Starting in too high a key.
There is another limitation to the kind of public speaking which partakes of the nature of oratory. The idea which the speaker seeks to have realized in the vote, or verdict, or conduct of others, must be carried back to the necessary ideas of the hearer. The full discussion of this peculiarity in the stream of thought belongs to treatises on rhetoric. Such a discussion can be found in Theremin’s Rhetoric, translated by Shedd. Suffice it to say that the recognition of this principle makes the speaker a more thoughtful man. It causes him to rely for the effect he seeks to produce upon solid and sterling qualities rather than showy rhetoric. It tends to makethe stream of thought flow deeper, fuller, yet clearer and with more power. Any interference with the stream of thought while the speaker is before the audience may be disastrous. The crying of a child, or an outburst of feeling in the audience, or some other mishap may disconcert his mind. Legouvé tells how the world-renowned advocate, Berryer, lost a very good cause by unconsciously starting his speech in too high a key. “His temples soon felt the unusual fatigue of the larynx; from the temples it passed to the brain; the strain being too great, the brain gave way; the thought became confused, and the language disarranged and indistinct.” He broke down in open court because he never thought of descending from the lofty perch on which his voice started at the beginning of his plea. Legouvé claims, and the experience of many speakers confirms the claim, that the abuse of the high notes has not infrequently affected injuriously the orator’s very flow of thought.
The three generals.
Three generals made stump speeches on a joint trip during the last Presidential campaign. One day the name of the candidate of the other great political party was mentioned, when there was a perfect storm of applause in the gallery. A second reference elicited similar applause, and the disconcerted general, who had bravely faced the enemy on the battle-field, took his seat. The next general, walking on a crutch, came forward, and requested that all who had been sent to disturb the meeting should rise. Ho one moved. He exclaimed, “There are some cowards here.” Then he asked that all who had come to listen and learn should rise. Everybody rose. He exclaimed, “There are some liars here.” Next he announced that any one attempting to disturb the meeting would be pitched out of doors, the general on the crutch declaring he would lead the attack.Soon a man arose as if to ask a question. Whereupon a big burly policeman threw the fellow out, and there was no further outside interference with the stream of thought in the mind of speaker or listeners. The man on the platform always has the advantage over disturbers in the audience, provided he is master of his faculties, full of resources, and quick at repartee.
The schools of France.
The reading lesson.
The schools of France have been quoted to show the uselessness of exercises in oral reading. As in other things, so in school matters, distance lends enchantment to the view. Legouvé, in his lectures on the “Art of Reading,” mentions with approval that in the great Republic of North America reading aloud is justly considered one of the very first elements of a child’s education, whilst in France, reading aloud does not reach even the sorry dignity of a diverting art, but is regarded as a curiosity, a luxury, often something hardly better than a pretension.[43]This was written several decades ago, and may not be just to the French nation at this time. The value of oral reading depends upon the way in which it is done. If it amounts to no more than calling words and parrot-like imitation of the teacher’s manner of reading, the exercise is a waste of time. The mastery of the new words and of the thought embodied should precede the attempt to read a lesson aloud. The mastery of the words involves ability to recognize them at sight, to pronounce them with fluency and ease, and to spell them by letter and by sound. It implies both a knowledge of their meaning and ability to use them in a sentence.An average series of readers has a vocabulary of five thousand words. The meaning of all these words may be known at sight, but ability to use them by tongue or pen is quite another thing, the vocabulary of most persons being not much in excess of a thousand words. The thought can be mastered by an exercise in silent reading, followed by the oral and written reproduction of the lesson. The mastery of the thought is a condition of proper vocal utterance.
Acting and reading.
Reading and talking.
