FIG. 1.
It is evident that all of the smaller circle belongs to the larger. This diagram will then fit any proposition where it may be said that all of the subject belongs to a part of the predicate, or which may be symbolized as “All S is some P.” (All the subject is some of the predicate.)
The student knows that circles are plane surfaces and when such a statement as “All men are mortal” is given, reference is made to only that part of the “mortal” circle which is directly underneath the “men” circle. Nothing has been said relative to the remaining part of the “mortal” circle.
“A” propositions which may be interpreted as meaning “All S is all P” are called co-extensive A’s because the subject and predicate are exactly equal in extension. Such propositions are best illustrated by definitions; e. g.:
1. “A man is a rational biped.”
2. “A trigon is a polygon of three sides.”
3. “Teaching is the art of occasioning those activities which result in knowledge, power and skill.”
To represent the meaning of the co-extensive A by the Euler diagram, two circles of the same size may be drawn, one coinciding at every point with the other. If the first circle is drawn heavily in black and the second dotted in red, it will make clear to the eye that there are two circles.
(2) The Universal Negative or E Proposition.
“No S is P” best symbolizes the E proposition, though sometimes the universal negative is written “All S is not P.” This latter form, as has been explained, is ambiguous and therefore illogical.