It will be seen that the process of Inductive Reasoning is essentially a synthetic process, because it operates in the direction of combining and uniting particular facts or truths into general truths or laws which comprehend, embrace and include them all. As Brooks says: "The particular facts are united by the mind into the general law; the general law embraces the particular facts and binds them together into a unity of principle and thought. Induction is thus a process of thought from the parts to the whole—a synthetic process." It will also be seen that the process of Inductive Reasoning is essentially an ascending process, because it ascends from particular facts to general laws; particular truths to universal truths; from the lower to the higher, the narrower to the broader, the smaller to the greater.
Brooks says of Inductive Reasoning: "The relation of induction to deduction will be clearly seen. Induction and Deduction are the converse, the opposites of each other. Deduction derives a particular truth from a general truth; Induction derives a general truth from particular truths. This antithesis appears in every particular. Deduction goes from generals to particulars; Induction goes from particulars to generals. Deduction is an analytic process; Induction is a synthetic process. Deduction is a descending process—it goes from the higher truth to the lower truth; Induction is an ascending process—it goes from the lower truth to the higher. They differ also in that Deduction may be applied to necessary truths, while Induction is mainly restricted to contingent truths." Hyslop says: "There have been several ways of defining this process. It has been usual to contrast it with Deduction. Now, deduction is often said to be reasoning from general to particular truths, from the containing to the contained truth, or from cause to effect. Induction, therefore, by contrast is defined as reasoning from the particular to the general, from the contained to the containing, or from effect to cause. Sometimes induction is said to be reasoning from the known to the unknown. This would make deduction, by contrast, reasoning from the unknown to the known, which is absurd. The former ways of representing it are much the better. But there is still a better way of comparing them. Deduction is reasoning in which the conclusion is contained in the premises. This is a ground for its certitude and we commit a fallacy whenever we go beyond the premises as shown by the laws of the distribution of terms. In contrast with this, then, we may call inductive reasoning the process by which we go beyond the premises in the conclusion.... The process here is to start from given facts and to infer some other probable facts more general or connected with them. In this we see the process of going beyond the premises. There are, of course, certain conditions which regulate the legitimacy of the procedure, just as there are conditions determining deduction. They are that the conclusion shall represent the same general kind as the premises, with a possibility of accidental differences. But it goes beyond the premises in so far as known facts are concerned."
The following example may give you a clearer idea of the processes of Inductive Reasoning:
First Step. Preliminary Observation. Example: We notice that all the particular magnets which have come under our observation attract iron. Our mental record of the phenomena may be stated as: "A, B, C, D, E, F, G, etc., and also X, Y, and Z, all of which are magnets, in all observed instances, and at all observed times, attract iron."
Second Step. The Making of Hypotheses. Example: Upon the basis of the observations and experiments, as above stated, and applying the axiom of Inductive Reasoning, that: "What is true of the many, is true of the whole," we feel justified in forming a hypothesis or inference of a general law or truth, applying the facts of the particulars to the general, whole or universal, thus: "All magnets attract iron."
Third Step. Deductive Reasoning. Example: Picking up a magnet regarding which we have had no experience and upon which we have made no experiments, we reason by the syllogism, as follows: (1) All magnets attract iron; (2) This thing is a magnet; therefore (3) This thing will attract iron. In this we apply the axiom of Deductive Reasoning: "Whatever is true of the whole is true of the parts."
Fourth Step. Verification. Example: We then proceed to test the hypothesis upon the particular magnet, so as to ascertain whether or not it agrees with the particular facts. If the magnet does not attract iron we know that either our hypothesis is wrong and that some magnets do not attract iron; or else that our judgment regarding that particular "thing" being a magnet is at fault and that it is not a magnet. In either case, further examination, observation and experiment is necessary. In case the particular magnet does attract iron, we feel that we have verified our hypothesis and our judgment.
CHAPTER XII.
REASONING BY INDUCTION
The term "Induction," in its logical usage, is defined as follows: "(a) The process of investigating and collecting facts; and (b) the deducing of an inference from these facts; also (c) sometimes loosely used in the sense of an inference from observed facts." Mill says: "Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class, is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times."