The foregoing simplified: “Some men are not unwise.” In comparing the first proposition with the last it is observed that the first is an I while the last is an O; it is also observed that the predicate of the first was _negated_ in order to form the predicate of the last. Thus the rule: “Negate the predicate and change the I to an O.” The use of circles may make this clearer: Illustration: FIG. 7. The significant part of Fig. 7 is that which is inked. Here we have represented the part of the “men” circle which is common to the “wise” circle. Thus the inked part represents “Some men are wise.” If the inked part is entirely inside of the “wise” circle, no part of it can belong to the “unwise” space without. Thus the obverse, “Some men are not unwise.” _Summary._ The obversion of an I proposition. 1. Principle: Same as with A. 2. Rule: Negate the predicate and change the I to an O. 3. Process illustrated. _The Original Proposition (I)_ _The Obverse (O)_ Some water is pure. Some water is not impure. Some curves are perfect. Some curves are not imperfect. Some friends are loyal. Some friends are not disloyal. Some men are true. Some men are not not-true. Some precious stones are Some precious stones are not imperfect. perfect. Some plants are not-trees. Some plants are not trees. Some boys are not-honest. Some boys are not honest. It must be borne in mind that when “_not_” is used without the hyphen it makes the proposition negative, because when “_unhyphened_,” “_not_” must be thought of in connection with the copula and not in connection with the predicate; while “_not_” attached to the predicate with a hyphen simply makes the predicate negative without affecting the quality of the proposition; e. g., “Some plants are not trees” is a negative proposition, while “Some plants are not-trees” is an affirmative proposition with a negative predicate. It may not be clearly seen how it is possible, by following the rule given, to pass from such a proposition as “Some plants are _not-trees_,” to “Some plants are _not trees_.” Let us illustrate the steps: 1. The original: “Some plants are not-trees.” 2. Negating predicate: “Some plants are trees.” 3. Changing to an O: “Some plants are not trees.” Dropping the not from “1” and then adding it again to “2” is simply putting into operation the double negative idea, so that there is no violation of the principle. _The O Proposition._ O bears the same relation to I that E bears to A. The principle involved is the same. The process is illustrated by reading reversely the scheme of illustrations under I. The rule is as follows: _To obvert an O negate the predicate and change the O to an I by eliminating the not._ _Summary of Obverting the Four Logical Propositions._ 1. Principle: Two negatives are equivalent to one affirmative. 2. Rules: