II. _The division should be complete and exhaustive._ For instance, the analysis of a genus should extend to every known species of it, upon the principle that _the genus is merely the sum of its several species_. A textbook illustration of a violation of this rule is given in the case of the concept _actions_, when divided into _good-actions_ and _bad-actions_, but omitting the very important species of _indifferent-actions_. Carelessness in observance of this rule leads to fallacious reasoning and cloudy thinking.
III. _The division should be in logical sequence._ It is illogical to skip or pass over intermediate divisions, as for instance, when we divide _animals_ into _horses_, _trout and swallows_, omitting the intermediate division into _mammals_, _fish and birds_. The more perfect the sequence, the clearer the analysis and the thought resulting therefrom.
IV. _The division should be exclusive._ That is, the various species divided from a genus, should be reciprocally exclusive–should exclude one another. Thus to divide _mankind_ into _male_, _men and women_, would be illogical, because the class _male_ includes _men_. The division should be either: “_male and female_;” or else: “men, women, boys, girls.”
The exercise of Division along these lines, and according to these rules, will tend to improve one’s powers of conception and analysis. Any class of objects–any general concept–may be used for practice. A trial will show you the great powers of unfoldment contained within this simple process. It tends to broaden and widen one’s conception of almost any class of objects.
There are also several rules for Partition which should be observed, as follows:
I. _The partition should be complete and exhaustive._ That is, it should unfold the full meaning of the term or concept, so far as is concerned its several general qualities, properties and attributes. But this applies only to the qualities, properties and attributes which are _common_ to the class or concept, and not to the minor qualities which belong solely to the various sub-divisions composing the class; nor to the accidental or individual qualities belonging to the separate individuals in any sub-class. The qualities should be _essential_ and not _accidental_–general, not particular. A famous violation of this rule was had in the case of the ancient Platonic definition of “Man” as: “A two-legged animal without feathers,” which Diogenes rendered absurd by offering a plucked chicken as a “man” according to the definition. Clearness in thought requires the recognition of the distinction between the general qualities and the individual, particular or accidental qualities. Red-hair is an accidental quality of a particular man and not a general quality of the class _man_.
II. _The partition should consider the qualities, properties and attributes_, according to the classification of logical division. That is, the various qualities, properties and attributes should be considered in the form of genus and species, as in Division. In this classification, the rules of Division apply.
It will be seen that there is a close relationship existing between Partition and Definition. Definition is really a statement of the various qualities, attributes, and properties of a concept, either stated in particular or else in concepts of other and larger classes. There is perhaps no better exercise for the cultivation of clear thought and conception than Definition. In order to define, one must exercise his power of analysis to a considerable extent. Brooks says: “Exercises in logical definition are valuable in unfolding our conception. Logical definition, including both the genus and the specific difference, gives clearness, definiteness and adequacy to our conceptions. It separates a conception from all other conceptions by fixing upon and presenting the essential and distinctive property or properties of the conception defined. The value of exercises in logical definition is thus readily apparent.”
If the student will select some familiar term and endeavor to define it correctly, writing down the result, and will then compare the latter with the definition given in some standard dictionary, he will see a new light regarding logical definition. Practice in definition, conducted along these lines, will cultivate the powers of analysis and conception and will, at the same time, tend toward the acquiring of correct and scientific methods of thought and clear expression.
Hyslop gives the following excellent Rules of Logical Definition, which should be followed by the student in his exercises:
“I. A definition should state the essential attributes of the species defined.
“II. A definition must not contain the name or word defined. Otherwise the definition is called _a circulus in definiendo_ (defining in a circle).
“III. The definition must be exactly equivalent to the species defined.
“IV. A definition should not be expressed in obscure, figurative or ambiguous language.
“V. A definition must not be negative when it can be affirmative.”