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

THE LOGICAL PROPOSITION. 57
use the word "may" e.g.,
if a person says "Some
Irishmen are not Nationalists," he tells us that any
chance Irishman may not be a Nationalist.
" Some S
are not P" means that there is no inseparable con
nection between S and P ;
"
"
some S are P means that
there is no incompatibility between S and P.
We must distinguish the propositions
"
S is not
necessarily P," and "S is necessarily not P"
impossible
i.e., it is
that S should be P. The latter is an asser
tion of impossibility, and of course forms an E pro
position, as in
" The circumference of a circle is neces
sarily not commensurable with its diameter." The
former is merely a denial of necessity, as in "A republic
does not necessarily secure good government," or
paths are not necessarily
"
Old
the best." The sense of these
propositions is that "Some S is not P," "Some republics
do not secure good government," "Some old paths are
not the best."
The last division of propositions which we need
notice here is that of verbal and real, also spoken of
as explicative and ampliative, or analytic and synthetic
respectively. This distinction depends on the assumed
fixity of definitions, to which we referred before (ch. II.
7), and it is not applicable unless the fixed definitions
of the terms concerned are actually known. The pro
position S is P is analytic when P is the definition or
part of the definition of S ;
it is synthetic when P is
not part of the definition of S. It is evident that only
when we have an accepted definition of the subject,
can we tell whether the proposition is synthetic or not.
And owing to the very various amounts of knowledge
possessed by different minds, a proposition may be
analytic to one person, who knows the definition of the
subject, and synthetic to another, who does not know