FIG. 5.
Now representing thoughtful men by a smaller circle and placing it inside the larger we have,
FIG. 6.
Referring to [Fig. 6] we note that all of the smaller circle belongs to the larger or that none of the smaller circle belongs to the space outside of the larger. Hence the two propositions: “All thoughtful men are wise” (A), and “No thoughtful men are unwise” (E) have virtually the same meaning though the same subject is related to different predicates.
The use of the positive or negative form depends upon circumstances. Often the negative puts the thought in a more forceful way.
In passing from, “All thoughtful men are wise,” to “No thoughtful men are unwise,” it was necessary to prefix not to the predicate wise and substitute for not its equivalent un. If the original predicate were unwise or not-wise, then the reverse order of dropping the un or not could be followed. This process of prefixing the not to an affirmative predicate or of dropping the not from a negative predicate is referred to as negating the predicate. Before substituting in, im, un, etc., for not, one must make sure that the substitution really gives the contradictory; there are some logicians who claim that unwise, for instance, is not the contradictory of wise.
In comparing the first proposition with the second it is observed that the first is an A, while the second is an E, also that the predicate of the first was negated to form the predicate of the second. Thus the rule: Negate the predicate and change A to E.
To sum up: