are
principles of intelligence. Here, then, as in proof, induction is
implied in deduction, and deduction in induction. Still, the two modes
of procedure may be usefully distinguished: in deduction, we proceed
from the idea of a whole to its parts, from general to special; in
induction, from special (or particular) to general, from parts to the
idea of a whole.

Sec. 4. The process of Deductive Classification, or Formal Division, may be
represented thus:

A
|
-------------------
| |
A B A b
| |
---------- ----------
| | | |
A B C A B c A b C A b c

Given any class (A) to be divided:

1. Select one important character, attribute, or quality (B), not common
to all the individuals comprehended in the class, as the basis of
division (_fundamentum divisionis_).

2. Proceed by Dichotomy; that is, cut the given class into two, one
having the selected attribute (say, B), the other not having it (b).
This, like all formal processes, assumes the principles of Contradiction
and Excluded Middle, that 'No A is both B and not-B,' and that 'Every A
is either B or not-B' (chap. vi. Sec. 3); and if these principles are not
true, or not applicable, the method fails.

When a class is thus subdivided, it may be called, in relation to its
subclasses, a Genus; and in relation to it, the subclasses may be called
Species: thus--genus A, species AB and Ab, etc.

3. Proceed gradually in the order of the importance of characters; that
is, having divided the given class, subdivide on the same principle the
two classes thence arising; and so again and again, step by step, until
all the characters are exhausted: _Divisio ne fiat per saltum_.

Suppose we were to attempt an exhaustive classification of things by
this method, we must begin with 'All Things,' and divide them (say) into
phenomenal and not-phenomenal, and then subdivide phenomena, and so on,
thus:

All Things
|
------------------
| |
Phenomenal Not-phenomenal
|
--------------------
| |
Extend