XVII
THINKING AND KNOWING

One morning a teacher was awakened by a noise, the like of which he had never heard and hopes never to hear again. It was unlike anything in his former experience. Soon he began to distinguish the hissing of steam and the moaning of men, but the cause was still a mystery. Later, he learned that the blast furnace in the neighborhood had exploded, and that several men were killed and others had been seriously injured by the explosion.

The cause of the noise could not be inferred, because there was nothing in his former experience with which it could be compared. The escaping steam and the voices of the suffering workmen were recognized because they could be interpreted in the light of what he had seen and heard before. In order that any one may derive definite knowledge from sense-impressions, there must be something in past experience to give meaning to the new experience.

Observation that issues in knowing is coupled with a process of thought in which the new perception is linked to the ideas which the mind brings to the perception. In other words, observation always involves the element of thinking; without thinking, sense-impressions cannot give us knowledge.

Knowing is impossible without thinking, and yet not all thinking gives ripe to knowing. What is the relation between the two?

Knowledge has been defined as firm belief in what is true on sufficient ground. The explanation of this definition which Locke gives is well known to every student of philosophy. “If any one is in doubt respecting one of Euclid’s demonstrations, he cannot be said to know the proposition proved by it; if again he is fully convinced of anything that is not true, he is mistaken in supposing himself to know it; lastly, if two persons are each fully confident, one that the moon is inhabited, and the other that it is not (though one of these opinions must be true), neither of them could properly be said to know the truth, since he cannot have sufficient proof of it.”[46]

The foregoing definition consists of three parts,—1, firm belief; 2, in what is true; 3, on sufficient ground. In common parlance, belief is distinguished from knowledge, the latter implying a higher degree of assurance than the former. In some treatises on psychology belief denotes all forms of assent, including the highest possible certainty and conviction. The expression firm belief excludes the element of doubt from knowledge.

Truth, according to the etymology of the word, signifies that which the mind trows or believes to be fact or reality. It has its source in God, whilst knowledge proceeds from man. To be true, a proposition must be in exact accordance with what is or has been or shall be. Truth exists apart from the cognitions of the human mind. It would continue to exist if the mind of man were blotted out of existence, and there was truth long before the intelligence of man was called into being. The aim of thinking is to find out and lay hold of the truth. Thinking in which truth and error are mixed may have value as partial knowledge and as a stepping-stone to fuller knowledge. Knowledge becomes full and complete only in so far as it contains the truth, the whole truth, and nothing but the truth.

Full knowledge implies a basis upon which it may rest. There may be sufficient ground for the firm belief which constitutes the essence of knowledge even when the truth cognized is incapable of full and complete demonstration.

It is natural for a child to believe. The statements of others are accepted as true without question, so long as the child has not been deceived by others. Hence many teachers have assumed that their chief function is to ask the reason why, so that belief in what is true may be based upon sufficient ground, and that nothing shall be accepted as true until it is proved. This was one of the erroneous views under which Pestalozzi labored. He justified the undue attention paid to mathematics in his school on the ground that he wished his pupils to believe nothing which cannot be demonstrated as clearly as two and two make four. Whereupon PÈre Girard replied, “In that case, if I had thirty sons I would not intrust one of them to you; for it would be impossible for you to demonstrate to him, as you can that two and two make four, that I am his father and that I have a right to his obedience.”[47]

The progress of a pupil may be hindered by too much emphasis upon the ground of knowledge. The human mind cannot make an exhaustive study of very many things. Exhaustion is a term applied by logicians to a method of proof in which “all the arguments tending to an opposite conclusion are brought forward, discussed, and proved untenable or absurd, thus leaving the original proposition established by the exclusion of every alternate.” Speaking positively, we may say that exhaustive study of a subject explores it in all its bearings and relations as well as in its nature and essence. In every subject the known is bounded by the unknown; new methods of preparation and investigation constantly reveal novelties in whole classes of objects which it was supposed had been studied exhaustively. The specialist seeks to know all that has been brought to light in his field of research, and to push out the limits of knowledge beyond the goal reached by his predecessors. The thoroughness of the specialist is not required in elementary instruction. The writer knows of a teacher who for an entire term kept a class of boys at work upon highest common factor and least common multiple on the plea that they did not thoroughly understand these subjects. No better plan of disgusting boys with arithmetic and algebra could have been devised. Thorough knowledge of these two subjects involves reasoning and demonstrations more difficult to grasp than half the theorems in Euclid. Instead of aiming at exhaustive treatment, the true teacher is satisfied with knowledge adequate for the subsequent work of the course. If the pupil has reached the stage where he can appreciate the reason why, it may be (though it is not always) wise to raise this question, and to insist on a comprehension of the proof. Very often the mind has enough to do in trying to see how; the question why then interferes with the mastery of the mechanical operations. Let any adult take up a system of arithmetic with which he is unfamiliar, say the arithmetic based on counting by fives, or by twelves, or by thirties (each of the last two, mathematically speaking, better than the arithmetic based on tens), he will soon find it is work enough at first for his intellect to perform the operations of adding, subtracting, multiplying, and dividing without reference to the philosophic explanations which exhaustive study would require at every step in the operations.

