Thought-Culture; Or, Practical Mental Training

by William Walker Atkinson

In the above processes it will be seen that the third and final Judgment is derived from a comparison of the first two Judgments. Brooks states the process as follows: "Looking at the process more closely, it will be seen that in inference in Reasoning involves a comparison of relations. We infer the relation of two objects from their relation to a third object. We must thus grasp in the mind two relations and from the comparison of these two relations we infer a third relation. The two relations from which we infer a third, are judgments; hence, Reasoning may also be defined as the process of deriving one judgment from two other judgments. We compare the two given judgments and from this comparison derive the third judgment. This constitutes a single step in Reasoning, and an argument so expressed is called a Syllogism."

The Syllogism consists of three propositions, the first two of which express the grounds or basis of the argument and are called the premises; the third expresses the inference derived from a comparison of the other two and is called the conclusion. We shall not enter into a technical consideration of the Syllogism in this book, as the subject is considered in detail in the volume of this series devoted to the subject of "Logic." Our concern here is to point out the natural process and course of Reasoning, rather than to consider the technical features of the process.

Reasoning is divided into two general classes, known respectively as (1) Inductive Reasoning; (2) Deductive Reasoning.

Inductive Reasoning is the process of arriving at a general truth, law or principle from a consideration of many particular facts and truths. Thus, if we find that a certain thing is true of a great number of particular objects, we may infer that the same thing is true of all objects of this particular kind. In one of the examples given above, one of the judgments was that "all fish are cold-blooded animals," which general truth was arrived at by Inductive Reasoning based upon the examination of a great number of fish, and from thence assuming that all fish are true to this general law of truth.

Deductive Reasoning is the reverse of Inductive Reasoning, and is a process of arriving at a particular truth from the assumption of a general truth. Thus, from the assumption that "all fish are cold-blooded animals," we, by Deductive Reasoning, arrive at the conclusion that the particular fish before us must be cold-blooded.

Inductive Reasoning proceeds upon the basic principle that "What is true of the many is true of the whole," while Deductive Reasoning proceeds upon the basic principle that "What is true of the whole is true of its parts."

Regarding the principle of Inductive Reasoning, Halleck says: "Man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. By induction, we examine what seems to us a sufficient number of individual cases. We then conclude that the rest of these cases, which we have not examined, will obey the same general law. The judgment 'All men are mortal' was reached by induction. It was observed that all past generations of men had died, and this fact warranted the conclusion that all men living will die. We make that assertion as boldly as if we had seen them all die. The premise, 'All cows chew the cud,' was laid down after a certain number of cows had been examined. If we were to see a cow twenty years hence, we should expect to find that she chewed the cud. It was noticed by astronomers that, after a certain number of days, the earth regularly returned to the same position in its orbit, the sun rose in the same place, and the day was of the same length. Hence, the length of the year and of each succeeding day was determined, and the almanac maker now infers that the same will be true of future years. He tells us that the sun on the first of next December will rise at a given time, although he cannot throw himself into the future to verify the conclusion."

Brooks says regarding this principle: "This proposition is founded on our faith in the uniformity of nature; take away this belief, and all reasoning by induction fails. The basis of induction is thus often stated to be man's faith in the uniformity of nature. Induction has been compared to a ladder upon which we ascend from facts to laws. This ladder cannot stand unless it has something to rest upon; and this something is our faith in the constancy of nature's laws."

There are two general ways of obtaining our basis for the process of Inductive Reasoning. One of these is called Perfect Induction and the other Imperfect Induction. Perfect Induction is possible only when we have had the opportunity of examining every particular object or thing of which the general idea is expressed. For instance, if we could examine every fish in the universe we would have the basis of Perfect Induction for asserting the general truth that "all fishes are cold-blooded." But this is practically impossible in the great majority of cases, and so we must fall back upon more or less Imperfect Induction. We must assume the general law from the fact that it is seen to exist in a very great number of particular cases; upon the principle that "What is true of the many is true of the whole." As Halleck says regarding this: "Whenever we make a statement such as, 'All men are mortal,' without having tested each individual case or, in other words, without having seen every man die, we are reasoning from imperfect induction. Every time a man buys a piece of beef, a bushel of potatoes or a loaf of bread, he is basing his action on inference from imperfect induction. He believes that beef, potatoes and bread will prove nutritious food, although he has not actually tested those special edibles before purchasing them. They have hitherto been found to be nutritious on trial and he argues that the same will prove true of those special instances. Whenever a man takes stock in a new national bank, a manufactory or a bridge, he is arguing from past cases that this special investment will prove profitable. We instinctively believe in the uniformity of nature; if we did not we should not consult our almanacs. If sufficient heat will cause phosphorus to burn today, we conclude that the same result will follow tomorrow if the circumstances are the same."

But, it will be seen, much care must be exercised in making observations, experiments and comparisons, and in making generalizations. The following general principles will give the views of the authorities regarding this: