INDUCTION
780
INDUCTION
class of universal judgments only, generalizations
based on experience, that induction proper has to
deal.
II. Scientific Indcction. — Although induction is equally applicable in all departments of generalization from experience, in the historical and anthropological no less than in the physical sciences, still it is in its apphcation to the discovery of the causes and laws of physical phenomena, animate and inanimate, that it lends itself most readily to logical analysis. Hence it is that logical textbooks ordinarily speak of " physical " induction. The process is often described as a ratio- cinative or inferential process, and from this stand- point is contrasted with deductive reasoning. But if by logical inference we are to understand the con- scious passage of the mind from one or more judg- ments as premises to another new judgment involved in them as conclusion, then this is certainly not the essence of the inductive process, although there are indeed ratiocinative steps involved in the latter, subsidiary to its essential function which is the dis- covery and proof of some universal truth or causal law of phenomena. Induction is really a logical method involving many stages and processes besides the central step of generalization itself; and it is opposed to deduction only in the sense that it ap- proaches reality from the side of the concrete and individual, while deduction does so from that of the abstract and universal.
The first of these steps is the observation of some fact or facts of sense-experience, usually a repeated coexistence in space or sequence in time of certain things or events. This naturally prompts us to seek its explanation, i. e. its cau.ses, the total combination of proximate agencies to which it is due, the law- according to which these causes secure its regular recurrence, on the assumption that the causes opera- tive in the physical universe are such that acting in similar circumstances they will always produce similar results. Logic prescribes practical directions to guide us in observing, in finding out accurately what accompanies or follows what, in eliminating all the merely accidental concomitant circumstances of a phenomenon, so as to retain for analysis only those that are likely to be causally, as distinct from casually, connected with the event under investi- gation.
Next comes the stage at which the tentative, em- pirical generalization is made; the suggestion occurs that the observed connexion (between S and P) may be universal in space and time, may be a natural causal connexion the ground of which lies in a sus- pected agency or group of agencies operative in the total sense-experience that gives us the elements rmder investigation (S and P). This is the formation of a scientific hypothesis. All discovery of laws of physical nature is by way of hj^pothesis; and dis- covery precedes proof; we must suspect and guess the caus;d law that explains the phenomenon before we can verify or establish the law. A hj^Dothesis is conceived as an abstract judgment: "If S is M it is P ", which we — relying on the uniformity of nature — forthwith formally generalize: "Whenever and wherever S is M it is P", a generalization which has next to be tested to see whether it is also materially accurate. A h^'pothesis is therefore a provisional supposition as to the cause of a phenomenon, made with the object of ascertaining the real cause of the latter. Logic cannot, of course, suggest to us what particular sup- position we ought to make in a given case. This is for the investigator himself. This is where the scien- tific imagination, originality, and genius come into play. But logic does imlicate in a general way the sources from which hypotheses are usually drawn, and, more especially, it lays down conditions to which a hypothesis must conform if it is to be of any scientific value. The most fertile source of hypotheses is the
observation of analogies, i. e. resemblances between
the phenomenon under investigation and other phe-
nomena whose causes are already partially or fully
known. When the state of our knowledge does not
enable us to make any likely guess aljout the cause of
the phenomenon, we must be content with a working
hypothesis which will be perhaps merely a description
of the events observed. A hypothesis that purports
to be explanatory must be consi-stent with itself
throughout, free from evident and irremediable con-
flict with known facts and laws, and capaljle of verifi-
cation. This latter condition will be fulfilled only
when the hjTJothesis is based on some analogy with
known causes. Were the supposed cause totally
unique and siii generis, we could form no conjecture as
to how it would work in any given or conceivable set
of circumstances, and we could therefore never detect
whether it was really there or not. A hypothesis may
be legitimate and useful in science even though it
may turn out to be inaccurate; few hypotheses are
altogether accurate at first. It may even have to
be rejected altogether as disproved after a time and
yet have served to lead to other discoveries or have
put investigators on the right track. Or, as is more
usually the case, it may have to be moulded, modified,
limited, or extended in the course of verifying it by
further observation and experiment.
It is to help the investigator in this work of analyz- ing the facts of sense-experience so as to discover and prove causal connexions or natural laws by the formation and verification of hypotheses, that modern logicians have dealt so exhaustivelv with the "canons of inductive inquiry", or "experimental methods", first outlined by Herschel in his "Preliminary Dis- course on the Studv of Natural Philosophy" and first popularized by John Stuart Mill in his "System of Logic ". These canons — of agreement, difference, concomitant variations, residues, positive and nega- tive agreement, combined agreement and difference — all merely formulate various ways of applying to the analysis of phenomena the principle of eliminating what is ca.sual or accidental so as to leave behind what is causal or essential; they arc all based upon the prin- ciple that whatever can be eliminated from a .set of things or events without thereby eliminating the phenomenon under investigation, is not causally con- nected with the latter, and whatever cannot be so eliminated without also eliminating the phenomenon is cau.sally connected with it. Stating a hypothesis in the symbols, "If S is M it is P", we have in M the supposed real or objective cause of P, and also the mental or logical grounil for predicating P of S. We test or verify such a hj-pothesis by endeavouring to establish, through a series of positive experiments or observations, that whenever and wherever M occurs so does P; that M necessitates P; and, secondly, through a series of negative experiments or observa- tions, that wherever and whenever M is absent so is P, that M is indispensable to P, that it is the only po.s.sible cause of P. If these tests can be applied successfully the hj'pothesis is fully verified. The supposed cau.se of the phenomenon is certainly the real one if it can be shown to be indispen.sable, in the sense that the phenomenon cannot occur in its absence, and necessitating, in the sense that the phe- nomenon must occur when it is present and oper- ative. This sort of verification (often only very imperfectly and sometimes not at all attainable) is what the scientist aims at. It establishes the two propositions " If S is M it is P ", and " If S is not M it IS not P " — the latter being equivalent to the recip- rocal of the former (to " If S is P it is M "). Whenever we attain to this ideal (of the reciprocal hypothetical) we can infer from consequent to antecedent, from effect to cause, just as reliably as vice versa. But over what range of phenomena are we to carrj' on our negative observations and experiments in order to
