lustrated. When you began the study of geometry you faced a
multitude of new terms; we call them technical terms, such as
projection, scalene, theory of limits. These had to be clearly
understood before you could reason in the subject. And when, in the
progress of your study, you experienced difficulty in reasoning out
problems, it was very likely due to the fact that you did not master
the technical terms, and as soon as you encountered the difficulties of
the course, you failed because your foundation laying did not involve
the acquisition of clear ideas. Examine your difficulties in reasoning
subjects and if you find them traceable to vagueness of ideas, take
steps to clarify them.

Ideas may be clarified in two ways: by definition and by
classification. Definition is a familiar device, for you have had much
to do with it in learning. The memorization of definitions is an
excellent practice, not as an end in itself, but as a means to the end
of effective reasoning. Throughout your study, then, pay much attention
to definitions. Some you will find in your texts, but others you will
have to make for yourself. In order to get practice in this, undertake
the manufacture of a few definitions, using terms such as charity,
benevolence, natural selection. This exercise will reveal what an
exacting mental operation definition is and will prove how vague most of
your thinking really is.

A large stock of definitions will help you to think rapidly. Standing
as they do for a large group of experiences, definitions are a means of
mental economy. For illustration of their service in reasoning, suppose
you were asked to compare the serf, the peon and the American slave. If
you have a clean-cut definition of each of these terms, you can readily
differentiate between them, but if you cannot define them, you will
hardly be able to reason concerning them.

The second means of clarifying ideas is classification. By this is
meant the process of grouping similar ideas or similar points of ideas.
For example, your ideas of serf, peon and slave have some points in
common. Group the ideas, then, with reference to these points. Then in
reasoning you can quickly place an idea in its proper group.

The third stage of the reasoning process is decision, based on belief,
and it comes inevitably, provided the other two processes have been
performed rightly. Accordingly, we need say little about its place in
study. One caution should be pointed