Descartes applied several of the technical terms of optics to the science of mind, and in this he has been followed by Locke, Leibnitz, and others. An object seen at a great distance or in insufficient light looks obscure; as the eye approaches, or as the dawn increases, the object, as a whole, becomes clear enough to be distinguished from other objects, although its constituent parts are still confused. Increasing light or a nearer approach finally enables us to discern the parts, and the vision of the object grows distinct. Clear vision occurs where the object, as a whole, can be recognized; distinct vision occurs when the parts of the object seen can be recognized. In like manner ideas are said to be clear as distinguished from obscure, when they are discerned in outline; they are distinct (opposed to indistinct or confused) when they are discerned in their elements or constituent parts. Distinct mental vision requires analytic and synthetic thinking.

Of many objects the mind needs only clear knowledge for ordinary purposes. One may distinguish two brothers by the total impression of each which he carries in his mind, and yet be totally unable to tell any specific marks by which he knows the one from the other. The painter, on the other hand, cannot be satisfied with this total impression; he studies the individual features until he has a distinct impression of their likenesses and differences.

Of the map of one’s own country it pays to know the States and Territorial divisions. Of one’s State, a knowledge of the counties, and of one’s county, a knowledge of the townships may be helpful. For specific vocations more minute knowledge may be desirable. Each individual mind can well afford to stop with a measure of geographical knowledge that is adequate for the duties of his vocation and the purposes of his reading of books and newspapers.

Very little of our knowledge of geography is based upon experience; most of it rests upon testimony. The eye at a glance may take in the outlines of an island of the Susquehanna river. The fact that Great Britain is an island rests upon the testimony of maps; our belief is based upon what we have always heard and read, and is further strengthened by the absence of testimony to the contrary. If the fact had ever been questioned, the mind might hold its judgment in suspense until sufficient ground was found to warrant a conclusion.

When the knowledge which a pupil has is to be deepened or made more distinct a series of well-chosen questions may beget the required thinking. For instance, let us take the case of a pupil who has reached the stage where his knowledge of the properties of the parts of speech should be made more complete. Let the teacher ask for the difference between a pencil and a part of speech, between a noun and a name, between gender and sex, between number in grammar and number in arithmetic, between person in grammar and a person like the President of the United States, between case in grammar and a case in division of fractions, between tense and time, between mode and manner, between action and a verb, between the object of an action and the object of a verb. Comparison will soon show the inaccuracy of the statement that the direct object of an action is in the accusative case; and the learner will see that case is a property of nouns, not of objects, and cannot be predicated of the object of an action, but of the word which denotes the object of the action, which word may be either in the nominative or the accusative case as the verb is either in the passive or active voice. Comparison will lead the pupil to see clearly that gender is a property of nouns, whereas sex or the absence of sex is predicated of that for which nouns stand. Comparison will serve to bring out the distinction between number in grammar as a property of nouns indicating one or more than one, and numbers in arithmetic, of which there are as many as there are units or collections of units in the universe. Thinking by comparison will lead to the detection of similarities and differences, to discrimination, combination, and generalization, and through these to more distinct and more adequate knowledge.

Questions which draw attention to likenesses and differences, to causal relations and logical sequences, stimulate analysis and comparison; the resulting judgments clarify the stream of thought and push the boundary of knowledge into the regions of the hitherto unknown.

