Logical Division and Its Rules

In one line

Logical division is the sorting of the things a term denotes into subclasses, on a single principle, so that nothing is left out and nothing falls into two places.

In the wording a student can write in an examination: logical division is the process of dividing a genus into its constituent species according to a principle of division called the fundamentum divisionis. The genus divided is the totum divisum, the classes into which it is divided are the membra dividentia, and the division is governed by rules whose breach produces the fallacies of division.

The vocabulary

The totum divisum is what is divided: the class, considered as a whole.

The membra dividentia are the members of the division: the subclasses produced.

The fundamentum divisionis is the principle on which the division is made: the attribute whose presence or absence sorts the members.

Example. Divide contracts by whether they are in writing. The totum divisum is contracts; the membra dividentia are written contracts and unwritten contracts; the fundamentum divisionis is the presence of writing.

Change the fundamentum and you get a different division of the same class. Divide contracts by whether they are executed or executory; by whether they are bilateral or unilateral; by whether they are valid, void or voidable. Four divisions, one class, and none of them is the true one, exactly as with definitions at sequence 540.

Division against definition

The two halves of Module IV are mirror images and the mirror is the pair from sequence 180.

A definition states a connotation. It lists the attributes something must have.

A division sorts a denotation. It takes the things that have them and puts them into groups.

So the two operate on opposite sides of one relation, and each can be checked by the other. If a division produces a subclass with no members, the definition of the genus and the fundamentum are inconsistent. If a definition cannot be applied to sort a case, the fundamentum has not been made definite enough.

The rules

Rule one: there must be one fundamentum divisionis, and only one at a time.

A division must be made on a single principle. Sorting contracts into written, oral and void uses two principles at once, form and validity, and produces classes that overlap and gaps that are invisible.

Rule two: the membra dividentia must be mutually exclusive.

No member of the genus may fall into two of the subclasses. This follows from rule one where the fundamentum is a single attribute, and it has to be stated separately because a single principle can still be applied in a way that overlaps, as where a class is divided by an attribute that admits of degrees.