The first error is the less common, for though occurring among all thinkers, it is comparatively infrequent among those who proceed with caution. It is, moreover, more easily discovered than the second. Consider the clas­si­fi­ca­tion of constructive methods into comparison, observation, and experiment. It is apparent that these methods overlap. We cannot compare without observing, much of our observation involves comparison, when we experiment we must of course observe the results obtained, and the results are usually always compared. All three methods could be classed under observation. It is well to remember, however, that the first clas­si­fi­ca­tion may be useful—even more so than one strictly logical, and that the nature of a subject will often make impracticable, divisions which do not overlap in some degree.

The second error—that of not making a clas­si­fi­ca­tion cover all the objects or phenomena it is supposed to cover—is not so easy to detect. It is one to which the greatest philosophers have been heir. Some of our Socialist friends say there are but two kinds of people: capitalists and laborers, “the people who live on others and the people who are lived on.” They overlook that class of farmers who own a little piece of land and do their own tilling. Even if they insist that such a class “is rapidly becoming extinct,” the fact remains that it is still with us and must be taken into account.

All clas­si­fi­ca­tions are made with a certain number of facts in mind, and fortunate is he who happens to have just the right facts. We cannot hold many facts in mind at once, and we often generalize upon thousands of things by taking a supposedly representative dozen. To avoid error all we can do is to keep constantly on the lookout for examples, especially those which apparently will not fit into our gen­er­al­i­za­tion. If they go in without straining anything, our clas­si­fi­ca­tion receives added warrant. But sometimes you will find that where you have three classes a new fact will necessitate a fourth, and that often it will overturn your whole beautiful structure.

There is another phase of thinking, which while chiefly cautionary, is also in part constructive. We have so often been warned to “avoid the treachery of words” and to “define all our terms” that a repetition of the advice seems unnecessary. But we cannot overlook the excellent counsel of Blaise Pascal. He urges that we not only define our terms, but that whenever we use them we mentally substitute the definition. However, this needs to be qualified. If every time we used a term we stopped to substitute its definition, our thought might be exact but would hardly move forward very rapidly. It will usually be sufficient simply to substitute the definition a few times, for after doing this we shall gradually come to know exactly what we mean by a term, and further substitution would merely waste time. Of course, all this need be applied only to terms new, technical or equivocal; or those used in a mooted proposition.

I have spoken of analogy as a constructive method. This, however, should be used only for sug­ges­tion, for it is most dangerous. Often we use an analogy and are quite unaware of it. Thus many social and political thinkers have called society an “organism,” and have proceeded to deal with it as if it were a large animal. They have thought not in terms of the actual phenomena under con­si­der­a­tion, but in terms of the analogy. In so far as the terms of the analogy were more concrete than those of the phenomena, their thinking has been made easier. But no analogy will ever hold good throughout, and consequently these thinkers have often fallen into error.

The quickest way to detect error in analogy is to carry it out as far as it will go—and further. Every analogy will break down somewhere. Any analogy if carried out far enough becomes absurd. We are most likely to err when we carry an analogy too far, but not to the point where the absurdity is apparent. Take the analogy employed in our first chapter, comparing thinking and a ship. For the sake of the image I shall make this a motor-boat. We might carry this out further. We might compare the effect on the mind of books and experience to the fuel used for the engine. The brain, transforming outward experience into thought, might be paralleled with a carburetor transforming fuel into usable form. An idea may be compared to a spark. All this is very fascinating. It may even lead to sug­ges­tions of real value. But it is bound soon or late to develop into the ludicrous. The analogy in question, however, does not need to be developed to be confuted. For unless a boat has a propeller and a rudder, its engine is useless. A mind is capable of attaining truth without even being aware of the existence of a science of thinking or of logic.

Another way to find whether an analogy is fallacious is to see whether you can discover a counter analogy. Surely this is the most effective practice in refuting analogy in argument. This suggests the case of the man who had a ticket from New York to Chicago, and tried to use it from Chicago to New York. The railroad refused to accept it, whereupon the man brought suit. The lawyer for the defendant, in the heat of the debate, said, “Why, a man might just as well pay for a barrel of potatoes and then demand a barrel of apples!” Whereupon the attorney for the plaintiff replied, “It would be rather like a grocer selling a man a barrel of potatoes and then trying to compel him to eat them from the top down, refusing to allow him to turn the barrel upside down and begin eating them from the bottom up.” It is best to avoid analogy except for purposes of sug­ges­tion, or as a rhetorical device for explaining an idea already arrived at by other means.

I have been forced to defend my advice to take as many viewpoints as possible, by pointing out that the conclusions obtained from these viewpoints might disagree; in fact would be almost sure to disagree. Of course, this disagreement might be avoided if we allowed the conclusions reached by one method or viewpoint to influence our conclusions in another. But if we do this we give our problem more shallow treatment, and we are not so sure of a result when we get it. When a mathematician adds a column of figures from the top down, he confirms by re-adding from the bottom up. He knows that if he added in the same manner the second time he would be liable to fall into the same errors. And in thinking, when we leave one method and take up another, we should try to forget entirely the first conclusion and begin on the problem as if we had never taken it up before. After we have taken up all the applicable methods, then, and then only, should we begin to compare conclusions.

Time forbids doing this with all problems. Time forbids even attacking all problems from different points of view. But there are some problems where this unquestionably ought to be done. The problem of whether or not char­ac­ter­is­tics acquired during the life time of one individual may be inherited by his offspring, if dealt with at all, is too important to be left to the a priori method alone. This problem asks whether the children of educated parents will necessarily be innately superior to the children of uneducated parents; it asks whether the man of today is superior to the ancient Greek, or even the present day savage; or, assuming that the negro race is inferior to the white race, it asks whether generations of education will bring it to the white race level or leave it unchanged; it asks whether the hope of improving the human race lies in education or eugenics. No question can be more important than this in its practical bearings. The answer to it will profoundly influence our opinions in education, psychology, ethics, economics, political science—even philosophy and metaphysics. The answer we obtain to this question from deductive reasoning, no matter how unanswerable or conclusive it may seem, should be checked up by nothing short of the most thoroughgoing experiment.

Unfortunately the experiments needed for this par­tic­u­lar question cannot be carried on by the layman. It is equally to be regretted that scientists have been none too thorough in carrying them out themselves. But we should remember that any result we arrive at should be subject to revision, and that if we take up this problem at all, we should at least make it our duty to read about and criticise all the experiments that come to our notice.