THE order we purpose to observe in the treatment of the subject of this book, is the following: We shall begin with the definition and general explanation of the Inductive Method; then, by the aid of the lights thus furnished, inquire whether this method may be followed in the interpretation of the holy Scriptures; having determined this affirmatively, we shall proceed to a particular analysis of the method, giving illustrations of the use and application of the several steps, drawn both from science and revelation. This will conclude the first part. The second will be devoted to the Axioms, Principles, and Rules involved in determining the exact signification of words, together with such kindred matter as may arise in the discussion of the main subject. [177]

      We shall now attempt to define in general terms, and to explain so clearly the meaning of the inductive method, that even those who are not familiar with philosophical and scientific terminology may have no difficulty in comprehending the scope and design of the ensuing part of the present work. And as all we have yet written has been but a preparation for what is still to come, it is hardly necessary for us to solicit from the reader his undivided attention.

      We begin with the word Induction, and give its definition as contained in the highest lexicographical authority--Ogilvie's Webster's Imperial Dictionary. This defines it to be "a material illation of a universal from a singular, as warranted either by the general analogy of nature, or the special presumptions afforded by the object matter of any real science." The same work quotes a perspicuous explanation from Isaac Taylor. "Induction," says he, "is the drawing or leading off an inference or general fact from a number of instances, or it is the summing up of the result of observations and experiments. It was Lord Bacon who introduced this term into philosophy; and who, moreover, taught the true method of acquiring a knowledge of the laws of nature, by attending to facts, and by carefully comparing a great number of instances; instead of the old method of philosophizing, which consisted in forming a theory, or supposition, independently of all facts, and then explaining the appearances of nature on the blind assumption that the theory was true. The old method was the shortest and the easiest; but it was utterly fallacious. The [178] modern or Baconian method is laborious and difficult; but it is successful, and has proved in the highest degree beneficial."

      Let us next hear from Lord Bacon himself. He says: "In forming axioms, we must invent a different form of induction from that hitherto in use; not only for the proof and discovery of principles, (as they are called,) but also of minor, intermediate, and, in short, every kind of axioms. The induction which proceeds by simple enumeration (per enumerationem simplicem) is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance, deciding generally from too small a number of facts, and those only the most obvious. But a really useful induction for the discovery and demonstration of the arts and sciences, should separate nature by proper rejections and exclusions, and then conclude for the affirmative, after collecting a sufficient number of negatives."¹

      While, then, the word induction signifies the illation of a universal from a singular, the drawing or leading, off a general inference from a number of instances, the rising from particular facts to general laws,--this would very inadequately define that induction introduced and advocated by Lord Bacon; for in this there was nothing new and nothing valuable. And hence, some eminent authors, overlooking, it would seem, the peculiarity of the Baconian induction, have sought to detract from his fame as the father of experimental science. But the case assumes an entirely [179] different aspect, when it is remembered that it was not simply induction, but a peculiar method of induction that he proposed, He did not originate, nor did he advocate the method of simple induction; on the contrary, he was sedulously careful to guard men against it, and to expose and oppose it with all the clearness and strength of his great mind. The induction which he advocated required the collection of numerous facts or particulars; that they should be carefully studied and compared; that whatever was special and exceptional, should be excluded or rejected; that contrary or negative instances should be duly weighed; and that there should be no ascent to the general conclusion, until after all this care, diligence, and circumspection.

      But even this, though it may indicate the meaning of the word induction as used by Bacon, by no means furnishes a complete idea of the inductive method. That included, besides this careful induction, which was always the first step in the process, another element which was exactly the reverse of it, namely, deduction; which descends from the general to the particular; from the whole to the parts included in it; which arms that if a given general proposition be true, it follows of necessity that some other one embraced in it must also be true. It is true that this element of his method was not fully drawn out by Bacon himself, because he did not live to finish his Great Instauration. It is, nevertheless, an essential part of the magnificent scheme he projected, and has been ably unfolded and illustrated by successors of his, who are not unworthy to be [180] ranked even with a name so illustrious and a genius so wonderful.

      If asked to specify the precise province of deduction in this method, we reply that it is twofold: first, to verify the conclusions or generalizations of induction; and secondly, to conduct to new truth embraced in those conclusions. But, strictly speaking, it is not, perhaps, so accurate to say that deduction serves to verify, as that it starts us on the track that leads to verification. It says, if this conclusion be true, then this also must be true, and this, and this; and here it pauses. Having pointed out to us the direction that our conclusion must take, if it be true, and the goal to which it is obliged to conduct, it leaves us to watch the result; to determine by observation whether our induction holds good in its consequences; and to ascertain whether other particulars of the same class, not embraced in the original process, are explicable by the conclusion we have reached. Thus deduction points out the means of verification. It tells us where to look for our law if it be what it purports to be; and then, but not till then, after we have thus looked and discovered the fulfillment of the prediction, after we have put our generalization to the proof, are we fully satisfied of its truth. It is verified; it is proved; it is scientific; it enables us to predict. Thus we go up and down the ladder; from particulars to generals, and from generals to particulars; from individuals to classes, and from these back to individuals. Everything has its place and its use, and unites with everything else in proclaiming that truth must be consistent with fact, upon which it depends. [181]

