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 INDUCTION

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INDUCTION

make sure that our hypothesis offers the only possible explanation of the phenomenon, that M is the only cause in the universe capable of producing P — that, for instance, the necessity which beset the early Christians of securing a place of refuge for themselves and of burial for their dead could alone account for the formation of the Roman catacombs as we find them? This is obviously a matter for the prudence of the investigator, and, incidentally, it indicates one limit- ation of the certitude we can reach by induction. What is known as a crucial instance or experiment will, if it occur, enable us summarily to dismiss one of two conflicting hypotheses as erroneous, thus es- tablishing the other, provided this other is the only conceivable one in the circumstances — that is to say, the only one reasonably suggested by the facts; for there is scarcely any hypothesis to which some fanciful alternative might not be imagined; and here again prudence must guide the investigator in forming his conviction. Is he, for instance, to suspend his assent to the physical hypothesis of a universal ether because the alternative of actio in distans is at any rate not evidently an intrinsic impossibility?

When a hypothesis cannot be rigorously verified by establishing the reciprocal universal judgment, it may nevertheless steadily grow in probability in proportion to the number and importance of other cognate phe- nomena which it is found capable of accounting for, in addition to the one it was invented to explain. A hy- pothesis is rendered highly probable if it foretells or ex- plains cognate phenomena; this is called by Whewell consilience of inductions (Novum Organum Reno- vatum, pp. 86, 95, 96). This process of verification runs somewhat on these lines: "If M be a really operative cause, then in such and such circumstances it ought to produce or account for the effect X, and in such others for Y and so on ; but (by observation or experiment we proceed to find that) in these circum- stances these effects are produced or explained by it; therefore probably they are due to M." They are probabl;/ attributable only, because the argument does not formally yield a certain conclusion; but the more we extend our hypothesis, and the larger the groups of phenomena it is found competent to ex- plain, the firmer does our conviction naturally grow, until it reaches practical or moral certitude that we have hit on the true law of the phenomena examined. Thus, for instance, was Newton's gravitation hypoth- esis gradually extended by him so as to explain the motions of the moon and the tides, the motions of the satellites around the planets and of these around the sun, until finally it came to be regarded as applicable throughout the whole material universe. The aim of the inductive process is to explain isolated facts by bringing them under some law, i. e. by discovering all the cau.ses to the co-operation of which they are due and laying down those general propositions called laws of nature which embody and express the constant mode of operation of those causes. It is thus that we transform the observed sequences of sense-ex- perience into understood or intellectually explained consequences of cause and effect. Scientific ex- planation also aims at reducing these separate and narrower laws themselves to higher and wider laws by showing them to be partial applications of the latter, thus obeying the innate tendency of the human mind to synthesize and unify, as far as may be, the manifold and chaotic data of sense experience.

III. Rational Foundations and Scope of Induction. - — The inductive generalization by which, after examin- ing a limited number of instances of some connexion or mode of happening of phenomena, we assert that this connexion, being natural, will always recur in the same way, is a mental passage from particular to general, from what is within experience to what is beyond experience. Its legitimacy needs justifica- tion. It rests on the assumption of a few important

metaphysical principles. One of these is the principle of causality: "Whatever happens has a cause." Since by the cause of a thing or event we mean what- ever contributes positively to its being or happening, the principle of causality is clearly a self-evident, necessary, analytic principle. And it is obviously presupposed in all inductive inquiry: we should not seek for the causes of phenomena did we believe it possible that they could be or happen without causes. A somewhat wider objective principle than this is the principle of sufficient reason: "Nothing real can be as it is without a sufficient reason why it is so "; and, applied to the subjective, mental, or logical order, the principle states: "No judgment can be true without a sufficient reason for its truth ". This principle, too, is presupposed in induction; we should not seek for general truths as an explanation or reason for the individual judgments that embody our sense-ex- perience did we not believe it possible to find in the former a rational explanation of the latter. But there is yet another principle, more directly assumed, involved in the inductive generalization, viz. the principle of the uniformity of nature: "Natural or non-free causes, i. e. the causes operative in the physical universe apart from the free will of man, when they act in similar circumstances always ana everywhere produce similar results"; "Physical causes act uniformly."

Since human free will is excluded from the scope of this principle, it follows that the phenomena which issue directly from the free activity of man do not furnish data for strict induction. It would, however, be a mistake to conclude that the influence of free will renders all science of human and social phenomena impossible. Such is not the case. For even those phenomena have a very large measure of uniformity, depending largely, as they do, on a whole group of influences and agencies other than free will: on racial and national character, social habits and sur- roundings, education, climate, etc. They are, therefore, manifestations of stable causes and laws, though not of mechanical or physical laws, and form a suitable, though difficult domain, for inductive in- quiry — difficult, because the operative influences are hidden under a mass of chaotic data which must be prepared by statistics and averages based on pains- taking and long-continued observations and com- parisons.

In the domain of physical induction proper we have to do only with natural or non-free causes. Above these, therefore, the question next arises: by what right do we assume the universal truth of the principle of uniformity as just stated, or what kind or degree of certitude does it guarantee to our inductive gener- alizations? Obviously it can give us no higher degree of certitude about the latter than we have about the principle itself. And this latter certitude will be determined by the grounds and origin of our belief in the principle. How, then, do we come to formulate consciously for ourselves, and give our assent to, the general proposition that the causes operative in the physical universe around us are of such a kind that they are determined each to one line of action, that they will not act capriciously, but regularly, uniformly, always in the same way in similar circumstances? The answer is that by our continued experience of the order and regularity and uniformity of the ordinary course of nature we gradually come to believe that physical causes have by their nature a fixed, deter- mined line of action, and to expect that unless some- thing unforeseen and extraordinary interfere with them, they act beyond our experience as they do within it. Mill is right in saying that the principle is a gradual generalization from experience, and, further- more, that it need not be consciously grasped in all its fullness anterior to any particular act of inductive generalization. But this is not enough; for, whether