This form of reasoning is deductive, that is, it proceeds from the general to the particular. Much of our reasoning is an abbreviated form of the syllogism, and will readily expand into it. For instance, we say, "It will rain tonight, for there is lightning in the west." Expanded into the syllogism form it would be, "Lightning in the west is a sure sign of rain; there is lightning in the west this evening; therefore, it will rain tonight." While we do not commonly think in complete syllogisms, it is often convenient to cast our reasoning in this form to test its validity. For example, a fallacy lurks in the generalization, "Lightning in the west is a sure sign of rain." Hence the conclusion is of doubtful validity.
Induction.—Deduction is a valuable form of reasoning, but a moment's reflection will show that something must precede the syllogism in our reasoning. The major premise must be accounted for. How are we able to say that all men are mortal, and that lightning in the west is a sure sign of rain? How was this general truth arrived at? There is only one way, namely, through the observation of a large number of particular instances, or through induction.
Induction is the method of proceeding from the particular to the general. Many men are observed, and it is found that all who have been observed have died under a certain age. It is true that not all men have been observed to die, since many are now living, and many more will no doubt come and live in the world whom we cannot observe, since mortality will have overtaken us before their advent. To this it may be answered that the men now living have not yet lived up to the limit of their time, and, besides, they have within them the causes working whose inevitable effect has always been and always will be death; likewise with the men yet unborn, they will possess the same organism as we, whose very nature necessitates mortality. In the case of the premonitions of rain, the generalization is not so safe, for there have been exceptions. Lightning in the west at night is not always followed by rain, nor can we find inherent causes as in the other case which necessitates rain as an effect.
The Necessity for Broad Induction.—Thus it is seen that our generalizations, or major premises, are of all degrees of validity. In the case of some, as the mortality of man, millions of cases have been observed and no exceptions found, but on the contrary, causes discovered whose operation renders the result inevitable. In others, as, for instance, in the generalization once made, "All cloven-footed animals chew their cud," not only had the examination of individual cases not been carried so far as in the former case when the generalization was made, but there were found no inherent causes residing in cloven-footed animals which make it necessary for them to chew their cud. That is, cloven feet and cud-chewing do not of necessity go together, and the case of the pig disproves the generalization.
In practically no instance, however, is it possible for us to examine every case upon which a generalization is based; after examining a sufficient number of cases, and particularly if there are supporting causes, we are warranted in making the "inductive leap," or in proceeding at once to state our generalization as a working hypothesis. Of course it is easy to see that if we have a wrong generalization, if our major premise is invalid, all that follows in our chain of reasoning will be worthless. This fact should render us careful in making generalizations on too narrow a basis of induction. We may have observed that certain red-haired people of our acquaintance are quick-tempered, but we are not justified from this in making the general statement that all red-haired people are quick-tempered. Not only have we not examined a sufficient number of cases to warrant such a conclusion, but we have found in the red hair not even a cause of quick temper, but only an occasional concomitant.
The Interrelation of Induction and Deduction.—Induction and deduction must go hand in hand in building up our world of knowledge. Induction gives us the particular facts out of which our system of knowledge is built, furnishes us with the data out of which general truths are formed; deduction allows us to start with the generalization furnished us by induction, and from this vantage ground to organize and systematize our knowledge and, through the discovery of its relations, to unify it and make it usable. Deduction starts with a general truth and asks the question, "What new relations are made necessary among particular facts by this truth?" Induction starts with particulars, and asks the question, "To what general truth do these separate facts lead?" Each method of reasoning needs the other. Deduction must have induction to furnish the facts for its premises; induction must have deduction to organize these separate facts into a unified body of knowledge. "He only sees well who sees the whole in the parts, and the parts in the whole."
7. PROBLEMS IN OBSERVATION AND INTROSPECTION
1. Watch your own thinking for examples of each of the four types described. Observe a class of children in a recitation or at study and try to decide which type is being employed by each child. What proportion of the time supposedly given to study is given over to chance or idle thinking? To assimilative thinking? To deliberative thinking?
2. Observe children at work in school with the purpose of determining whether they are being taught to think, or only to memorize certain facts. Do you find that definitions whose meaning is not clear are often required of children? Which should come first, the definition or the meaning and application of it?
3. It is of course evident from the relation of induction and deduction that the child's natural mode of learning a subject is by induction. Observe the teaching of children to determine whether inductive methods are commonly used. Outline an inductive lesson in arithmetic, physiology, geography, civics, etc.