y, however, not very recondite in their
origin--to show that dialectic, when it seems to control existence, must
have taken more than one hint from the subject world, and that in the
realm of logic, too, nothing submits to be governed without
representation.

[Sidenote: Confusion comes of imperfect abstraction, or ambiguous
intent.]

When dialectic is employed, as in ethics and metaphysics, upon highly
complex ideas--concretions in discourse which cover large blocks of
existence--the dialectician in defining and in deducing often reaches
notions which cease to apply in some important respect to the object
originally intended. Thus Socrates, taking "courage" for his theme,
treats it dialectically and expresses the intent of the word by saying
that courage must be good, and then develops the meaning of good,
showing that it means the choice 01 the greater benefit; and finally
turns about and ends by saying that courage is consequently the choice
of the greater benefit and identical with wisdom. Here we have a process
of thought ending in a paradox which, frankly, misrepresents the
original meaning. For "courage" meant not merely something desirable but
something having a certain animal and psychological aspect. The emotion
and gesture of it had not been excluded from the idea. So that while
the argument proves to perfection that unwise courage is a bad thing, it
does not end with an affirmation really true of the original concept.
The instinct which we call courage, with an eye to its psychic and
bodily quality, is not always virtuous or wise. Dialectic, when it
starts with confused and deep-dyed feelings, like those which ethical
and metaphysical terms generally stand for, is thus in great danger of
proving unsatisfactory and being or seeming sophistical.

The mathematical dialectician has no such serious dangers to face. When,
having observed the sun and sundry other objects, he frames the idea of
a circle and tracing out its intent shows that the circle meant cannot
be squared, there is no difficulty in reverting to nature and saying
that the sun's circle cannot be squared. For there is no difference in
intent between the circularity noted in the sun and that which is the
subject of the demonstration. The geometer has made in his first
reflection so clear and violent an abstraction from the sun's actual
bulk and qualities that he will never imagine himself to be speaking of
anything but a concretion in discourse. Th