There is a difference between acting and reading. The actor endeavors to speak and act after the exact manner of the character whom he impersonates. The reader aims to suggest the thought instead of imitating the original actors. An actor will go through the motion of stabbing or shooting an enemy; the reader simply aims to suggest the thought of what was done. Exercises in breathing, gesture, tone, pitch, cadence, voice may be needed for the sake of correcting defects; nevertheless, everything connected with oral reading should turn on and culminate in the stream of thought. If anything else is made the object of chief regard, the main purpose of oral reading is lost. It furnishes an excellent test by means of which the teacher can determine whether the pupil understands what he reads or is merely calling words after the manner of a parrot. To correct the unnatural tones acquired in the school-room, the pupil is wisely exhorted to read as he would talk. In the effort to develop a style of reading exactly like talking, some teachers ruin their natural way of talking and reading. In conversation, they talk as if they were trying to read. While reading, they seem to be trying to talk. The human voice is so made that it puts the quotation marks to selections recited from memory and to sentences read from a manuscript or book. As a rule, a person canread best what he himself has written; yet his voice tells whether his sentences and thoughts are framed and evolved at the moment of delivery, or taken from a manuscript prepared beforehand. As a matter of fact, no one can read as he talks or speaks. A blindfolded listener could tell when Spurgeon was reading or speaking. The same was true of Charles Sumner, and of every other great speaker America has produced.
Abiding thoughts.
To think the best thoughts of the best men is the privilege of him who can read. To plant these thoughts in other minds by reading aloud is a noble achievement. To give in speech something from our own resources that others shall treasure is nobler still, because it links our life with the creative workers of the world. But noblest of all is it to write what shall be read by our own and future generations, in our own and other lands, as a source of light and life, of uplift and enjoyment. The worst punishment that can befall a human being is to be cut off from participation in the movement of the race towards greater well-being and perfection. One naturally desires to employ his gifts and powers for the benefit of mankind. The stream of thought determines what we shall accomplish. If others are to be benefited by our thinking, they must think our thoughts. The stream of our thought must carry ideas of interest and value to them, ideas they will care to get and keep. If our thinking is busy with things of transient interest, transient will be our influence over others. If our thought is to abide, it must deal with verities of eternal moment to humanity, with the works of Him who made the heavens and the earth, with the truth of Him who is “the same yesterday, to-day, and forever.”
“What we want is not the example of Democritus, who put out his eyes that, ceasing to read, he might think the more; or the example of Pythagoras, who devoted his evenings to solemn reflections on the events of the day. We want men and women of all-round activities who will set apart an hour for thought’s own sake, and thus fulfil the exhortation of a wise man whose practice it was to ‘sort his thoughts and label them.’”T. S. Knowlson.“People read a great deal more than they used to do,—there is more to be read,—but they think less. The chief danger of to-day is that of intellectual apathy. Life is so complex, the struggle for existence is so keen, and pleasures of various kinds so cheap and abundant, that men and women seem to live entirely on the surface of things. What we need is a call to independent thought.”Ibid.
“What we want is not the example of Democritus, who put out his eyes that, ceasing to read, he might think the more; or the example of Pythagoras, who devoted his evenings to solemn reflections on the events of the day. We want men and women of all-round activities who will set apart an hour for thought’s own sake, and thus fulfil the exhortation of a wise man whose practice it was to ‘sort his thoughts and label them.’”
T. S. Knowlson.
“People read a great deal more than they used to do,—there is more to be read,—but they think less. The chief danger of to-day is that of intellectual apathy. Life is so complex, the struggle for existence is so keen, and pleasures of various kinds so cheap and abundant, that men and women seem to live entirely on the surface of things. What we need is a call to independent thought.”
Ibid.
Equivocal terms.
The termthinking.
Kinds of thinking.
As was pointed out in the first chapter, the wordthinkinghas several meanings. One can hardly write or speak on education without using the word in more senses than one, and it is not always convenient to break the line of thought or discussion by indicating with a definition the meaning intended. This is a violation of Pascal’s rule, that no terms in the least obscure or equivocal shall be used without defining them. Pascal possessed one of the most remarkable intellects the world has ever known. His style has been described as a garment of light. Few thinkers have attained, to an equal degree, clearness of expression and perfect grasp of the truth. Nowhere are these qualities more essential than in lectures and treatises on teaching. It is a misfortune that so useful a word asthinkingshould ever be ambiguous. The use of equivocal terms leads to misunderstandings in theory and faults in practice. The advantage of technical terms lies in the fact that after they have been clearly defined they can always be used in the same sense. The disadvantage in the use of technical terms is that they convey no meaning to minds unfamiliar with the terminology of the specific science to which they belong. Hence the best thinkers cannot escape the necessity of employing words in current use to convey their thoughts. As soon as words pass into common parlance they acquire a variety of meanings and of shades of meaning. Thethought of a people is always more or less in advance of their vocabulary; the same word must be used in several meanings, because no other term equally simple and convenient can serve as a substitute. No one, for instance, can write or speak in the English language without using the wordisin both its figurative and its literal sense. The connection must show what signification is intended. The same remark applies to the wordthinking. The connection must show whether it is used in the colloquial sense of guessing, or in the logical sense of a comparison of two ideas through their relation to a third, or in the broader sense of imaging, reflecting, and reacting upon what one reads or hears, or in a still broader sense, to designate any form of mental activity. Since the popular mind employs the word as a general term to cover the entire intellectual life, it is convenient to specify kinds of thinking by the use of adjectives like independent, loose, continuous, organic, technical, scientific, and other qualifying phrases. Inasmuch as these distinctions are made for the purpose of characterizing differences observed in the thought-processes of the maturer life for which our pupils are to be trained, it is helpful to glance at them for the purpose of seeing the bearing of what we do at school upon habits of thought beyond the school.
