An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

AND THE LAWS OF THOUGHT. 45
alternatives. Great care is necessary to avoid confusing
propositions whose predicates are contrary terms with
the contradictory propositions which the law of excluded
middle has in view.
When we come to deal with the
propositions, in the following chapter,
"
opposition
"
of
the student will
find that we deal only with propositions which expressly
say whether all or part of the subject is referred to,
"
"
All S is P,"
some S is P," and that when the subject
is thus quantified, the contradictory judgments are found
to be "All S is P, Some S is not and also
P,"
is P, Some S is
"
P ; for in each case one and one
" No
S
only of the propositions must be true. In the particular
case when the subject refers to a single or individual
thing, in other words, when S is a singular term,
the contradictory propositions are simply
"
S is P, S is
not P"; e.g., "This stone is old, This stone is not
old." Propositions are said to be contradictory when
one of them states exactly what is sufficient to deny
the other, including no more and no less than what is
sufficient to deny it.
The three laws of Identity, Contradiction, and
Excluded Middle, correspond in each sense in which
they are taken. Thus, as applied to the meaning of
a term, the first law states that the meaning must be
definite and fixed for each term ; the second, that the
with that of
meaning of a term is not interchangeable
another term ; the third, that we must be able to say
whether any given definite idea belongs to a given term
as its meaning, or does not belong. As applied to the
consistency of propositions, the first law says that true
statements must be self-consistent; the second, that they
must be not inconsistent that is, deny each other the
;
third, that of two statements which deny each other, one