INDUCTION (Lat. inductio, inference, from inducere, to lead in, from in, in + ducere, to lead). A form of the logical process of discover ing the general character of individual phe nomena. In order to understand any fact or event, we need not only to be able to tell of its sensible qualities or constituents, but also to know what identity (q.v.) it has with other facts or events. Such an identity is a general char acter, or, as it is called in logic, a universal. When in the case of several objects we discover an identity in color or shape, we perform the act of conception. lf, using some already discovered identity between some objects as a point of departure, we assume some other iden tity to exist between the same objects. we are said to generalize or to make an induction. Induction may thus be defined as the univer salizing of perceived relations or connections be tween objects. Among these relations one of the most important is that of antecedence and con sequence. (See CAUSALITY.) This universaliza tion is corrected or confirmed by further ob servation of these connections in other individual cases until at last often a valid judgment assert ing unconditional connection is reached. A valid induction is one which, starting from particular observations, thus reaches a valid universal judg ment. Scientific inductions do not differ in principle from the naive inductions we have al ready described; the difference is one of degree. not of kind.
Looking now at inductions ascertained to be valid, we discover three stages in the process of arriving at certified results. The first stage is called preliminary obscrration. At this point actual coexistences and sequences or other rela tions are observed and form the data for the induction. The second stage consists in the generalization of some actually ascertained co existence or sequence, or other relations. This is induction proper. The third stage is verification, the correcting or confirming of the validity of the generalization by further observation. Fre quently the term induction is used to include all these three steps; in this case the second step is called generalization. Let us now take up these three steps in order.
I. Preliminary observation may be quite casual and accidental, or it may be intentional. z1 person may happen to see some connection between phenomena, or he may be intently look ing for connections. In the latter etitse, the observer may simply look at things as they offer themselves to his notice, or he may set about to interfere with the spontaneous course of wefts in order that he Inns the better observe the connection. file latter sort of observation is called nn experiment. When experiment is possible, it is usually of great assistance in eol lecting data for generalization. Indeed. almost nil the great advances in modern science' have been due to experimentation rather than to mere observation. lit intentional observation. whether it he simple er experimental. it is extremely important fur the observer to know what he is to look for Not every detail in the complex of details under observation is pertinent to the matter in hand: and vet no a priori can he given to direct an investigator. Aluch depends on experience and skill not subject to rules. But Icy- analyzing successfully conducted inductions, logicians are able to formulate several important rules Of procedure, tints are a posteriori. For our present purposes we can do no better than quote John Stuart Mill's canons of imbue tion. These state the conditions under which generalization may be made. hence the observer
should he on the watch for the occurrence of these The canons are as follows: First Canon, for the :Method of Agreement: If Iwo or more instanCCR of the phenoMe71011 under inrestigation hare only one eireumRtance in common, the cir cumstance in which alone all the instances agree, is the cause (or effect) of the giren phenomenon. Second Canon, for the Method of Difference: If an instance in. which the phenomenon under inrestigation occurs, and an instance in which it does not occur, hare every eirenmstanee in common save one, that one occurring only in the farmer, the circumstance in which alone the two instances differ, IR the effect, or the raise, or an indi.spensubir part of the cause, of the phe TIOnlellOn. Third Canon, for the Joint Method of Agreement and Difference: If Iwo or more in stances in which the phenomenon occurs hare only one circumstance in common, while two or more instances fit which it does not occur hare nothing in common sore the absence' of that cir cumstance: the circumstance ice which alone the two sets of instances differ, is the effect, or the Cause. or an indispensable part of the CallRe, of the phenomenon. Fourth ('anon, for the i\lethnil of Iti•siducs: Subdue, from any phenomenon such part as is known by precious inductions to be the effect of certain antecedents, and the resi due of tier phenomenon iR the effect of the re maining onteceele tits. Fifth Canon, for the "Method of Concomitant Variations: Trhaierer phenono'non varies in any manner tchererer an other phenomenon caries in some particular man ner. is a cause or an effect of that phe nomenon, or is connected with it throngh sonic fact of causation. These are statements of the conditions under Mild' scientific men make in duetive inferences. llenee in our observations for the purposes of, induction we should keep the following, questions in mind: Is it the ease that any instance in which the phenomenon under investigation oecurs, and any instanee in which it does not occur, have every eirenin.tnnec in common save one? Ts it the ease that two or more instances of the phenomenon under inves tigation have only one circumstance in common? Is it true that two or more instances in which the phenomenon under investigation occurs have only one circumstanee in common, while two or more instances in which it does not occur hats. nothing in common save the absence of that cirrunistance? 14 a part of this under investigation known to be the effect of curtain causes? Does the pheinonenim tinder in vestigation vary in any manner Whatever when ever some particular circumstance, varies in some particular manner? In ease any of these mu., lions can he answered in the affirmative, an induction may la made. it not. however, be supposed that an investigator sets .shout his work with only such general clews as are fur Wished by these questions. In Slily particular investigation, n knowledge of exactly what has already been done by previous workers is indis pensable. If lie has this knowledge. the tigator is in a position tee ask much more definite eonerete questions than the five we have just. mentioned. lint, however nmell more liefIllite his problem may be, it may always be reduced to general expression. and when so reduced it will assume the form of one la the five questions stated above. whieli give the headings for the treatment of the methodology of otisenation. Any more specifie methodology can he worked out only on the basis of the practiced experience of the expert in any particular line of research.