REASONING

In the preceding chapters we have seen that in the group of mental processes involved in the general process of Understanding, there are several stages or steps, three of which we have considered in turn, namely: (1) Abstraction; (2) Generalization or Conception; (3) Judgment. The fourth step, or stage, and the one which we are now about to consider, is that called Reasoning.

Reasoning is that faculty of the mind whereby we compare two Judgments, one with the other, and from which comparison we are enabled to form a third judgment. It is a form of indirect or mediate comparison, whereas, the ordinary Judgment is a form of immediate or direct comparison. As, when we form a Judgment, we compare two concepts and decide upon their agreement or difference; so in Reasoning we compare two Judgments and from the comparison we draw or produce a new Judgment. Thus, we may reason that the particular dog "Carlo" is an animal, by the following process:

(1) All dogs are animals; (2) Carlo is a dog; therefore, (3) Carlo is an animal. Or, in the same way, we may reason that a whale is not a fish, as follows:

(1) All fish are cold-blooded animals; (2) A whale is not a cold-blooded animal; therefore, (3) A whale is not a fish.

In the above processes it will be seen that the third and final Judgment is derived from a comparison of the first two Judgments. Brooks states the process as follows: "Looking at the process more closely, it will be seen that in inference in Reasoning involves a comparison of relations. We infer the relation of two objects from their relation to a third object. We must thus grasp in the mind two relations and from the comparison of these two relations we infer a third relation. The two relations from which we infer a third, are judgments; hence, Reasoning may also be defined as the process of deriving one judgment from two other judgments. We compare the two given judgments and from this comparison derive the third judgment. This constitutes a single step in Reasoning, and an argument so expressed is called a Syllogism."

The Syllogism consists of three propositions, the first two of which express the grounds or basis of the argument and are called the premises; the third expresses the inference derived from a comparison of the other two and is called the conclusion. We shall not enter into a technical consideration of the Syllogism in this book, as the subject is considered in detail in the volume of this series devoted to the subject of "Logic." Our concern here is to point out the natural process and course of Reasoning, rather than to consider the technical features of the process.

Reasoning is divided into two general classes, known respectively as (1) Inductive Reasoning; (2) Deductive Reasoning.

Inductive Reasoning is the process of arriving at a general truth, law or principle from a consideration of many particular facts and truths. Thus, if we find that a certain thing is true of a great number of particular objects, we may infer that the same thing is true of all objects of this particular kind. In one of the examples given above, one of the judgments was that "all fish are cold-blooded animals," which general truth was arrived at by Inductive Reasoning based upon the examination of a great number of fish, and from thence assuming that all fish are true to this general law of truth.

Deductive Reasoning is the reverse of Inductive Reasoning, and is a process of arriving at a particular truth from the assumption of a general truth. Thus, from the assumption that "all fish are cold-blooded animals," we, by Deductive Reasoning, arrive at the conclusion that the particular fish before us must be cold-blooded.

Inductive Reasoning proceeds upon the basic principle that "What is true of the many is true of the whole," while Deductive Reasoning proceeds upon the basic principle that "What is true of the whole is true of its parts."

Regarding the principle of Inductive Reasoning, Halleck says: "Man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. By induction, we examine what seems to us a sufficient number of individual cases. We then conclude that the rest of these cases, which we have not examined, will obey the same general law. The judgment 'All men are mortal' was reached by induction. It was observed that all past generations of men had died, and this fact warranted the conclusion that all men living will die. We make that assertion as boldly as if we had seen them all die. The premise, 'All cows chew the cud,' was laid down after a certain number of cows had been examined. If we were to see a cow twenty years hence, we should expect to find that she chewed the cud. It was noticed by astronomers that, after a certain number of days, the earth regularly returned to the same position in its orbit, the sun rose in the same place, and the day was of the same length. Hence, the length of the year and of each succeeding day was determined, and the almanac maker now infers that the same will be true of future years. He tells us that the sun on the first of next December will rise at a given time, although he cannot throw himself into the future to verify the conclusion."

Brooks says regarding this principle: "This proposition is founded on our faith in the uniformity of nature; take away this belief, and all reasoning by induction fails. The basis of induction is thus often stated to be man's faith in the uniformity of nature. Induction has been compared to a ladder upon which we ascend from facts to laws. This ladder cannot stand unless it has something to rest upon; and this something is our faith in the constancy of nature's laws."

There are two general ways of obtaining our basis for the process of Inductive Reasoning. One of these is called Perfect Induction and the other Imperfect Induction. Perfect Induction is possible only when we have had the opportunity of examining every particular object or thing of which the general idea is expressed. For instance, if we could examine every fish in the universe we would have the basis of Perfect Induction for asserting the general truth that "all fishes are cold-blooded." But this is practically impossible in the great majority of cases, and so we must fall back upon more or less Imperfect Induction. We must assume the general law from the fact that it is seen to exist in a very great number of particular cases; upon the principle that "What is true of the many is true of the whole." As Halleck says regarding this: "Whenever we make a statement such as, 'All men are mortal,' without having tested each individual case or, in other words, without having seen every man die, we are reasoning from imperfect induction. Every time a man buys a piece of beef, a bushel of potatoes or a loaf of bread, he is basing his action on inference from imperfect induction. He believes that beef, potatoes and bread will prove nutritious food, although he has not actually tested those special edibles before purchasing them. They have hitherto been found to be nutritious on trial and he argues that the same will prove true of those special instances. Whenever a man takes stock in a new national bank, a manufactory or a bridge, he is arguing from past cases that this special investment will prove profitable. We instinctively believe in the uniformity of nature; if we did not we should not consult our almanacs. If sufficient heat will cause phosphorus to burn today, we conclude that the same result will follow tomorrow if the circumstances are the same."

But, it will be seen, much care must be exercised in making observations, experiments and comparisons, and in making generalizations. The following general principles will give the views of the authorities regarding this:

Atwater gives the two general rules:

Rule of Agreement: "If, whenever a given object or agency is present, without counteracting forces, a given effect is produced, there is a strong evidence that the object or agency is the cause of the effect."

Rule of Disagreement: "If when the supposed cause is present the effect is present, and when the supposed cause is absent the effect is wanting, there being in neither case any other agents present to effect the result, we may reasonably infer that the supposed cause is the real one."

Rule of Residue: "When in any phenomena we find a result remaining after the effects of all known causes are estimated, we may attribute it to a residual agent not yet reckoned."

Rule of Concomitant Variations: "When a variation in a given antecedent is accompanied by a variation of a given consequent, they are in some manner related as cause and effect."

Atwater says, of the above rules, that "whenever either of these criteria is found, free from conflicting evidence, and especially when several of them concur, the evidence is clear that the cases observed are fair representatives of the whole class, and warrant a valid universal inductive conclusion."

We now come to what is known as Hypothesis or Theory, which is an assumed general principle—a conjecture or supposition founded upon observed and tested facts. Some authorities use the term "theory" in the sense of "a verified hypothesis," but the two terms are employed loosely and the usage varies with different authorities. What is known as "the probability of a hypothesis" is the proportion of the number of facts it will explain. The greater the number of facts it will explain, the greater is its "probability." A Hypothesis is said to be "verified" when it will account for all the facts which are properly to be referred to it. Some very critical authorities hold that verification should also depend upon there being no other possible hypotheses which will account for the facts, but this is generally considered an extreme position.

A Hypothesis is the result of a peculiar mental process which seems to act in the direction of making a sudden anticipatory leap toward a theory, after the mind has been saturated with a great body of particular facts. Some have spoken of the process as almost intuitive and, indeed, the testimony of many discoverers of great natural laws would lead us to believe that the Subconscious region of the mind is most active in making what La Place has called "the great guess" of discovery of principle. As Brooks says: "The forming of hypotheses 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."

Thomson says: "The system of anatomy which has immortalized the name of Oken, is the consequence of a flash of anticipation which glanced through his mind when he picked up in a chance walk the skull of a deer, bleached and disintegrated by the weather, and exclaimed, after a glance, 'It is part of a vertebral column.' When Newton saw the apple fall, the anticipatory question flashed through his mind, 'Why do not the heavenly bodies fall like this apple?' In neither case had accident any important share; Newton and Oken were prepared by the deepest previous study to seize upon the unimportant fact offered to them, and show how important it might become; and if the apple and the deer-skull had been wanting, some other falling body, or some other skull, would have touched the string so ready to vibrate. But in each case there was a great step of anticipation; Oken thought he saw the type of the whole skeleton in a single vertebra, whilst Newton conceived at once that the whole universe was full of bodies tending to fall."

Passing from the consideration of Inductive Reasoning to that of Deductive Reasoning we find ourselves confronted with an entirely opposite condition. As 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."

Deductive Reasoning is, as we have seen, dependent upon the process of deriving a particular truth from a general law, principle or truth, upon the fundamental axiom that: "What is true of the whole is true of its parts." It is an analytical process, just as Inductive Reasoning is synthetical. It is a descending process, just as Inductive Reasoning is ascending.

Halleck says of Deductive Reasoning: "After induction has classified certain phenomena and thus given us a major premise, we 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 major premise, e.g. 'All scorpions are dangerous.' Deduction takes this as a fact, making no inquiry about its truth. When a new object is presented, say a possible scorpion, the only troublesome step is to decide whether the object is really a scorpion. This may be a severe task on judgment. The average inhabitant of the temperate zone would probably not care to risk a hundred dollars on his ability to distinguish a scorpion from a centipede, or from twenty or thirty other creatures bearing some resemblance to a scorpion. Here there must be accurately formed concepts and sound judgment must be used in comparing them. As soon as we decide that the object is really a scorpion, we complete the deduction in this way:—'All scorpions are dangerous; this creature is a scorpion; this creature is dangerous.' The reasoning of early life must be necessarily inductive. The mind is then forming general conclusions from the examination of individual phenomena. Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed."

What is called Reasoning by Analogy is really but a higher degree of Generalization. It is based upon the idea that if two or more things resemble each other in many particulars, they are apt to resemble each other in other particulars. Some have expressed the principle as follows: "Things that have some things in common have other things in common." Or as Jevons states it: "The rule for reasoning by analogy is that if two or more things resemble each other in many points, they will probably resemble each other also in more points."

This form of reasoning, while quite common and quite convenient, is also very dangerous. It affords many opportunities for making false inferences. As Jevons says: "In many cases Reasoning by Analogy is found to be a very uncertain guide. In some cases unfortunate mistakes are committed. Children are sometimes killed by gathering and eating poisonous berries, wrongly inferring that they can be eaten, because other berries, of a somewhat similar appearance, have been found agreeable and harmless. Poisonous toadstools are occasionally mistaken for mushrooms, especially by people not accustomed to gather them.... There is no way in which we can really assure ourselves that we are arguing safely by analogy. The only rule that can be given is this, that the more things resemble each other, the more likely is it that they are the same in other respects, especially in points closely connected with those observed."

Halleck says: "In argument or reasoning we are much aided by the habit of searching for hidden resemblances. We may here use the term analogy in the narrower sense as a resemblance of ratios. There is analogical relation between autumnal frosts and vegetation on the one hand, and death and human life on the other. Frosts stand in the same relation to vegetation that death does to life. The detection of such a relation cultivates thought. If we are to succeed in argument, we must develop what some call a sixth sense for the detection of such relations.... Many false analogies are manufactured and it is excellent thought training to expose them. The majority of people think so little that they swallow false analogies just as newly-fledged robins swallow small stones dropped into their open mouths.... The study of poetry may be made very serviceable in detecting analogies and cultivating the reasoning powers. When the poet brings clearly to mind the change due to death, using as an illustration the caterpillar body transformed into the butterfly spirit, moving with winged ease over flowing meadows, he is cultivating our apprehension of relations, none the less valuable because they are beautiful."

There are certain studies which tend to develop the power or faculty of Inductive Reasoning. Any study which leads the mind to consider classification and general principles, laws or truth, will tend to develop the faculty of deduction. Physics, Chemistry, Astronomy, Biology and Natural History are particularly adapted to develop the mind in this particular direction. Moreover, the mind should be directed to an inquiry into the causes of things. Facts and phenomena should be observed and an attempt should be made not only to classify them, but also to discover general principles moving them. Tentative or provisional hypotheses should be erected and then the facts re-examined in order to see whether they support the hypotheses or theory. Study of the processes whereby the great scientific theories were erected, and the proofs then adduced in support of them, will give the mind the habit of thinking along the lines of logical induction. The question ever in the mind in Inductive Reasoning is "Why?" The dominant idea in Inductive Reasoning is the Search for Causes.

In regard to the pitfalls of Inductive Reasoning—the fallacies, so-called, Hyslop says: "It is not easy to indicate the inductive fallacies, if it be even possible, in the formal process of induction.... It is certain, however, that in respect to the subject-matter of the conclusion in inductive reasoning there are some very definite limitations upon the right to transcend the premises. We cannot infer anything we please from any premises we please. We must conform to certain definite rules or principles. Any violation of them will be a fallacy. These rules are the same as those for material fallacies in deduction, so that the fallacies of induction, whether they are ever formal or not, are at least material; that is they occur whenever equivocation and presumption are committed. There are, then, two simple rules which should not be violated. (1) The subject-matter in the conclusion should be of the same general kind as in the premises. (2) The facts constituting the premises must be accepted and must not be fictitious."

One may develop his faculty or power of Deductive Reasoning by pursuing certain lines of study. The study of Mathematics, particularly in its branch of Mental Arithmetic is especially valuable in this direction. Algebra and Geometry have long been known to exercise an influence over the mind which gives to it a logical trend and cast. The processes involved in Geometry are akin to those employed in Logical reasoning, and must necessarily train the mind in this special direction. As Brooks says: "So valuable is geometry as a discipline that many lawyers and others review their geometry every year in order to keep the mind drilled to logical habits of thinking." The study of Grammar, Rhetoric and the Languages, are also valuable in the culture and development of the faculty of Deductive Reasoning. The study of Psychology and Philosophy have value in this connection. The study of Law is very valuable in creating logical habits of thinking deductively.

But in the study of Logic we have possibly the best exercise in the development and culture of this particular faculty. As Brooks well says: "The study of Logic will aid in the development of the power of deductive reasoning. It does this first by showing the method by which we reason. To know how we reason, to see the laws which govern the reasoning process, to analyze the syllogism and see its conformity to the laws of thought, is not only an exercise of reasoning, but gives that knowledge of the process that will be both a stimulus and a guide to thought. No one can trace the principles and processes of thought without receiving thereby an impetus to thought. In the second place, the study of logic is probably even more valuable because it gives practice in deductive thinking. This, perhaps, is its principal value, since the mind reasons instinctively without knowing how it reasons. One can think without the knowledge of the science of thinking, just as one can use language correctly without a knowledge of grammar; yet as the study of grammar improves one's speech, so the study of logic cannot but improve one's thought."

The study of the common fallacies, such as "Begging the Question," "Reasoning in a Circle," etc., is particularly important to the student, for when one realizes that such fallacies exist, and is able to detect and recognize them, he will avoid their use in framing his own arguments, and will be able to expose them when they appear in the arguments of others.

The fallacy of "Begging the Question" consists in assuming as a proven fact something that has not been proven, or is not accepted as proven by the other party to the argument. It is a common trick in debate. The fact assumed may be either the particular point to be proved, or the premise necessary to prove it. Hyslop gives the following illustration of this fallacy: "Good institutions should be united; Church and State are good institutions; therefore, Church and State should be united." The above syllogism seems reasonable at first thought, but analysis will show that the major premise "Good institutions should be united" is a mere assumption without proof. Destroy this premise and the whole reasoning fails.

Another form of fallacy, quite common, is that called "Reasoning in a Circle," which consists in assuming as proof of a proposition the proposition itself, as for instance, "This man is a rascal, because he is a rogue; he is a rogue, because he is a rascal." "We see through glass, because it is transparent." "The child is dumb, because it has lost the power of speech." "He is untruthful, because he is a liar." "The weather is warm, because it is summer; it is summer, because the weather is warm."

These and other fallacies may be detected by a knowledge of Logic, and the perception and detection of them strengthens one in his faculty of Deductive Reasoning. The study of the Laws of the Syllogism, in Logic, will give to one a certain habitual sense of stating the terms of his argument according to these laws, which when acquired will be a long step in the direction of logical thinking, and the culture of the faculties of deductive reasoning.

In concluding this chapter, we wish to call your attention to a fact often overlooked by the majority of people. Halleck well expresses it as follows: "Belief is a mental state which might as well be classed under emotion as under thinking, for it combines both elements. Belief is a part inference from the known to the unknown, and part feeling and emotion." Others have gone so far as to say that the majority of people employ their intellects merely to prove to themselves and others that which they feel to be true, or wish to be true, rather than to ascertain what is actually true by logical methods. Others have said that "men do not require arguments to convince them; they want only excuses to justify them in their feelings, desires or actions." Cynical though this may seem, there is sufficient truth in it to warn one to guard against the tendency.

Jevons says, regarding the question of the culture of logical processes of thought: "Monsieur Jourdain, an amusing person in one of Moliere's plays, expressed much surprise on learning that he had been talking prose for more than forty years without knowing it. Ninety-nine people out of a hundred might be equally surprised on hearing that they had long been converting propositions, syllogizing, falling into paralogisms, framing hypotheses and making classifications with genera and species. If asked if they were logicians, they would probably answer, No. They would be partly right; for I believe that 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. It may be asked:—If we cannot help being logicians, why do we need logic books at all? The answer is that there are logicians, and logicians. All persons are logicians in some manner or degree; but unfortunately many people are bad ones and suffer harm in consequence. It is just the same in other matters. Even if we do not know the meaning of the name, we are all athletes in some manner or degree. No one can climb a tree or get over a gate without being more or less an athlete. Nevertheless, he who wishes to do these actions really well, to have a strong muscular frame and thereby to secure good health and personal safety, as far as possible, should learn athletic exercises."