The independent thinker.
What is meant by an independent thinker? Evidently one who is not indebted to others for the inferences which he draws or the conclusions at which he arrives. Many practices at school are subversive of habits of independent thinking. The assignment of lessons of such length and difficulty that the weaker pupils must rely upon their stronger classmates for help, or resort to “coaches, keys, and ponies” for assistance, makes them helpless instead of self-reliant, and cultivates the memory at the expense of the understanding.The lessons should be graded so as to beget the sense of mastery. Every difficulty that is overcome by a pupil’s own efforts tends to develop in him an ambition to conquer other difficulties. Few, if any, joys can be compared with the ecstatic joy of victory. Moreover, it should be the aim of the teacher to beget in the pupil a love of truth more potent and profound than reverence for a favorite authority. On the contrary, the feeling of independence and the desire of distinction by differing from other people may grow into a passion. This seldom does much harm in the case of an editor or a professor. If you give either of them leave to criticise and to print, he is well satisfied. If he is elected to a board of managers or the national assembly, his critical faculty and his fondness for finding fault and thinking differently from other people may make him a hinderance to the leaders, who must get things done, or cause him to stand apart, like Ewald, in the German Reichstag, as a one-man party, whose views must be ignored on all questions requiring prompt action or immediate decision. To counteract this tendency in a youth of strong personality, it is difficult to devise anything better than the moulding supremacy of class-spirit, the chastening influence of a contest in the literary society, and the relentless lessons which a boy gets on the play-ground when he will not play because the game does not go his way. Independence of thought in the quest of truth, on the one hand, and concert of action for the public good, on the other, are two of the most useful lessons to be learned at school. At this point there is room for a kind of child-study apart from a syllabus of set questions, and leading to results which cannot be tabulated in statistics or averages. The average in such cases is untrue as a guide, and may be utterly subversive of correct habits of thinking, or the correct method of dealing with the individual. Togive enough optional or specific work for the brightest, and not too much general or required work for the slowest, is an ideal hard to realize in the assignment of work, and yet of supreme importance in the endeavor to develop habits of independent thinking.
Independent thinking and popular government.
There is great need for independent thinking under a system of popular government, especially on the part of those who exercise the elective franchise. In the modern caucus or convention one man often does the thinking for the rest. “If he is the man whom I follow, I call him my leader. If he is the man whom you follow, I call him your boss.” When the leader or boss is not sufficiently sure of his ability to bind the others by his orders, those who have a following are invited to a conference, at which a line of action is agreed upon to relieve the multitudes of the trouble of thinking. A delegate who was giving very vociferous vent to his feelings was rebuked by a colleague, saying, “Just think where you are.” He replied with more emphasis than elegance, “I was not brought here to think, but to shout.” Independent thinking is as hard work as the average man cares to do. He craves a guide, an authority to relieve him of the trouble of thinking for himself. Outside of their particular vocation or profession it is absolutely necessary at times for the strongest intellects to accept the conclusions of other thinkers. The man who has been successful at making money, and who finds that his thinking in financial matters is trustworthy, often makes himself obnoxious by assuming that his opinions and conclusions should be accorded equal weight in every other sphere of human activity. There is no better place to teach the individual his limitations without destroying his independence as a thinker than the atmosphere of a great university.
