_Immediate inference is inference without the use of a middle term._
_Mediate inference is inference by means of a middle term._
Many logicians recognize four forms of immediate inference. These four forms are (1) _opposition_, (2) _obversion_, (3) _conversion_, (4) _contraversion._[8]
We have learned that to be logical all categorical assertions must be reduced to some one of the four propositions, A, E, I, O. If these four logical propositions be given the _same subject and predicate_, certain definite relations will become evident; therefore, _Opposition is said to exist between propositions which are given the same subject and predicate, but differ in quality, or in quantity, or in both_.
The following illustrative outline will make this clear:
1. _Original Proposition._ I. All men are mortal. (A) II. No men are immortal. (E) III. Some men are wise. (I) IV. Some men are mortal. (I) V. Some men are not wise. (O) VI. Some men are not immortal. (O)
2. _Opposite in Quantity._ I. Some men are mortal. (I) II. Some men are not immortal. (O) III. All men are wise. (A) IV. All men are mortal. (A) V. No men are wise. (E) VI. No men are immortal. (E)
3. _Opposite in Quality._ I. No men are mortal. (E) II. All men are immortal. (A) III. Some men are not wise. (O) IV. Some men are not mortal. (O) V. Some men are wise. (I) VI. Some men are immortal. (I)
4. _Opposite in Both._ I. Some men are not mortal. (O) II. Some men are immortal. (I) III. No men are wise. (E) IV. No men are mortal. (E) V. All men are wise. (A) VI. All men are immortal. (A)
Granting the truth of the propositions in the first column, it follows that those in the second column differ in quantity. That is, in “Some men are mortal” a _smaller_ number of men is referred to than in “All men are mortal.” A similar variation in quantity obtains with the other propositions in the second column. Moreover, the propositions in the third column are the negative of the corresponding ones in the first; while the fourth column propositions differ from the first in _both_ quantity and quality. Thus opposition exists to a greater or less degree between all. We may now ask ourselves the question, “When the propositions are related to each other in opposition which ones are true and which ones are false?” Giving attention to the propositions in row “I,” we note that if the universal affirmative, “All men are mortal,” is true, then the particular affirmative, “Some men are mortal,” is likewise true; because of the principle, “What is true of the whole of the class is true of a part of that class.” But the universal negative, “No men are mortal,” and the particular negative, “Some men are not mortal,” are both false. Briefly stated: If A is true, then I is true, but, both E and O are false.