Thus far we have con­sidered only pos­i­tive and con­struc­tive think­ing, and means for ob­tain­ing relevant sug­ges­tions. We have had almost nothing to do with cautions, means for avoiding fallacy and error, and means for testing the truth and value of sug­ges­tions. Most writers who have discussed thinking have dwelt so much on the negative aspect—so much on what we should not do—and have so slighted the question of what we should do, that I have perhaps been led to adopt this order, more from a feeling of revolt than because it is logically better. But I believe I have logic on my side. Constructive methods make thinking “go”; cautions steer it in the right path. An auto­mo­bile with­out a steer­ing gear is almost as useless as one without a motor. But an auto­mo­bile can go without being steered, whereas it cannot be steered unless it is going.

But while with automobiles we can clearly divide moving from steering, we cannot do this with thinking. The two processes are so inextricably bound up, that we cannot engage in one without engaging in the other; we cannot even speak of one without implying the other. I have divided them for convenience of exposition. But in the last chapter we were forced to deal slightly with cautions, and here we shall have to consider constructive methods to some extent.

A case in point is clas­si­fi­ca­tion. In taking this up from a constructive standpoint, I remarked that all clas­si­fi­ca­tions ought to be logical. But I did not say what I meant by logical, nor did I tell how a logical clas­si­fi­ca­tion could be secured. The two most prominent errors made in classifying are (1) not making clas­si­fi­ca­tions mutually exclusive, (2) not making them cover all the objects or phenomena supposed to be classified.

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.

A question has perhaps just occurred to the reader. If the deductive method is to be checked up by experiment, and the results of the experiment are always to be taken, why not experiment first, and omit theory altogether?

Leaving aside the fact that theory is the best guide for experiment—that were it not for theory and the problems and hypotheses that come out of it, we would not know the points we wanted to verify, and hence would experiment aimlessly—a more serious objection is that experiment is seldom if ever perfect, for it nearly always involves some unverified assumption. I have referred to empirical observation and experiment as two different methods. But the difference is mainly, if not solely, one of degree. If we experimented to find out whether acquired char­ac­ter­is­tics were inherited, it is obvious that our experiments would have to be confined to animals. If we found, let us say, that no acquired char­ac­ter­is­tic was ever transmitted to offspring, we could not say that this would be equally true of man, but would be justified in concluding only that the acquired char­ac­ter­is­tics of animals are not transmitted to descendants. Nay, we could not go even this far. We would have to confine ourselves to the statement that certain acquired char­ac­ter­is­tics of the few score animals we had experimented upon were not transmissible. But even this statement would involve assumption. We could say only that certain acquired char­ac­ter­is­tics of the few score animals we had experimented upon had not been transmitted in these par­tic­u­lar instances. We would have to limit ourselves to a bare statement of fact; we could draw no conclusion whatever. But if we had attacked this problem from the deductive standpoint, and had concluded that owing to certain conditions holding alike in all animals and in man, acquired char­ac­ter­is­tics could not possibly be transmitted, we would have sufficient ground for deriving from our experiments a broad gen­er­al­i­za­tion.

Experiment and deduction are not the only methods which can be checked up against each other. We can do likewise with the comparative and the experimental, the historical and the theoretical—in fact, all viewpoints applicable to any one problem.

When you encounter a question about which there is a controversy, and where the adherents of both sides nearly equal each other in number and in­tel­lec­tual status, you may be almost certain that each side has caught sight of some truth, but that neither has seen the whole truth; and you should endeavor to unite both sides by a broader and deeper solution. A classic philosophical example of this method is Herbert Spencer’s attempt to reconcile science and religion, and his effort to unite the “intuitional” and “experiential” schools of thought. The intuitionists maintained that the mind had from birth intuitions by which it knew certain truths in­de­pen­dently of experience. Such truths as the axiom that a straight line is the shortest distance between two points, or that it is morally wrong to do certain acts, were regarded as among these intuitions. The “empiricists” or “sensa­tion­alists,” on the other hand, maintained that all our knowledge—even of such a fact, for instance, as that two and two are four, where we cannot conceive otherwise—is learned solely from the individual’s experience, taken in its broadest sense. Herbert Spencer thought he recognized some truth in both these doctrines, and came forward with the theory that there are certain truths which are intuitions so far as the individual is concerned, but that these intuitions have been inherited from our ancestors, were originally built up through the ages, and represent the accumulated experience of the race. Whatever may be thought of Spencer’s success in this case, the value of the method itself is undoubted. It was frequently used by Kant, Hegel, Fichte and other German philosophers.