The dependent thinker is aptly described by a writer inLeisure Hoursin the following language:
The dependent thinker.
“It is sometimes amusing to hear a man of this order coming out strongly with opinions which he would have you believe are thoroughly independent and original, but which you can trace directly to the source from which he got them. You could indicate those sources if it were not uncivil to do so, very much as a shrewd but not very well-behaved old gentleman is said to have indicated at church, in a tone sufficiently loud to be heard by the clergyman and the congregation, too,—which was especially galling,—the authors to whom the said clergyman had been indebted for his sermon, ‘That’s Sherlock; that’s Tillotson; that’s Jeremy Taylor.’ ‘I tell you what, fellow, if you don’t hold your tongue, I’ll have you turned out of church.’ ‘That’s his own.’”
The men who must depend upon others to do their thinking for them deserve pity and commiseration. The bureaus which thrive by furnishing essays and orations for commencements, sermons for special occasions, and even for the regularly recurring Sunday services, show how often our schools make their pupils dependent instead of self-reliant. On being cast upon the sea of life, their minds resemble a craft which has lost its rudder; they drift with wind and tide, uncertain where they shall land. Their thinking is not grounded on first principles; hence their minds reflect transient views on every question. The strong personality in the sunlight of whose influence they happened last to bask moulds their opinions and directs their intellectual life until they move into the sphere of new influences, constantly resembling those whom Randolph of Roanoke stigmatized as dough-faces because their votes were under the control of party leaders and were cast regardless of their convictions of right.
Continuous thought.
The men whom the world reveres as great thinkers have been distinguished by their ability to give continuous thought to whatever engaged their serious attention. Newton claimed that he made his discoveries by always thinking about them. His biographers relate how he would for hours remain seated upon his bed, half dressed, absorbed in thought, forgetful of his surroundings. Stories of the absent-mindedness of Socrates, Sydney Smith, Neander, Edison, and many others who attained eminence as philosophers, authors, or inventors, are interesting indeed, but they throw no light upon the way in which these men acquired their marvellous powers; they merely show a capacity for focussing all the energies of the soul upon one point to the exclusion of sense impressions from without. It is very certain that men who excel in any line of work acquire habits of concentrated and continuous thought in one direction. Very different from these are the mental habits of the boy and the average man. A writer inCornhill Magazinedescribes their intellectual activity as follows:
“The normal mental locomotion of even well-educated men and women (save under the spur of exceptional stimulus) is neither the flight of an eagle in the sky, nor the trot of a horse upon the road, but may better be compared to the lounge of a truant school-boy in a shady lane, now dawdling passively, now taking a hop-skip-jump, now stopping to pick blackberries, and now turning to right or left to catch a butterfly, climb a tree, or make dick-duck-drake on a pond; going nowhere in particular, and only once in a mile or so proceeding six steps in an orderly and philosophical manner.”
Loose thinkers.
Organic thinking.
The thoughts of some men resemble mosaic work. Each part is beautiful in itself, but has no inner connectionwith those next to it. Men of this class are called loose thinkers; it is always difficult to retain what they say. The thinking of a totally opposite class of men resembles the growth of an organism. They start from a germinal idea, which, like seed sown into good soil, begins to grow, throwing out parts which have inward connection and which together constitute an organic unity. In a machine any part can be replaced by another. In the organism no such substitution is possible. For each organ bears a life relation to the whole, and if it is wanting the unity of the organism is destroyed. Organic thinking gives the hearer the feeling that the several parts and inferences of a discourse are evolved from his inner consciousness. Having had the germ-idea in his mind, he feels as if he had held all it involves; the speaker supplied the conditions of development as the sun supplies warmth for vegetable growth. The effect of such thinking is irresistible. The branches of study which thus grow out of a fundamental idea, and show the inner relation between the subjects not as a mere sequence, but as a living organic relation, have an educative value which cannot be too highly prized. The organic thinker, if he makes himself understood, has the audience on his side; and his cogency can seldom be refuted except by showing either that his germinal idea is wrong or that his conclusions have no connection with his premises.
Harris on stages of thinking.
