William Atkinson - The Complete Works of William Walker Atkinson

Imperfect Induction , or as it is sometimes called "Practical Induction," by which is meant the inductive process of reasoning in which we assume that the particulars or facts actually known to us correctly represent those which are not actually known, and hence the whole class to which they belong. In this process it will be seen that the conclusion extends beyond the data upon which it is based. In this form of Induction we must actually employ the principle of the axiom: "What is true of the many is true of the whole"—that is, must assume it to be a fact, not because we know it by actual experience, but because we infer it from the axiom which also agrees with past experience. The conclusion arrived at may not always be true in its fullest sense, as in the case of the conclusion of Perfect Induction, but is the result of an inference based upon a principle which gives us a reasonable right to assume its truth in absence of better knowledge.

In considering the actual steps in the process of Inductive Reasoning we can do no better than to follow the classification of Jevons, mentioned in the preceding chapter, the same being simple and readily comprehended, and therefore preferable in this case to the more technical classification favored by some other authorities. Let us now consider these four steps.

First Step. Preliminary observation. It follows that without the experience of oneself or of others in the direction of observing and remembering particular facts, objects, persons and things, we cannot hope to acquire the preliminary facts for the generalization and inductive inference necessary in Inductive Reasoning. It is necessary for us to form a variety of clear Concepts or ideas of facts, objects, persons and things, before we may hope to generalize from these particulars. In the chapters of this book devoted to the consideration of Concepts, we may see the fundamental importance of the formation and acquirement of correct Concepts. Concepts are the fundamental material for correct reasoning. In order to produce a perfect finished product, we must have perfect materials, and a sufficient quantity of them. The greater the knowledge one possesses of the facts and objects of the outside world, the better able is he to reason therefrom. Concepts are the raw material which must feed the machinery of reasoning, and from which the final product of perfected thought is produced. As Halleck says: "There must first be a presentation of materials. Suppose that we wish to form the concept fruit . We must first perceive the different kinds of fruit—cherry, pear, quince, plum, currant, apple, fig, orange, etc. Before we can take the next step, we must be able to form distinct and accurate images of the various kinds of fruit. If the concept is to be absolutely accurate, not one kind of fruit must be overlooked. Practically this is impossible; but many kinds should be examined. Where perception is inaccurate and stinted, the products of thought cannot be trustworthy. No building is firm if reared on insecure foundations."

In the process of Preliminary Observation, we find that there are two ways of obtaining a knowledge of the facts and things around us. These two ways are as follows:

I. By Simple Observation , or the perception of the happenings which are manifested without our interference. In this way we perceive the motion of the tides; the movement of the planets; the phenomena of the weather; the passing of animals, etc.

II. By the Observation of Experiment , or the perception of happenings in which we interfere with things and then observe the result. An experiment is: "A trial, proof, or test of anything; an act, operation, or process designed to discover some unknown truth, principle or effect, or to test some received or reputed truth or principle." Hobbes says: "To have had many experiments is what we call experience ." Jevons says: "Experimentation is observation with something more; namely, regulation of the things whose behavior is to be observed. The advantages of experiment over mere observation are of two kinds. In the first place, we shall generally know much more certainly and accurately with what we are dealing, when we make experiments than when we simply observe natural events.... It is a further advantage of artificial experiments, that they enable us to discover entirely new substances and to learn their properties.... It would be a mistake to suppose that the making of an experiment is inductive reasoning, and gives us without further trouble the laws of nature. Experiments only give us the facts upon which we may afterward reason.... Experiments then merely give facts, and it is only by careful reasoning that we can learn when the same facts will be observed again. The general rule is that the same causes will produce the same effects. Whatever happens in one case will happen in all like cases, provided that they are really like, and not merely apparently so.... When we have by repeated experiments tried the effect which all the surrounding things might have on the result, we can then reason with much confidence as to similar results in similar circumstances.... In order that we may, from our observations and experiments, learn the law of nature and become able to foresee the future, we must perform the process of generalization. To generalize is to draw a general law from particular cases, and to infer that what we see to be true of a few things is true of the whole genus or class to which these things belong. It requires much judgment and skill to generalize correctly, because everything depends upon the number and character of the instances about which we reason."

Having seen that the first step in Inductive Reasoning is Preliminary Observation, let us now consider the next steps in which we may see what we do with the facts and ideas which we have acquired by this Observation and Experiment.

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Following Jevons' classification, we find that the Second Step in Inductive Reasoning is that called "The Making of Hypotheses."

A Hypothesis is: "A supposition, proposition or principle assumed or taken for granted in order to draw a conclusion or inference in proof of the point or question; a proposition assumed or taken for granted, though not proved, for the purpose of deducing proof of a point in question." It will be seen that a Hypothesis is merely held to be possibly or probably true , and not certainly true ; it is in the nature of a working assumption , whose truth must be tested by observed facts. The assumption may apply either to the cause of things, or to the laws which govern things. Akin to a hypothesis, and by many people confused in meaning with the latter, is what is called a Theory.

A Theory is: "A verified hypothesis; a hypothesis which has been established as, apparently, the true one." An authority says " Theory is a stronger word than hypothesis . A theory is founded on principles which have been established on independent evidence. A hypothesis merely assumes the operation of a cause which would account for the phenomena, but has not evidence that such cause was actually at work. Metaphysically, a theory is nothing but a hypothesis supported by a large amount of probable evidence." Brooks says: "When a hypothesis is shown to explain all the facts that are known, these facts being varied and extensive, it is said to be verified, and becomes a theory. Thus we have the theory of universal gravitation, the Copernican theory of the solar system, the undulatory theory of light, etc., all of which were originally mere hypotheses. This is the manner in which the term is usually employed in the inductive philosophy; though it must be admitted that it is not always used in this strict sense. Discarded hypotheses are often referred to as theories; and that which is actually a theory is sometimes called a hypothesis."