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
