FOURTH RULE. _The division must proceed from the proximate genus to the immediate species._ There should be no sudden jumps from a high genus to a low species. The division must be gradual and continuous; step by step. To divide government into limited monarchy, absolute monarchy, pure democracy and representative democracy would be a violation of this rule, as government is the proximate genus of monarchy, not of limited monarchy, therefore one step has been omitted. Such an omission involves a step from grandfather to grandchild, so to speak, the generation of father having been left out.
A violation of this rule is most insidious when some of the species of a subdivision are immediate while others are not. To wit: dividing government into monarchy, aristocracy, pure democracy and republic, or dividing quadrilaterals into trapeziums, trapezoids, rectangles, squares, rhomboids and rhombs.
Dichotomy comes from the Greek, meaning _to cut in two_. _Dichotomy is a continual division of a genus into two species which are contradictory in nature._
Contradictory terms are such as admit of no middle ground. They divide the whole universe of thought into two classes. For example, honest and not-honest, pure and impure, perfect and imperfect, are contradictory terms. Dichotomy thus affords an easy opportunity for an exhaustive division as in the use of contradictories nothing in the universe need be omitted.
An historical illustration of dichotomy is the “Tree of Porphyry” named after Porphyrius, a Neo-Platonic philosopher of the third century.
Substance. / \ / \ Corporeal Incorporeal \ \ Body / \ / \ Animate Inanimate \ \ Living Being / \ / \ Sensible Insensible \ \ Animal / \ / \ Rational Irrational \ \ Man / | \ / | \ / | \ Socrates Plato Other Men
This kind of division is not altogether satisfactory as the negative side is too indefinite. On the other hand, if both subdivisions are made positive then there is danger of making the opposing terms contrary rather than contradictory. This, of course, would be a serious logical fallacy, as contrary terms admit of middle ground while contradictory terms give no choice, it is either the one or the other.
The use of dichotomy becomes evident in situations where new and unexpected discoveries may be made. Without disturbing the classification the new species may be appended to the negative side of the division. The following illustrates: