Expressed in this form, the reasoning process, as already mentioned, is known as a syllogism. The whole syllogism is made up of three parts, major premise, minor premise, and conclusion. The three concepts involved in the syllogism are known as the major, the minor, and the middle term. In the above syllogism, heavy, the predicate of the major premise, is the major term; flint, the subject of the minor premise, is the minor term; and stone, to which the other two are related in the premises, is known as the middle term. Because of this previous comparison of the major and the minor terms with the middle term, deduction is sometimes said to be a process by which the mind discovers a relation between two concepts by comparing them each with a third concept.
Purpose of Deduction.—It is to be noted, however, as pointed out in [Chapter XV], that deductive reasoning takes place normally only when the mind is faced with a difficulty which demands solution. Take the case of the boy and his lost coin referred to in [Chapter II]. As he faces the problem, different methods of solution may present themselves. It may enter his mind, for instance, to tear up the grate, but this is rejected on account of possible damage to the brickwork. Finally he thinks of the tar and resorts to this method of recovery. In both of the above cases the boy based his conclusions upon known principles. As he considered the question of tearing up the grate, the thought came to his mind, "Lifting-a-grate is a-thing-which-may-cause-damage." As he considered the use of the tar, he had in mind the judgment, "Adhesion is a property of tar," and at once inferred that tar would solve his problem. In such practical cases, however, the mind seems to go directly from the problem in hand to a conclusion by means of a general principle. When a woman wishes to remove a stain, she at once says, "Gasoline will remove it." Here the mind, in arriving at its conclusion, seems to apply the principle, "Gasoline removes spots," directly to the particular problem. Thus the reasoning might seem to run as follows:
Problem: What will remove this stain?
Principle: Gasoline will remove stains.
Conclusion: Gasoline will remove this stain.
Here the middle term of the syllogism seems to disappear. It is to be noted, however, that our thought changes from the universal idea "stains," mentioned in the statement of the principle, to the particular idea "this stain" mentioned in the problem and in the conclusion. But this implies a middle term, which could be expressed thus:
Gasoline will remove stains;
This is a stain;
∴ Gasoline will remove this.
The syllogism is valuable, therefore, because it displays fully and clearly each element in the reasoning process, and thus assures the validity of the conclusion.
Deduction in School Recitation.—It will be recalled from what was noted in our study of general method, that deduction usually plays an important part during an ordinary developing lesson. In the step of preparation, when the pupil is given a particular example in order to recall old knowledge, the example suggests a problem which is intended to call up certain principles which are designed to be used during the presentation. In a lesson on the "Conjunctive Pronoun," for instance, if we have the pupil recall his knowledge of the conjunction by examining the particular word "if" in such a sentence as, "I shall go if they come," he interprets the word as a conjunction simply because he possesses a general rule applicable to it, or is able to go through a process of deduction. In the presentation also, when the pupil is called on to examine the word who in such a sentence as, "The man who met us is very old," and decides that it is both a conjunction and a pronoun, he is again making deductions, since it is by his general knowledge of conjunctions and pronouns that he is able to interpret the two functions of the particular word who. Finally, as already noted, the application of an ordinary recitation frequently involves deductive processes.
INDUCTION
Nature of Induction.—Induction is described as a process of reasoning in which the mind arrives at a conclusion by an examination of particular cases, or judgments. A further distinguishing feature of the inductive process is that, while the known judgments are particular in character, the conclusion is accepted as a general law, or truth. As in deduction, the reasoning process arises on account of some difficulty, or problem, presented to the mind, as for example:
What is the effect of heat upon air?
Will glass conduct electricity?
Why do certain bodies refract light?