Sis P

PROPOSITIONS.
54
[PART IJ.
the copula and the predicate are not separated ; e.g., The
man runs, AU that love virtue love angling. In the latter,
the copula and the predicate are made distinct; e.g., The
man is running, All lovers of virtue are lovers of angling.
To complete our analysis we ought to note a fourth
element in the categorical proposition, namely, the sign
of quantity attached to the subject. In the proposition
Al! Sis P that sign of quantity is al!~ and we accordingly
understand the affirmation to be made of each and every
individual denoted by the term S.
CHAP. I.]
(4) the particular. negative,_Some S is not P, (or Not
all Sis P,or Sorne S's are not P's, or Not all S's are P's),
usually denoted by the symbol O.
These symbols A, I, and E, 0, are taken from the Latin
words ajfirmo and nego, t_he affirmative symbols being the
first two vowels of the former, and the negative symbols
the two vowels of the latter.
Besides these symbols, it will also be found convenient
sometimes to use the following,-
SaP=All Sis P;
SiP=Some Sis P;
SeP= No Sis P;
· SoP = Sorne S is not P.
(it.\ :-{7
(j\. \
I
E
(
1
We may say that the subject and predicate of a proposition
constitute its malter; while its quantity and quality constitute its?form.
2
. Instead of these terms Professor Bain suggests the tcnns total. and
partial.
55
Q
36. The Quantity and Quality of Propositions 1•
The Quality of a proposition is determined by the
copula, being a rmative or negative according as the copula
~ ,~~ is of the fo_r~ " ~' or ''is n~~-" .
Propositions are also d1v1ded mto universa!. and particular2, according as the affirmation or denial is made of
the whole or of a part of the subject. This division of
Propositions is said to be according to their Quanti~+
Combining the two principles of division, we get four
fondamental forms of propositions : A
(1) the universal. Cl rmative, AU S is P, (or Every S
is P, or Any S is P, or All s are P's), usually denoted
by the symbol A ;
2 ) the ~ticular cdfirmative, Sorne Sis P, (or Sorne
S's are P's), usually denoted by thê symbol 1.
(3) the universal. negative, No S is P, (o~ No S's are
P's), usually denoted by the symbol E.,
PROPOSITIONS.
The above are useful when we wish that the symbol
which is used to denote the proposition as a whole should
also indicate what symbols have been chosen for the subject
and the predicate respectively. Thus,
MaP=All Mis P;
PoQ = Sorne Pis not Q.
The universal negative should not be written in the
fo rm Ail Sis not P; for this form is ambiguous and would
usually be understood to be merely particular. Thus, "All
that glitters is not gold" is really an 0 proposition, and is
cquivalent to "Sorne things that glitter are not gold."
37.
Exponible, Copulative, Remotive, and Ex-
cptive Propositions.
Propositions that are resolvable into more propositio~s
t han one have been called e.xponible, in consequence of therr
·uscep tibility of analysis. Copulative propo~itions are ~o~ed
lly a direct combination of simple affirmative propositions;