III. Testing the hypothesis by deductive reasoning is the third step in inductive reasoning. This test is made by applying the hypothetical principle to particular facts or things; that is, to follow out mentally the hypothetical principle to its logical conclusion. This may be done in this way: "If so and so is correct, then it follows that thus and so is true," etc. If the conclusion agrees with reason, then the test is deemed satisfactory so far as it has gone. But if the result proves to be a logical absurdity or inconsistent with natural facts, then the hypothesis is discredited.
IV. Practical verification of the hypothesis is the fourth step in inductive reasoning. This step consists of the actual comparison of observed facts with the "logical conclusions" arising from applying deductive reasoning to the general principle assumed as a premise. The greater number of facts agreeing with the conclusions arising from the premise of the hypothesis, the greater is deemed the "probability" of the latter. The authorities generally assume an hypothesis to be verified when it accounts for all the facts which properly are related to it. Some extremists contend, however, that before an hypothesis may be considered as absolutely verified, it must not only account for all the associated facts but that also there must be no other possible hypothesis to account for the same facts. The "facts" referred to in this connection may be either (1) observed phenomena, or (2) the conclusions of deductive reasoning arising from the assumption of the hypothesis, or (3) the agreement between the observed facts and the logical conclusions. The last combination is generally regarded as the most logical. The verification of an hypothesis must be "an all-around one," and there must be an agreement between the observed facts and the logical conclusions in the case—the hypothesis must "fit" the facts, and the facts must "fit" the hypothesis. The "facts" are the glass slipper of the Cinderella legend—the several sisters of Cinderella were discarded hypotheses, the slipper and the sisters not "fitting." When Cinderella's foot was found to be the one foot upon which the glass slipper fitted, then the Cinderella hypothesis was considered to have been proved—the glass slipper was hers and the prince claimed his bride.
CHAPTER XXVII.
Deductive Reasoning.
WE have seen in the preceding chapter that from particular facts we reason inductively to general principles or truths. We have also seen that one of the steps of inductive reasoning is the testing of the hypothesis by deductive reasoning. We shall now also see that the results of inductive reasoning are used as premises or bases for deductive reasoning. These two forms of reasoning are opposites and yet complementary to each other; they are in a sense independent and yet are interdependent. Brooks says: "The two methods of reasoning are the reverse of each other. One goes from particulars to generals; the other from generals to particulars. One is a process of analysis; the other is a process of synthesis. One rises from facts to laws; the other descends from laws to facts. Each is independent of the other, and each is a valid and essential method of inference."
Halleck well expresses the spirit of deductive reasoning as follows: "After induction has classified certain phenomena and thus given us a major premise, we may proceed deductively to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made premise. Deduction takes that as a fact, making no inquiry regarding its truth. Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed."
Deductive reasoning proceeds from general principles to particular facts. It is a descending process, analytical in its nature. It rests upon the fundamental axiomatic basis that "whatever is true of the whole is true of its parts," or "whatever is true of the universal is true of the particulars."
The process of deductive reasoning may be stated briefly as follows: (1) A general principle of a class is stated as a major premise; (2) a particular thing is stated as belonging to that general class, this statement being the minor premise; therefore (3) the general class principle is held to apply to the particular thing, this last statement being the conclusion. (A "premise" is "a proposition assumed to be true.")
The following gives us an illustration of the above process:—
I. (Major premise)—A bird is a warm-blooded, feathered, winged, oviparous vertebrate.
II. (Minor premise)—The sparrow is a bird; therefore
III. (Conclusion)—The sparrow is a warm-blooded, feathered, winged, oviparous vertebrate.