Part 10 (1/2)
II. The second step in inductive reasoning is the making of an hypothesis. An hypothesis is a proposition or principle a.s.sumed as a _possible_ explanation for a set or cla.s.s of facts. It is regarded as a ”working theory,” which must be examined and tested in connection with the facts before it is finally accepted. For instance, after the observation that a number of magnets attracted steel, it was found reasonable to advance the hypothesis that ”all magnets attract steel.”
In the same way was advanced the hypothesis that ”all birds are warm-blooded, winged, feathered, oviparous vertebrates.” Subsequent observation and experiment established the hypothesis regarding the magnet, and regarding the general qualities of the bird family. If a single magnet had been found which did not attract steel, then the hypothesis would have fallen. If a single bird had been discovered which was not warm-blooded, then that quality would have been stricken from the list of the necessary characteristics of all birds.
A theory is merely an hypothesis which has been verified or established by continued and repeated observation, investigation, and experiment.
Hypotheses and theories arise very frequently from the subconscious a.s.similation of a number of particular facts and the consequent flas.h.i.+ng of a ”great guess,” or ”sacred suspicion of the truth,” into the conscious field of attention. The scientific imagination plays an important part in this process. There is, of course, a world of difference between a ”blind guess” based upon insufficient data and a ”scientific guess” resulting from the acc.u.mulation of a vast store of careful and accurate information. As Brooks says: ”The forming of an hypothesis requires a suggestive mind, a lively fancy, a philosophic imagination that catches a glimpse of the idea through the form or sees the law standing behind the fact.” But accepted theories, in the majority of cases, arise only by testing out and rejecting many promising hypotheses and finally settling upon the one which best answers all the requirements and best explains the facts. As an authority says: ”To try wrong guesses is with most persons the only way to hit upon right ones.”
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 a.s.sumed 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 a.s.sume 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 a.s.sociated 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 a.s.sumption 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 gla.s.s 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 gla.s.s slipper fitted, then the Cinderella hypothesis was considered to have been proved--the gla.s.s 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 a.n.a.lysis; 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 cla.s.sified 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 cla.s.s. 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 cla.s.sified, after major premises have been formed, can deduction be employed.”
Deductive reasoning proceeds from general principles to particular facts. It is a descending process, a.n.a.lytical 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 cla.s.s is stated as a _major premise_; (2) a particular thing is stated as belonging to that general cla.s.s, this statement being the _minor premise_; therefore (3) the general cla.s.s principle is held to apply to the particular thing, this last statement being the _conclusion_. (_A ”premise” is ”a proposition a.s.sumed to be true.”_)
The following gives us an ill.u.s.tration 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.
Or, again:--
I. (_Major premise_)--Rattlesnakes frequently bite when enraged, and their bite is poisonous.
II. (_Minor premise_)--This snake before me is a rattlesnake; therefore
III. (_Conclusion_)--This snake before me may bite when enraged, and its bite will be poisonous.
The average person may be inclined to object that he is not conscious of going through this complicated process when he reasons about sparrows or rattlesnakes. But he _does_, nevertheless. He is not conscious of the steps, because mental habit has accustomed him to the process, and it is performed more or less automatically. But these three steps manifest in all processes of deductive reasoning, even the simplest. The average person is like the character in the French play who was surprised to learn that he had ”been talking prose for forty years without knowing it.” Jevons says that the majority of persons are equally surprised when they find out that they have been using logical forms, more or less correctly, without having realized it. He says: ”A large number even of educated persons have no clear idea of what logic is. Yet, in a certain way, every one must have been a logician since he began to speak.”
There are many technical rules and principles of logic which we cannot attempt to consider here. There are, however, a few elementary principles of correct reasoning which should have a place here. What is known as a ”syllogism” is the expression in words of the various parts of the complete process of reasoning or argument. Whately defines it as follows: ”A syllogism is an argument expressed in strict logical form so that its conclusiveness is manifest from the structure of the expression alone, without any regard to the meaning of the term.” In short, _if_ the two premises are accepted as correct, it follows that there can be only one true logical conclusion resulting therefrom. In abstract or theoretical reasoning the word ”_if_” is a.s.sumed to precede each of the two premises, the ”therefore” before the conclusion resulting from the ”if,” of course. The following are the general rules governing the syllogism:--
I. Every syllogism must consist of three, and no more than three, propositions, namely (1) the major premise, (2) the minor premise, and (3) the conclusion.
II. The conclusion must naturally follow from the premises, otherwise the syllogism is invalid and const.i.tutes a fallacy or sophism.