The sign of quantity attached to the subject indicates the extent to which the individuals denoted by the subject-term are referred to. Thus, in the proposition All S is P the sign of quantity is all, and the affirmation is understood to be made of each and every individual denoted by the term S.
The copula is the link of connexion between the subject and the predicate, and indicates whether the latter is affirmed or denied of the former.
The different elements of the proposition as here distinguished are by no means always separately expressed in the propositions of ordinary discourse; but by analysis and expansion they may be made to appear without any change of meaning. Some grammatical change of form is, therefore, often necessary before propositions can be dealt with in the traditional scheme. Thus in such a proposition as “All that love virtue love angling,” the copula is not separately expressed. The proposition may, however, be written—
| sign of quantity | subject | copula | predicate |
| All | lovers of virtue | are | lovers of angling ; |
and in this form the four different elements are made distinct. The older logicians distinguished between propositions secundi adjacentis and propositions tertii adjacentis. In the former, the copula and the predicate are not separated, e.g., The man runs, All that love virtue love angling; in the latter, they are made distinct, e.g., The man is running, All lovers of virtue are lovers of angling.
The traditional scheme of propositions is obtained by a combination of the division (according to quantity) into universal and particular, and the division (according to quality) into affirmative and negative. This combination yields four fundamental forms of proposition as follows:—
(1) the universal affirmative—All S is P (or Every S is P, or Any S is P, or All S’s are P’s)—usually denoted by the symbol A; 94
(2) the particular affirmative—Some S is P (or Some S’s are P’s)—usually denoted by the symbol I;
(3) the universal negative—No S is P (or No S’s are P’s)—usually denoted by the symbol E;
(4) the particular negative—Some S is not P (or Not all S is P, or Some S’s are not P’s, or Not all S’s are P’s)—usually denoted by the symbol O.
These symbols A, I, E, O, are taken from the Latin words affirmo and nego, the 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 sometimes be found convenient to use the following,—
SaP = All S is P ;
SiP = Some S is P ;