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

THE LOGICAL PROPOSITION. 63
"some at least." In either of these last cases, the pro
position is particular; otherwise it is universal.
Some verbal expressions indicating universality may be
mentioned. Words such as All, Every (Each\ Any, He
who ( Whoever), The, and (sometimes) A, when joined to the
Subject, signify an A proposition, just as No, None, signify
an E. Similarly Always, Never, in the predicate, signify A
and E respectively. I is indicated by Some, Certain, A few,
Many, Most, c., or by Generally, Often, standing in the
predicate ; O
by any of these words with a negative. Some
signs of quantity are not free from ambiguity ; and this is
a point requiring special attention, (i) All in a negative
proposition means some, in common language, that is,
"some only" ; and propositions of this form must usually be
treated as exclusives, and be analysed into two propositions.
One of these will be more immediately implied, by the
original proposition, than the other.
" Thus All the metals
are not denser than water," or "Not all the metals are
denser than water," is equivalent to
( (a) Some metals are not denser than water,
( (b) Some metals are denser,
where () may be called the primary, (b) the secondary im
plication. Similarly, "All cannot receive this saying," is
equivalent to
( (a) Some are not able to receive this saying.
} (b) Some are able to receive it.
A proposition of the form
possibly mean "
No
"
"
All S are not P of course might
S are but if P," so it should have stated
its meaning without ambiguity (see ex. 8, below). (2) The
words Few, Hardly any, Scarcely any, before the subject, or
Seldom in the predicate, require the proposition to be
"
"
analysed into two. Few men know how to think asserts
that some do and others do not know how to think. It must
be analysed into an O and an I
proposition, the former being
the primary implication. (3) When Certain means a definite
individual or group which I have in view, it makes the
Subject a singular term (sometimes a singular collective) :
"A certain man encountered him" ; "Certain Greek philo
sophers were the founders of Logic."
In the latter statement