Dr. Harris has drawn attention to three stages of thinking. He claims that in the first stage things are regarded as the essential elements of all being, that in the second the mind discovers relations,—truly essential relations,—and that in the third stage the mind thinks the self-related. “Self-relation is the category of the reason, just as relativity is the category of the understanding, or non-relativity(atomism) the category of sense-perception.” Theoretically this distinction is important as giving us a rational basis for the knowledge of God as revealed to man. Practically, every child thinks the idea of God. Where the study of science or philosophy leads to atheism, the wish is always father to the thought.
Technical and scientific thinking.
Clifford has made a distinction between technical and scientific thinking. The former enables one to do with skill and accuracy what has been done heretofore. The latter partakes of the nature of prophecy or prediction. He claims that scientific as well as merely technical thought make use of experience to direct human action, but that while technical thought or skill enables a man to deal with the same circumstances he has met before, scientific thought enables him to deal with circumstances different from any he has met before. In his opinion, scientific thought is human progress itself. An example or two can best be given in his own language.
“If you make a dot on a piece of paper, and then hold a piece of Iceland spar over it, you will see not one dot, but two. A mineralogist, by measuring the angles of a crystal, can tell you whether or not it possesses this property without looking through it. He requires no scientific thought to do that. But Sir Rowan Hamilton, the late Astronomer Royal of Ireland, knowing these facts, and also the explanation of them which Fresnel had given, thought about the subject, and predicted that by looking through certain crystals in a particular direction we should see not two dots, but a continuous circle. Mr. Lloyd made the experiment and saw the circle, a result which had never been even suspected. This has always been considered one of the most signal instances of scientific thought in the domain of physics. It is most distinctly an application of experience gainedunder certain circumstances to entirely different circumstances.”[44]
Clifford compares two well-known achievements in the domain of astronomy which help to set the distinction between technical and scientific thought in a still clearer light:
“Ancient astronomers observed that the relative motions of the sun and moon recurred all over again in the same order every nineteen years. They were thus enabled to predict the time at which eclipses would take place. A calculator at one of our great observatories can do a great deal more than this. Like them, he makes use of past experience to predict the future; but he knows of a great number of other cycles besides the one of nineteen years, and takes account of all of them; and he can tell about the solar eclipse of six years hence, exactly when it will be visible, and how much of the sun’s surface will be covered at each place, and to a second at what time of the day it will begin and finish there. This prediction involves technical skill of the highest order, but it does not involve scientific thought, as any astronomer will tell you. By such calculations the place of the planet Uranus at different times of the year had been predicted and set down. The predictions were not fulfilled. Then arose Adams, and from the errors in the prediction he calculated the place of an entirely new planet that had never yet been suspected; and you all know how the new planet was actually found in that place. Now this prediction does involve scientific thought, as any one who has studied it will tell you. Here, then, are two cases of thought about the same subject, both predicting events by the applicationof previous experience, yet we say one is technical and the other scientific.”[45]
Science as knowledge of things in their causes and relations.
The foregoing distinction may be valuable in the training of university students whose career is to be that of original research and discovery, but it has very little value for teachers in schools of lower grade. For ordinary purposes, science is the knowledge of things in their causes and relations. If the teacher begets the habit of asking why, and makes the pupils dissatisfied with simply knowing the how and the what, he has gone far towards making them thinkers in the scientific sense of the word.
How shall the knowledge of things in their causes and relations be attained? The mind first thinks things as isolated units apart from and without reference to other things. Under the impulse to know it resolves the thing into its elements or constituent parts, and then puts them together in a more complete idea of each thing as a whole. The boy whose curiosity impels him to take apart a watch or clock is following the bent of the mind to proceed analytically. If he does not try to put the pieces together, so that the reconstructed whole will keep time as before,he needs stimulus in the direction of synthetic thinking. Soon his interest in time-pieces leads him to detect similarities between American watches and those made in Switzerland, and he learns to classify time-pieces, to see a multitude of details and peculiarities at a glance, one characteristic or peculiarity bringing to his mind the distinctive parts and construction of every watch in a given class. From the way in which a given watch keeps time, he draws inferences in regard to the entire class. This is inductive thinking. From the conclusions he has framed, he makes up his mind as to the new watch which the jeweller offers him for sale. He is now thinking deductively.
Distinction between laws and causes.