The greatest minds when working under the influence of a false theory fail to arrive at truth. Socrates rejected the view of Anaxagoras that the sun is a fire, because we can look at a fire, but not at the sun, because plants grow by sunshine and are killed by fire, and because a stone heated in fire is not luminous, but soon cools, whereas the sun always remains equally hot and luminous. Newton did more than all other thinkers combined to make astronomy a science; his discoveries in physics and mathematics rank him among the greatest investigators the world has thus far known; yet he spent many nights trying to find the method by which the baser metals could be transmuted into silver and gold; his researches as an alchemist led to nothing, because he was working under the spell of a false theory.[48]

Faraday acknowledged that he was often compelled to give up his preconceived notions, and in some cases his failures are almost as instructive as his discoveries. It was characteristic of him to hold to his theories until he proved them either true or false, and he was ever ready to reject any hypothesis as soon as he found it inconsistent with the laws of nature. Newton was willing to suspend judgment for years upon his theory of gravitation, until more accurate measurements of the earth’s size and the moon’s distance showed his theory and calculations to be right. Socrates advised his followers to quit the study of astronomy, probably because he felt that in his time the data were not sufficient to warrant definite conclusions. Hosts of instances can be cited showing that the thinking of the strongest intellects does not issue in knowing when it is based upon or biassed by a wrong working hypothesis. And yet it must be confessed that wrong hypotheses may lead to valuable negative results, as in the case of Kepler’s investigations, each exploded theory making room for the construction of a theory more in accordance with the facts. The superiority of men of genius lies in their love of truth and fidelity to fact; in the facility with which they construct theories to account for observed phenomena; in the patience with which they test theory by fact, and in the readiness with which they reject every hypothesis as soon as it is found to be in irreconcilable conflict with well-established facts. The average life of a theory in science is said to be only ten years. The average would be lower still if all rejected theories had been put into books. The men possessed of a truly scientific spirit differ from ordinary men not only in the painstaking accuracy of their observations and in the surprising fertility with which they frame theories, but also in the habit of verifying every hypothesis until there is sufficient ground to establish its truth and to receive it as an addition to the sum total of human knowledge.

The common people are quite as ready to frame theories as the scientists and philosophers. It would be well if they were equally patient in testing their theories and in verifying their suppositions. The human mind cannot help generalizing. The moment a child uses a common noun it begins to classify. Its tendency to pull things to pieces and to put them together again are exhibitions of the mind’s tendency to treat everything by analysis and synthesis. Purpose and design, cause and effect early show themselves in the thinking of children. The teacher need but guide these activities and give the mind the proper material to work upon; the result cannot be doubtful if the mind which plays upon the learner’s mind has been trained to operate according to the laws of thought and the principles which must guide in the discovery of the truth.

Doubt is sometimes the prerequisite of knowledge. To raise a doubt in the mind of a growing youth may cause him to think. It may cause him to explore the grounds of his knowledge, to ascertain the rational basis upon which his beliefs rest, and to reject such as were of the nature of prejudice or of tradition with no sufficient warrant for acceptance. Rational belief is far superior to blind faith.

When the doubt is raised in regard to the verities of one’s religious faith there is grave danger of landing in scepticism or infidelity. What is truth? may be asked in the spirit of Pilate, who turned away from the Great Teacher with a despairing sneer and without waiting for a reply. Pilate had trifled with his own conscience until he could no longer discern truth and righteousness. Some men need better hearts in order that they may think and know the highest truth. The hope can be held out that whenever the truth is earnestly sought by the human heart the soul will ultimately be guided into a knowledge of the truth. To disturb the grounds upon which rest the principles of morality and religion is a dangerous experiment, especially in the case of immature minds. The flood of doubt may sweep away the solid foundations of a pupil’s moral nature and leave him a wreck upon the quicksands of vice or upon the rock of scepticism.

It is the nature of the child to believe, to cherish faith in what others tell him and in what the world presents to his vision. To disturb the fervor and strength of this trust before the understanding is ripe for fuller knowledge may result in life-long injury. The child’s faith in fairyland, in Santa-Claus, should, of course, be kept from becoming a source of terror. The stories of ghosts, spooks, and hobgoblins sometimes employed in the nursery to influence conduct may cause fears, terrors, and horrors from which it is well to emancipate the child as speedily as possible through the light of clearer knowledge.

Better than doubt as a stimulus to thought is the desire to know. St. Augustine was on fire to know. The teacher who kindles and keeps burning this fire in the soul of the pupil has supplied the most powerful incentive to thought; for without thinking knowledge is impossible of attainment.

