lusive, thus:

[Illustration: FIG. 4.]

That is, _No horned beasts are carnivorous_.

Lastly, the Particular Negative may be represented by any of the Figs.
1, 3, and 4; for it is true that _Some ruminants are not hollow-horned_,
that _Some horned animals are not domestic_, and that _Some horned
beasts are not carnivorous_.

Besides their use in illustrating the denotative force of propositions,
these circles may be employed to verify the results of Obversion,
Conversion, and the secondary modes of Immediate Inference. Thus the
Obverse of A. is clear enough on glancing at Figs. 1 and 2; for if we
agree that whatever term's denotation is represented by a given circle,
the denotation of the contradictory term shall be represented by the
space outside that circle; then if it is true that _All hollow horned
animals are ruminants_, it is at the same time true that _No
hollow-horned animals are not-ruminants_; since none of the
hollow-horned are found outside the palisade that encloses the
ruminants. The Obverse of I., E. or O. may be verified in a similar
manner.

As to the Converse, a Definition is of course susceptible of Simple
Conversion, and this is shown by Fig. 2: 'Men are rational animals' and
'Rational animals are men.' But any other A. proposition is presumably
convertible only by limitation, and this is shown by Fig. 1; where _All
hollow-horned animals are ruminants_, but we can only say that _Some
ruminants are hollow-horned_.

That I. may be simply converted may be seen in Fig. 3, which represents
the least that an I. proposition can mean; and that E. may be simply
converted is manifest in Fig. 4.

As for O., we know that it cannot be converted, and this is made plain
enough by glancing at Fig. 1; for that represents the O., _Some
ruminants are not hollow-horned_, but also shows this to be compatible
with _All hollow-horned animals are ruminants_ (A.). Now in conversion
there is (by definition) no change of quality. The Converse, then, of
_Some ruminants are not hollow-horned_ must be a negative proposition,
having 'hollow-horned' for its subject, either in E. or O.; but these
would be respectively the contrary and contradictory of _All
hollow-horned animals are ruminants_; and, therefore, if this be true,
they must both be false.

But (referring still to Fig. 1) the legitimacy of contrapositing O. is
equally clear; for if _Some ruminants are not hollow-horned_, _Some
animals that are not hollow-horne