4.2 Notes on Four Rules of Dividing Properly in Logic - From the "Reasonable Person" by Mark Grannis

When it comes to dividing wholes into their parts in a proper manner, there are four basic rules of logic that we should follow. 

The Single-Principle Rule

"Every good division must be performed on the basis of a single principle of division." In so many words we need to divide wholes by a rule of division if it is going to make any sense. If we use more than one rule at a time the division becomes meaningless. This doesn't mean that we can't create separate divisions of the same thing with different rules, but only that mixing rules at the same time make the reason and logic of the division unclear. 

Two or More Inferiors at Every Level 

"Every good division or subdivision must use two or more inferior parts." If one is dividing a whole, by definition, it is divided into more parts and thus is more than one thing now. Therefore, in division there should always be at least two parts mentioned as inferiors. 

Exhaustiveness

"Every good division must exhaustively assign the entire extension of the whole to one of the inferior parts." To divide well and in a meaningful way we must not leave out any parts of the whole, especially not essential parts to the whole. This may seem impossible but Grannis makes the point that we can always use the "other" category to collect all of the smaller or insignificant parts. 

Mutual Exclusivity

"Every good division must assign each inferior of the whole to only one of the inferior parts." Inferior parts must not be placed into multiple categories, as this would lead to contradictions. 

Grannis then gives a one sentence summary which includes all four of these rules. "Every single inferior of the logical whole must be assignable to one and only one of two or more inferiors parts on the basis of a single principle of division."