From thinking things as units, the mind passes to thinking the relations of things. The adaptation of means to ends in play, in ministering to bodily wants, occupies the mind in very early stages of thinking. The gifts of the kindergarten appeal to this tendency in the mind, and help to develop it into habit and faculty. Design and its execution, means and end, the tool and its use, the raw material and the purpose for which it is to be used, thought-material and the essay in which it is to be formulated,—these are so many ways of thinking things or ideas in their relations. Not only may a relation become a distinct object of thought, but relations between relations, classes of relations,—for instance, in simple and compound proportion,—can thus be made to stand apart before the mind as distinct objects of thought. The most important of all these relations is that of cause and effect. How things come to be, their origin and development, the forces that make them what they are, are the questions of profound and abiding interest to the scientific mind. Laws are often spoken of as if they were causes. A law is a generalized statement of an invariable sequence of things or motions of things. We sometimespersonify these sequences, and speak of them as if they were forces in nature. The laws are personified, as if they were conscious beings demanding obedience, and inflicting punishment for disobedience. The consciousness of the personification is lost, and then along with spelling nature with a capital letter, we fall into the mistake of making laws stand for the Maker and Creator of all things. Furthermore, it is very important to distinguish the ground of knowledge from causes that are operative in the world outside of mind. The rain of last night caused the streets to be muddy; but the condition of the streets, an effect of rainfall, may be the ground of our knowledge that it must have rained last night. The fact that the earth is flattened at the poles, or, in other words, that its curvature is less at the poles than at the equator, explains the fact that degrees of latitude get longer as we approach the poles. The former is the cause, the latter is an effect. But the mind drew the former as an inference from the determination of degrees of latitude by actual measurement. The effect became the ground of knowledge. Frequently the cause is known or inferred from its effect. That which is causal in the world of mind is effect in the world outside of mind; and that which is effect in nature becomes the ground of knowledge in the processes of thought. From this point as vantage-ground, we spy the land in which thinking becomes knowing.
When a man’s knowledge is not in order, the more of it he has the greater will be his confusion of thought. When the facts are not organized into faculty, the greater the mass of them the more will the mind stagger along under its burden, hampered instead of helped by its acquisitions.H. Spencer.That knowledge cannot be gained without more or less of correct and prolonged thinking is a practical maxim which no one would be found to dispute. But that there is much knowledge which does not come bymerethinking is a maxim scarcely more to be held in doubt. Thinking is, then, universally recognized as an important and even necessary part of knowing; but it is not the whole of knowing. Or, in other words, one must make use of one’s faculties of thought as an indispensable means to cognition; but there are other means which must also be employed, since it is not by thought alone that the human mind attains cognition.Ladd’s “Philosophy of Knowledge,”page 130.
When a man’s knowledge is not in order, the more of it he has the greater will be his confusion of thought. When the facts are not organized into faculty, the greater the mass of them the more will the mind stagger along under its burden, hampered instead of helped by its acquisitions.
H. Spencer.
That knowledge cannot be gained without more or less of correct and prolonged thinking is a practical maxim which no one would be found to dispute. But that there is much knowledge which does not come bymerethinking is a maxim scarcely more to be held in doubt. Thinking is, then, universally recognized as an important and even necessary part of knowing; but it is not the whole of knowing. Or, in other words, one must make use of one’s faculties of thought as an indispensable means to cognition; but there are other means which must also be employed, since it is not by thought alone that the human mind attains cognition.
Ladd’s “Philosophy of Knowledge,”page 130.
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.
Interpretation of sense-impressions.
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?
What is knowledge?
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 indoubtrespecting one of Euclid’s demonstrations, he cannot be said toknowthe proposition proved by it; if again he is fullyconvincedof anything that is not true, he is mistaken in supposing himself to know it; lastly, if two persons are eachfully 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 toknowthe truth, since he cannot have sufficientproofof it.”[46]
Belief.
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 expressionfirm beliefexcludes the element of doubt from knowledge.
Truth.
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 errorare 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.
The ground of knowledge.
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.
The reason why.
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 reasonwhy, 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]
Exhaustive study.
The question how.
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 seehow; the questionwhythen 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 atfirst 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.
When knowledge is clear, when distinct.
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 individualmind 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.
Value of questions.
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 thewordwhichdenotesthe object of the action, which word may be either in the nominative or the accusative case as theverb 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.
Theory, true and false.
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]