Thought-Culture or Practical Mental Training

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.”