As we may start our wood flaming by coals hot from another’s fire, so we may kindle a burning desire for knowledge by bringing the mind in contact with minds that are all aglow with the desire to know. A burning fire may soon exhaust its fuel if left to itself. The teacher supplies the fuel, fans the flame, directs its activity for well-defined purposes. Here the analogy breaks. Instead of smoke and ashes we want living products as the result of knowing. As thinking leads to knowing, so knowing should give rise to further thinking. Nowhere is the teacher’s function of guiding more indispensably necessary than in the interplay of these two activities. While the learner is engrossed in the pursuit of knowledge, the teacher is watching the process and the results. He is not satisfied unless the activity of thinking and knowing ends in full cognition. It has been well said that a dog knows his master, but does not cognize him; that to cognize means to refer a perception to an object by means of a conception. The objects of thought must be sorted and arranged in groups; the particular notion must take its place in the general concept; the materials upon which the mind acts must be assimilated and organized into a unity, showing how each has its origin and how it stands in living relation to every other part of the organic whole; otherwise thinking cannot lead to complete cognition.

The incident at the beginning of this chapter shows that some preparation is necessary to interpret sense-impressions and organize the materials of thought for the purpose of cognition. The degree of preparation determines how far the instruction at a given time shall aim to go. To get a clearer idea of the thing to be known may exhaust the learner’s strength. If so, the presentation should stop at that point. But as soon as his power and interest are equal to the task he should be led to analyze the object of thought so as to cognize the constituent elements, the essential attributes, a process whereby he will arrive at distinct knowledge. It may be advisable before dropping the inquiry to institute comparisons between objects of the same class, for the purpose of calling attention to differences and likenesses and evolving general concepts or universal propositions. For many thinkers these are the goal of thinking. If they can resolve the universe to a few simple generalizations, their minds are satisfied. Nothing more barren can well be imagined or conceived.

Cognition is not complete until the knowledge has been or can be applied. At times there may be a division of labor and glory in the discovery and application of truth. The discoveries of Professor Henry which made the electric telegraph possible involved thinking quite as valuable as the invention of Professor Morse. The achievement of Cyrus W. Field in laying the Atlantic cable involved thinking quite as important as the researches and experiments of Lord Kelvin which made the cable successful. Interesting examples of such division of labor in thinking cannot justify neglect of the applications after a general truth has been evolved and stated.

The instruction may sometimes begin with a statement of applications, in order to prepare the mind for the thinking that issues in knowing. The applications of color in the railway service, in navigation, and in the arts will create an interest in the study of color without which the presentation of the fundamental ideas may be in vain. Several lecturers have admitted that they failed, in the presentation of color lessons, to hold the attention of their pupil-teachers until they excited an interest in color by indicating important applications. This statement of applications by way of preparation must, however, not be confounded with the applications which should follow the framing of general propositions and the cognition of general truths.

The hypotheses of the scientist correspond to the general truths and principles which instruction always aims to reach. In all except the most advanced investigations, the pupil should work under the guidance of principles that have risen above the hypothetical stage. He should think under the inspiration of well-established truths. He should master the known in his chosen field before he seeks to enlarge the boundaries of human knowledge by invasions into the realm of the unknown. Sad is the spectacle of a talented mind wasting its strength in fruitless efforts to rediscover what is already well established.

