rm may be interpreted by a corresponding
concrete one distributed, as _Kindness is infectious_; that is, _All
kind actions suggest imitation_.

If, however, a controvertist has no other object in view than to refute
some general proposition laid down by an opponent, a particular
proposition is all that he need disentangle from any statement that
serves his purpose.

Sec. 2. Toward understanding clearly the relations of the terms of a
proposition, it is often found useful to employ diagrams; and the
diagrams most in use are the circles of Euler.

These circles represent the denotation of the terms. Suppose the
proposition to be _All hollow-horned animals ruminate_: then, if we
could collect all ruminants upon a prairie, and enclose them with a
circular palisade; and segregate from amongst them all the hollow-horned
beasts, and enclose them with another ring-fence inside the other; one
way of interpreting the proposition (namely, in denotation) would be
figured to us thus:

[Illustration: FIG. 1.]

An Universal Affirmative may also state a relation between two terms
whose denotation is co-extensive. A definition always does this, as _Man
is a rational animal_; and this, of course, we cannot represent by two
distinct circles, but at best by one with a thick circumference, to
suggest that two coincide, thus:

[Illustration: FIG. 2.]

The Particular Affirmative Proposition may be represented in several
ways. In the first place, bearing in mind that 'Some' means 'some at
least, it may be all,' an I. proposition may be represented by Figs. 1
and 2; for it is true that _Some horned animals ruminate_, and that
_Some men are rational_. Secondly, there is the case in which the 'Some
things' of which a predication is made are, in fact, not all; whilst the
predicate, though not given as distributed, yet might be so given if we
wished to state the whole truth; as if we say _Some men are Chinese_.
This case is also represented by Fig. 1, the outside circle representing
'Men,' and the inside one 'Chinese.' Thirdly, the predicate may
appertain to some only of the subject, but to a great many other things,
as in _Some horned beasts are domestic_; for it is true that some are
not, and that certain other kinds of animals are, domestic. This case,
therefore, must be illustrated by overlapping circles, thus:

[Illustration: FIG. 3.]

The Universal Negative is sufficiently represented by a single Fig. (4):
two circles mutually exc