by it.

2. The Sub-classes taken together should be equal to the Class to be
divided: the sum of the Species constitutes the Genus. This provides
that the division shall be exhaustive; which dichotomy always secures,
according to the principle of Excluded Middle; because whatever is not
in the positive class, must be in the negative: Red and Not-red include
all colours.

3. The Sub-classes must be opposed or mutually exclusive: Species must
not overlap. This again is secured by dichotomy, according to the
principle of Contradiction, provided the division be made upon one
attribute at a time. But, if we attempt to divide simultaneously upon
two attributes, as 'Musicians' upon 'nationality' and 'method,' we get
what is called a Cross-division, thus 'German Musicians.' 'Not-German,'
'Classical,' 'Not-Classical;' for these classes may overlap, the same
men sometimes appearing in two groups--Bach in 'German' and 'Classical,'
Pergolesi in 'Not-German' and 'Classical.' If, however, we divide
Musicians upon these attributes successively, cross division will be
avoided, thus:

Musicians
|
------------------------
| |
Classical Not-classical
| |
------------ ------------
| | | |
German Not-German German Not-German

Here no Musician will be found in two classes, _unless_ he has written
works in two styles, _or unless_ there are works whose style is
undecided. This "unless--or unless" may suggest caution in using
dichotomy as a short cut to the classification of realities.

4. No Sub-class must include anything that is not comprised in the class
to be divided: the Genus comprises all the Species. We must not divide
Dogs into fox-terriers and dog-fish.

Sec. 6. The process of Inductive Classification may be represented thus:

Given any multitude of individuals to be classified:

(1) Place together in groups (or in thought) those things that have in
common the most, the most widely diffused and the most important
qualities.

(2) Connect those groups which have, as groups, the greater resemblance,
and separate those that have the greater difference.

(3) Demarcate, as forming higher or more general classes, those groups
of groups that have important characters in common; and, if possible, on
the same principle, form these higher classes into c