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.
Two negatives are equivalent to one affirmative.
Negate the predicate and change the A to an E by using the sign _no_ instead of _all_.
_The Original Proposition (A)_ _The Obverse (E)_
All maples are trees. No maples are not-trees.
All teachers should be No teacher should be sympathetic. un-sympathetic.
All pain is unpleasant. No pain is pleasant.
All men are imperfect. No men are perfect.
All birds are feathered No birds are non-feathered animals. animals.
All scalene triangles are No scalene triangles are non-equilateral. equilateral.
It is obvious that the process of obverting an E is simply the reverse of obverting an A. Consequently, the same principle obtains; whereas the _process_ may be illustrated by reading the foregoing illustrations reversely.
The rule for obverting E is: _Negate the predicate and change the E to an A by changing the sign no to all._
Let us note the result when the double negative principle is applied to the I proposition.
Adding two negatives: “Some men are not not-wise.”
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.”