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

THE LOGICAL PROPOSITION. 55
metals decompose water,"
preted
as "some
here
"
"
some must be inter
only," for we know from Chemistry
that the statement applies only to a particular class of
metals. But as far as the logical form of the proposi
tion is concerned, the whole class is not excluded ; and
we are told nothing as to how much of it, a great or
small portion, is included, and nothing as to whether
any particular case or group of cases is referred to.
be made without
(ct) The affirmation or denial may
explicit reference either to the whole or to a part of the
class denoted by the subject. In this case we have an
indefinite or indesignate proposition,
as "Virtue is a
condition of happiness,"
"
Pleasure is not a good."
Such propositions cannot be dealt with in Logic until
their true and precise meaning is made apparent. As
Jevons says,
" The predicate must be true of the whole
or part of the subject, hence the proposition as it stands
is clearly incomplete ; but if we attempt to remedy this
and supply the marks of quantity, we overstep the
boundaries of Logic and assume ourselves to be
acquainted with the subject-matter
of science of which
the proposition treats." Indefinite propositions, therefore,
have no place in Logic, unless they are merely abbrevia
tions, and their real quantity is obvious, as in the follow
ing :
"
Triangles have their three interior angles together
equal to two right angles," or
" Men
are rational," &c.
On the whole, therefore, we have four possible logical
forms of the proposition :
Universal
affirmative All S is P.
f
NQ g ig p
( affirmative Some S is P.
Particular
^ negatiye gome g [s not p
The form "All S is P" is denoted by the letter A;
"
" No S is P by E ;
"
" Some S is P by I ; and
" Some