The formulation of truths in mathematical studies is sometimes carried to extremes. The pupil may at times be allowed to work under the guidance of principles which he knows by implication, and which he has never had occasion to formulate in explicit statements. The formulation of the principles of algebra can be carried into the statement of hundreds of general propositions. If the pupil is asked to fix all these in the crystallized or specific form given in the text-book, it may result in a prodigious waste of time. Furthermore, the effort to follow invariably any formal steps in the order of instruction is apt to make the instruction unduly formal and lifeless. No thinker can afford to think in the set forms of the syllogism while evolving a train of thought. Conscious conformity to these hinders progress in the spontaneous evolution of germinal ideas. In like manner, although the student of pedagogy may find a guide in the rules and principles of his science while preparing the subject-matter of a lesson, yet, in giving the instruction, the truth must be the object of chief regard, the centre of attention in consciousness. Constant thought of prescribed steps makes the teaching stiff and formal, and dissipates the joyous interest which accompanies free and spontaneous thinking. Formal rules are very often like hobbles on the feet of the horse. They impede his speed, rob him of half his power and energy, and spoil his enjoyment of the open field. Bearing this in mind, the young teacher will perhaps not be harmed by the advice that in his teaching he should ever seek to lead the learner to clear and distinct perception of likenesses and differences in the subject-matter of each and every lesson. The newer methods of teaching a beginner to read, wisely draw attention to the points of similarity and difference in the shapes and sounds of the letters of the alphabet. They even go to the extreme of comparing sounds with the noises of animals, with which the child in the larger cities is totally unfamiliar. This error is not half so bad as the opposite extreme. Very much of the bad teaching by which the schools are afflicted arises from the assumption that the learner sees the points of agreement and difference which are so very obvious to the mature mind of the teacher. The consequence is mental confusion and loss of the joy of definite thinking. The detection of likeness in objects having many points of diversity gives the mind an agreeable surprise. This emotion is an element in the pleasure afforded by the various forms of wit, metaphor, and allegory. Professor Bain has shown how greatly progress in science and art is indebted to the discovery of similarity in the midst of great diversity.[49] Much of the child’s progress in knowledge must be ascribed to the same principle. Children notice points of similarity that often escape older persons. On seeing the picture of a tiger, they call it a cat. A mother who showed her little daughter, just beginning to talk, the caricature of a man prominent in the public eye, was surprised to hear the child exclaim, “Papa.” It was the child’s word for man, as she afterwards discovered. Where she saw contrast, the child only noticed the points of similarity between one man and another. As the power of discrimination advances, the mind pays more attention to points of difference than to points of likeness. Indistinguishableness gives way to clear and distinct knowledge. With the further growth of intelligence the mind seeks the hidden resemblances in objects far removed from one another in space and time, or by surface appearances. At first sight the bat seems like a bird, because it can fly. Scientific discrimination assigns it to the class of mammals. The identification of the lightning in the clouds with the sparks of the electric machine gave Franklin world-wide reputation as a philosopher. The identification of the force which causes bodies to fall to the earth with the force which holds the moon in its orbit, and with the kind of force by which the sun attracts the bodies of the solar system, has been justly called the greatest example of the power to detect likeness in the midst of diversity. The power of detecting similarity in diversity should be appealed to whenever it is helpful either for purposes of illustration or discovery. Algebra is shorn of half its difficulty as soon as the learner is led to see that the operations in multiplication, division, involution and evolution of monomials turn on signs, coefficients, and exponents. Let him grasp the thought that the words add, subtract, multiply, and divide respectively express the law of exponents in the four operations above named; and he will not only escape the perplexities of the average student in the more difficult operations of ordinary algebra, but he will also see at a glance the beautiful truth which underlies the manipulation of logarithms.

Thinking that ripens in knowing involves comparison, discrimination, and formation of judgments. Through the detection of likeness and unlikeness in objects and their relations, judgments are formed, inferences are made, and conclusions are drawn, which mark the transition from thinking to knowing. Discrimination, identification, judgment, reasoning, definition, division, and classification mark the stages through which the mind passes in thinking things, their relations, more especially their causes, effects, laws, and ends. Analysis and synthesis, induction and deduction, are the processes by which the intellect explores the content and extent of concepts, and passes to general principles and truths, and to their applications in thought and action. As processes of mental activity, these are discussed in detail by the psychologist. The laws of thought to which they must conform in order to be correct are set forth in treatises on logic. It would be a mistake to underestimate the value of a knowledge of logic and psychology; but neither of them can supply the place and function of the living teacher. He who would learn to think in some special line of research should go to a master of that specialty, learn of him what is well established in the chosen field of study, imbibe his methods of work, think his thoughts, catch his spirit, and follow his advice until the hour for independent investigation comes. Great is the tonic effect of a university atmosphere; but greater still is the bracing influence of the atmosphere created by a specialist who is both a master in his department and a master in the art of teaching. The choice of a teacher is of more account than the choice of a university, either at home or abroad.

Thinking is not the whole of knowing. Feeling and willing play an important part in thinking and knowing. Words like heretic, sceptic, and sophist have a history which shows the distrust of mankind in pure intellectual effort. It would be hard to find a better commentary on the effect of a perverse heart upon the operations of the intellect than the following paragraph from Max MÜller, although it was penned for a purpose entirely different from the use here made of it.

“No title could have been more honorable at first than was that of Sophistes. It was applied to the greatest thinkers, such as Socrates and Plato; nay, it was not considered irreverent to apply it to the Creator of the Universe. Afterwards it sank in value because applied to one who cared neither for truth nor for wisdom, but only for victory, till to be called a sophist became almost an insult. Again, what name could have been more creditable in its original acceptation than that of sceptic? It meant thoughtful, reflective, and was a name given to philosophers who carefully looked at all the bearings of a case before they ventured to pronounce a positive opinion. And now a sceptic is almost a term of reproach, very much like heretic,—a word which likewise began by conveying what was most honorable, a power to choose between right and wrong, till it was stamped with the meaning of choosing from sheer perversity what the majority holds to be wrong.”[50]

There are realms in which thought cannot beget knowledge of the truth until there is a radical change in the wishes and desires of the heart, in the choice and alms of the will, in the movings of the inmost depths of the soul.