to a class,
because they are identified as possessing common characteristics. When,
however, a single abstracted quality is taken as a symbol of a class of
objects, for example, when the quality bitterness becomes the symbol for
the class of bitter things, there can be no real distinction between the
abstracted quality and the class concept. In other words, to fix
attention upon the quality bitterness as a quality distinct from the
object in which it is found, is at the same time to give it a general
character, recognizing it as something which may be found in a number of
objects--the class bitter things. Here the abstract term is in a sense
a general notion representative of a whole class of objects which agree
in the possession of the quality.

=Intension of Concepts.=--Certain of our general notions are, however,
much more complex than others. When a single attribute such as
four-footedness is generalized to represent the class four-footed
objects, the notion itself is relatively simple. In other words, a
single property is representative of the objects, and in apprehending
the members of the class all other properties they chance to possess may
be left out of account. In many cases, however, the class notion will
evidently be much more complex. The notion dog, for instance, in
addition to implying the characteristic four-footedness, may include
such qualities as hairy, barking, watchful, fearless, etc. This greater
or less degree of complexity of a general notion is spoken of as its
intensity. The notion dog, for instance, is more intensive than the
notion four-footed animals; the notion lawyer, than the notion man.

=Extension of Concepts.=--It is to be noted further that as a notion
increases in intension it becomes limited to a smaller class of objects.
From this standpoint, notions are said to differ in extension. The class
lawyer, for instance, is not so extensive as the class man; nor the
class dog, as the class four-footed objects. It will appear from the
above that an abstract notion viewed as a sign of a class of objects is
distinguished by its extension, while a class notion, so far as it
implies a synthesis of several abstracted qualities, is marked rather by
its intension.

AIMS OF CONCEPTUAL LESSONS

So far as school lessons aim to establish and develop correct class
notions in the minds of the pupils, three somewhat distinct types of
work may be noted:

1. TO DEFINE CLASSES

In some lessons