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."