very term has a contradictory_, and
that every predication concerning a term implies some predication
concerning its contradictory. But the name of the _suppositio_ itself
has no contradictory, except with reference to a wider and inclusive
_suppositio_.

The difficulty of actual reasoning, not with symbols, but about matters
of fact, does not arise from the principles of Logic, but sometimes from
the obscurity or complexity of the facts, sometimes from the ambiguity
or clumsiness of language, sometimes from the deficiency of our own
minds in penetration, tenacity and lucidity. One must do one's best to
study the facts, and not be too easily discouraged.

CHAPTER VII

IMMEDIATE INFERENCES

Sec. 1. Under the general title of Immediate Inference Logicians discuss
three subjects, namely, Opposition, Conversion, and Obversion; to which
some writers add other forms, such as Whole and Part in Connotation,
Contraposition, Inversion, etc. Of Opposition, again, all recognise
four modes: Subalternation, Contradiction, Contrariety and
Sub-contrariety. The only peculiarities of the exposition upon which we
are now entering are, that it follows the lead of the three Laws of
Thought, taking first those modes of Immediate Inference in which
Identity is most important, then those which plainly involve
Contradiction and Excluded Middle; and that this method results in
separating the modes of Opposition, connecting Subalternation with
Conversion, and the other modes with Obversion. To make up for this
departure from usage, the four modes of Opposition will be brought
together again in Sec. 9.

Sec. 2. Subalternation.--Opposition being the relation of propositions that
have the same matter and differ only in form (as A., E., I., O.),
propositions of the forms A. and I. are said to be Subalterns in
relation to one another, and so are E. and O.; the universal of each
quality being distinguished as 'subalternans,' and the particular as
'subalternate.'

It follows from the principle of Identity that, the matter of the
propositions being the same, if A. is true I. is true, and that if E. is
true O. is true; for A. and E. predicate something of _All S_ or _All
men_; and since I. and O. make the same predication of _Some S_ or
_Some men_, the sense of these particular propositions has already been
predicated in A. or E. If _All S is P, Some S is P_; if _No S is P, Some
S is not P_; or, if _All men are fond of laughing, Some men a