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

60 THE LOGICAL PROPOSITION.
The whole sense of this can be expressed in two
propositions :
(a) Self-supporting men who are honest and pious
(l>) Paupers
will be respected ;
who are honest and pious
will not be
respected.
Two other propositions are emphasised in the original
statement ; (c) is a particular case of (a), and (d) of (/ ) :
(c) Poor and illiterate men who are self-supporting,
honest, and pious, will be respected.
(dT) Poor, illiterate, honest, pious men who are paupers
will not be respected.
The best test for deciding whether a given proposition
is compound or not is to observe whether it admits of
being contradicted in more than one way.
The analysis of the compound propositions which are
called exclusive and exceptive is less simple. In
exclusive propositions the Subject is limited by words
like
"
alone,"
"
only,"
"
none but,"
"
none except,"
"none who is not" : as, "Graduates alone are eligible,"
"
S alone is P." This may be contradicted in two : ways
by asserting that some graduates are not eligible, or
that some persons are eligible who are not graduates.
An assertion is in fact made about graduates and about
persons who are not graduates ; none of the latter,
and some at least of the former, are eligible. Hence
the given proposition is equivalent to two simple
propositions :
{(a)
Some graduates are eligible.
(b) No non-graduates are eligible,
Some S is P.
j"
( No not-S is P.
This mode of treatment is applicable to all exclusive
propositions.