(16) Explain by the use of two pads (a small yellow one and a large white one) the distribution of terms.
(17) When the logician makes reference to the subject of a proposition, show that he should exercise care in designating it as the _logical_ subject.
_Inference is the thought process of deriving a judgment from one or two antecedent judgments._
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.”
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 infer that “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:
_Equation Form, _Ordinary Form._ Using Initial Letters._
Antecedent judgment: All men are fallible. All m are f ――――――――――― Conclusion: No men are infallible. No m are i
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: