Let us, then, give attention to the extension of the subject and predicate of the categorical propositions A, E, I, O.
(1) The Universal Affirmative or A Proposition.
All S is P symbolizes the A proposition. This may be interpreted as meaning that all of the subject belongs to a part of the predicate, or that all of the subject belongs to all of the predicate. The first interpretation is the usual one and may be illustrated by the following propositions:
1. “All men are mortal.”
2. “All trees grow.”
3. “All metals are elements.”
It is obvious that the subjects of these propositions include every specimen of the particular class mentioned. For example: The subject all men includes every specimen of the human family; all trees includes every object of that class; all metals covers everything which the scientist classes as such. In the three propositions, then, reference is made to the whole subject but to only a part of the predicate, as other beings beside men, such as the horse, are mortal; and other plants aside from trees, such as the sun flower, grow; other substances, namely oxygen, are elements.
For the sake of making the logical meaning of the four propositions clearer, recourse may be made to Euler’s diagrams, so named because the Swiss mathematician and logician, Leonhard Euler, first used them.
The first illustration of the A proposition, “All men are mortal,” may be represented by two circles, a larger circle standing for the predicate, mortal, and a smaller circle entirely inside the larger representing the subject, men. Thus:
