Part 7 (1/2)
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 const.i.tutes 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 cla.s.ses, 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 a.s.suming 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 a.s.sumption of a general truth. Thus, from the a.s.sumption 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 a.s.sertion 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...o...b..t, 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 a.s.serting 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 a.s.sume 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 circ.u.mstances 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:
At.w.a.ter 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.”
At.w.a.ter 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 cla.s.s, and warrant a valid universal inductive conclusion.”
We now come to what is known as Hypothesis or Theory, which is an a.s.sumed 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 antic.i.p.atory 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 antic.i.p.ation 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 antic.i.p.atory 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 antic.i.p.ation; 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.”
Pa.s.sing 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 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.”
_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 a.n.a.lytical process, just as Inductive Reasoning is synthetical. It is a descending process, just as Inductive Reasoning is ascending.