      Again, having risen to the general truth, and verified it, every legitimate conclusion from it is also true. Thus deduction multiplies the truths reached by the opposite process. In some instances in natural science, moreover, these conclusions have been deduced from hypotheses, and some of the greatest discoveries have been made in this way. Not that induction wars set aside, for all such conclusions were verified by it before they were held as truth; but in cases where it was difficult or impossible to resort in the first instance to direct induction, philosophers commenced by saying, IF such an hypothesis be true, such and such results will follow. This, however, is very different from dogmatism; it is not a positive declaration that their guess is true, but a mere temporary assumption of its truth for the sake of the experiment. And now, if the predicted results follow, what are we authorized to conclude? That the guess is true? That the hypothesis is sound? No. These furnish only a strong probability in its favor. How do we know but that the same phenomena might be accounted for upon each of several other hypotheses? How do we know that it does not contravene some law written upon hundreds of other phenomena of the same class, and that these are but the negative or exceptional cases? The hypothesis, then, must be verified. We must go to work inductively to collect facts, to weigh and compare them, in order to see what they teach. The mere fact that an hypothesis will serve to explain many phenomena, is not proof positive of its correctness, because that explanation may not be the most natural one. The Ptolemaic system of the universe served to explain [182] nearly if not quite all the phenomena. On Newton's hypothesis of light, all the phenomena were explained for many years, and it was not till quite recently that it was proved to be incorrect.² And hence, though we may, and often do, perceive a scientific truth before we resort to the inductive method, we can never know it to be truth till afterwards.

      This, then, is what we mean by the Inductive, or Baconian method,--not induction opposed to deduction, but both combined in opposition to dogmatism. It is the telescope by the aid of which we read the inscriptions upon facts, and perceive those general principles which presided when they were written. If these inscriptions can be made clearer by turning them for a moment to the light of an hypothesis, viewed as an hypothesis, it authorizes and even requires us to do so. But if, as is almost always the case, we prefer to hold the mind in abeyance, and compel it to wait, without even guessing the conclusion, till the testimony of all the facts, like so many individual witnesses, is heard, we shall in this way, too, be following the guiding direction of the Novum Organum Scientiarum. And when we are still in doubt, after hearing the evidence of all the witnesses, which of two possible conclusions is correct, the method requires us to settle the point by deduction. We are to assume first the one and then the other, and argue from them respectively to the facts, till we determine in which the logical consequences and the facts all agree. All this and more is [183] clearly presented by Playfair, in the following quotation from his Preliminary Dissertation, in the Encyclopedia Britannica:--³

      "Having collected the facts," he says, "the next object is to find out the cause of the phenomenon, its form, (in the language of Bacon,) or its essence. The form of any quality in a body is something convertible with that quality, i. e. where one is present, the other must be also. It differs nothing from cause, but we apply it when the result is not an event or change, but a permanent quality.

      "In order to inquire into the form, that is, the cause or essence of anything, we begin by inquiring what things are thereby excluded from the number of possible forms. This is the first part of the process of induction. It confines the field of hypothesis and brings the true explanation within narrower limits. Thus, if we were inquiring into the quality which is the cause of transparency in bodies, from the fact that the diamond is transparent we immediately exclude rarity or porosity as well as fluidity from those causes, the diamond being very solid and dense. Negative instances are those where the given form is wanting. Thus, in inquiring into the form of transparency, compounded glass, is a negative instance--being not transparent; so also are clouds and fogs.

      "After a great number of exclusions have left but few principles common to every case, one of these is to be assumed as the cause; and by reasoning from it synthetically, [184] we are to try if it will account for the phenomena."

      Again: "All facts are not equally valuable in the discovery of truth. Some of them show the thing sought for in its highest degree, some in its lowest; some exhibit it simple and uncombined, in others it appears confused with a variety of circumstances. Some facts are easily interpreted, others are very obscure, and are understood only in consequence of the light thrown on them by the former. This led Bacon to consider what he calls the Prerogatives of Instances, the comparative value of facts as means of discovery or as instruments of investigation."

      As an example of the pursuit of the inductive method, we may instance the process by which Sir Isaac Newton arrived at the theory of universal gravitation. From a large number of facts and experiments regarding the falling of bodies towards the earth's center, he reached the conclusion that all bodies gravitate towards the earth's center with forces proportioned to their masses, and inversely as the squares of their distance from the center. In other words, from the fact that stones, sticks, apples, snow, water, and all the various objects that could be observed, were seen to gravitate in this way, he "led or drew off" the general conclusion that this was true in all cases, or that such was the doctrine or rule of terrestrial gravitation. This being verified and established, he was enabled to carry the inductive process still higher. By examining the motions of the heavenly bodies, and availing himself of the laws of terrestrial gravitation, previously established, he [185] arrived at a still more general conclusion, namely, that every particle of matter in the universe attracts every other particle with a force proportional to the product of their masses directly, and the square of their mutual distance inversely, and is itself attracted with an equal force. This law has been verified a thousand times and in as many different ways, and it now stands out before us an eternal monument to the excellency of a method which could point out a principle so sublime and so important written upon the face of a falling apple.

      But notwithstanding the certainty we feel of the correctness of scientific conclusions thus reached and verified, let us not suppose, even for a moment, that Science or Nature addresses a higher faculty of our being than does Revelation; for in all these conclusions there is, and there must be, one assumption at least--one thing which is not known but believed--and this the most fundamental of all. The entire superstructure of science, with all its facts, data, propositions, reasonings and conclusions, rests primarily, like religion, upon faith. It is impossible to demonstrate, impossible to know, the universal and eternal uniformity of nature. We believe it; we take it for granted; we set out with this assumption; and we have confidence that though it cannot be demonstrated absolutely, it will be impossible to disprove it, or to show that our faith in it, which rests upon evidences so numerous and overwhelming, has been misplaced. Here then, in faith, is the pedestal of all knowledge; here science and revelation start upon the same level; and while with the inductive method applied to the one, we rise [186] to the highest generalizations in the physical universe, with the full, unquestioned and unquestionable assurance of their truth, let us see if the same method will not conduct us, with equal assurance, to the lofty heights of that revealed truth which is spiritual, living, and powerful. [187]

[TOOS 177-187]