be predicated of what has been produced: "a written contract is a contract" is true, so contracts into written and oral is a division, while "a section is an Act" is false, so an Act into sections is a partition. The rules of division apply only to the first.

7. Distinguish logical, physical and metaphysical division.

Logical division separates a class into subclasses on a principle of division, and the members of a subclass are members of the class. Physical division, or partition, separates a whole into its parts, and the parts are not members of the whole: a section is not an Act. Metaphysical division separates a thing into the constituent attributes that make it what it is, as man is divided into animality and rationality, and those attributes are neither members nor parts. The three are told apart by asking what is being separated: a class, a thing, or the connotation of a term.

8. Why is metaphysical division the mirror of definition?

Because it sets out exactly the attributes that a definition per genus et differentiam states. Section 10 of the Indian Contract Act 1872, read as the four requirements of free consent, competent parties, lawful consideration and lawful object, is at once a definition of a contract and a metaphysical division of it. The five rules of this chapter apply to logical division alone, so asking whether a metaphysical division is exhaustive of a class is asking a question about nothing.

6. Why is a list ending in "and others" not a division?

Because it has no fundamentum divisionis. It names some members and then sweeps up the rest, so it satisfies the requirement of exhaustiveness only formally and tells the reader nothing about anything it did not name. Extension cannot fix intension, as sequence 580 showed for denotative definitions, and a residual class is that failure appearing in the form of a division.