The process is simply a matter of expressing explicitly in a final judgment, a truth that was implied in one or two previous judgments. To exemplify: From the antecedent truth, that “All teachers should be fair minded,” one may derive a consequent truth that “This teacher, Albert White, should be fair minded.” Or from the statement, “All men are mortal,” one may derive the judgment, “No men are immortal.” Because the ground is wet we conclude that it has rained. If all dogs are quadrupeds then surely some dogs are quadrupeds. Finally from the two propositions, “All training school students are high school graduates,” and “Mary Jones is a training school student,” we are led to conclude that “Mary Jones is a high school graduate.”
2. IMMEDIATE AND MEDIATE INFERENCE.
It has been noted that a truth may be derived from a consideration of one or two antecedent judgments. To illustrate further: From the judgment, “All men are fallible,” we may derive the conclusion that “No men are infallible”; or, from the two judgments, “All men are fallible,” and “Socrates was a man,” we may readily inferthat “Socrates was fallible.” These two modes of inference take the names of immediate inference and mediate inference. Let us express these two kinds in equation form:
| I. | |
|---|---|
| Ordinary Form. | Equation Form, Using Initial Letters. |
| Antecedent judgment: All men are fallible. | All m are f |
| Conclusion: No men are infallible. | No m are i |
| II. | |
| First antecedent judgment: All men are fallible. | All m are f |
| Second antecedent judgment: Socrates was a man. | S was m |
| Conclusion: Socrates was fallible. | ∴ S was f |
Giving attention to the antecedent judgments of the second argument it is noted that the terms “f” and “S” are referred to the common term “m.” In logic this common term is known as the middle term. As there is but one antecedent judgment in the first argument there can be no common or middle term. The first argument is an illustration of immediate inference; the second of mediate inference. This suggests the definitions:
Immediate inference is inference without the use of a middle term.
Mediate inference is inference by means of a middle term.
3. THE FORMS OF IMMEDIATE INFERENCE.
Many logicians recognize four forms of immediate inference. These four forms are (1) opposition, (2) obversion, (3) conversion, (4) contraversion.[8]
(1) IMMEDIATE INFERENCE BY OPPOSITION.