In inference, therefore, there is always the extension of our knowledge, for the given judgment contains something which is not ap parent when observed in its own light simply, but which is revealed only in the light which plays upon it from our general body of knowl edge as a central source of illumination.
The ground of inference, indeed, that which makes the inferential process a possibility at all, is the supposition which we are constrained to make and upon which we are constantly rest ing, in the exercise of our reasoning faculty, namely, that the various elements which con stitute our body of knowledge as a whole must be related to each other in such a way as to form a system of interconnected and interde pendent parts. When we have given a single part, other parts of the whole to which the part belongs can he inferred, because of our knowl edge of the general system which binds them together through the inner connections of necessity. That which is implicit in any judg ment and which forms the germ of inference can be revealed only when one thoroughly un derstands the complete system of relations and connections which underlies the judgment in question. If our knowledge were not system atized, and the various parts duly related and properly co-ordinated and subordinated each to each, then there could he no basis for any inference, and no possibility of constancy and consistency in our thinking. As aids to sys temization there are the processes of definition, division and classification which are treated at length in textbooks on the formal logic and can only receive passing mention here.
While inference depends upon organized knowledge it is also instrumental in producing the very organization of our knowledge itself. It draws from it and at the same time it con tributes to it. This twofold function gives rise to the two kinds of inference, known as de.: ductive and inductive. In deductive inference we proceed from our general knowledge to the characterization of the special case which de pends upon it; or inasmuch as our general knowledge is expressed in the form of uni versal concepts we can put it simply — that de duction is from the universal to the particular. Induction, on the other hand, is from the par ticular case, or rather particular cases, to the universal. It is essentially a process of general ization, by which we rise in thought from the investigation of special cases to the universal principle or law which embraces them and underlies their nature. Inference is always either the interpretation or else the elaboration of knowledge. When that which is given is illuminated by some universal principle or law so that its implicit significance is thereby made explicit, we have the process of deduction.
But when there is no recognized universal, and such must evidently be sought, we turn naturally to the relevant instances before us so as to discover in them some suggestion of the desired law or principle. Such a procedure is induc tion. For example, when the physicist sees certain dark lines in the solar spectrum, he in fers that they indicate the presence, of iron vapor in the sun. This is deductive inference because it is a process of thought which rests upon the universal and well-known connection between certain definitely positioned lines in the solar spectrum and the presence of iron. On the other hand, however, suppose the in vestigator is ignorant of the meaning of these dark lines. In his knowledge they possess no significance whatever and suggest nothing to his mind. It is obvious that he must experi ment in various ways with the phenomena of these lines until he is able to discover their general relations and significance. Then he will be able to formulate the results of his investi gation in a universal law which not only shall embody the special cases coming under his observation but all others also of a similar nature. It will be readily seen that deduction and induction are complementary phases of one and the same process. With every special case which comes before consciousness one of two methods of procedure is possible, that is, if it is to be the subject of inference at all; if it evidently falls under some universal law or principle to which we do not hesitate to refer it, then it becomes invested with the full pur port and significance of such a universal; if, however, there is no recognized universal to which we can refer it, the special case presents a problem for us to solve by experiment and observation, namely, what is the universal which we are constrained to believe must underlie it, and which the special case in some way not yet revealed necessarily illustrates. Whenever, therefore, we face a new experi ence, a new fact or event we must treat it by one or the other of these two methods accord ing as our knowledge is adequate to its inter pretation or not. In the one case we are rea soning deductively; in the other, inductively. Where the limitations of knowledge obstruct progress in one direction, it is possible to pro ceed in the other direction so as to remove eventually these very limitations themselves. If we do not possess sufficient knowledge to suggest the appropriate universal from which to reason deductively, we can proceed in an inductive manner to search for the universal which invites our investigation.