I have remarked that it is almost possible to sum up the entire process of thinking as the occurrence of sug­ges­tions for the solution of difficulties and the testing out of those sug­ges­tions. The constructive methods discussed were called means for making good sug­ges­tions occur to us. From this standpoint the cautions with which we have just been dealing may be considered as tests of sug­ges­tions.

Let us refer back to the analysis of thinking given in the case of the man who discovered footprints on the beach. Even there, in order to give any adequate idea of his thought process, I was obliged to show that for various reasons he rejected certain suggested solutions. But this negative method could be more fully developed. Because the man rejected a certain solution, it does not follow that it was necessarily wrong. Suppose the final sug­ges­tion—that the unknown had been on the island all the time—were to have been tested out, and that certain further facts were discovered which tended to disprove it; the man might find it necessary to look for still another solution. But suppose this were not forthcoming, suppose that all the possibilities had been exhausted. It would be necessary to return to some of the original sug­ges­tions. He would have to see whether an error had been made in testing them. In rejecting the sug­ges­tion of a small boat he may have overestimated the distance of this island from other land. He may have underestimated the difficulties that a man in a small boat is capable of surmounting. In rejecting the sup­po­si­tion of a ship, he may have erred in his judgment of the time the footprints had been on the beach, or of the time it would take a large vessel to get out of sight.

What is essential is that all sug­ges­tions be tested out, either by memory, observation or experiment, in all their implications, and that the tendency be resisted to accept the first solution that suggests itself. For the uncritical thinker will always jump at the first sug­ges­tion, unless an objection actually forces itself into view. Remaining in a state of doubt is unpleasant. The longer the doubt remains the more unpleasant it becomes. But the man who is willing to accept this unpleasantness, the man who is willing carefully to observe, or experiment if need be, to test the validity of his sug­ges­tions, will finally arrive at a solution much deeper, and one which will give him far more satisfaction, than the superficial answer obtained by the man of careless habits of thought.

Thomas A. Edison says he always rejects an easy solution of any problem and looks for something difficult. But the inventor has one great advantage over any other kind of thinker. He can test his conclusion in a tangible way. If his device works, his thinking was right; if his device doesn’t work, his thinking was wrong. But the philosopher, the scientist, the social reformer, has no such satisfactory test. His only satisfaction is the feeling that his results harmonize with all his experience. The more critical he has been in arriving at those results, the more deep and permanent will be that feeling, the more valuable will be his thoughts to himself and to the world....

Even in the first chapter I intimated that logic would constitute a part of the science of thinking. I intimated, moreover, that it would constitute almost the whole of what may be called the negative side of thinking—those rules which serve to steer thought aright. Though cautionary, the advice given in this chapter is not usually given in books on logic. But though I cannot overemphasize the importance of a knowledge of logic, I cannot deal with it here. The science can receive justice only in a book devoted entirely to it.

If he has not already done so the would-be thinker should study a work on logic, for unless the present book is supplemented by some treatise on that science it cannot be regarded as complete.

In order not to confuse the reader I shall recommend only one book. In order to encourage him I shall recom­mend a small book, one not so deep as to be in­com­pre­hen­si­ble or re­pulsive to the beginner, but at the same time one which is recognized as a standard treatise:—Elementary Lessons in Logic, by Stanley Jevons.