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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.
The thinking that ripens into knowing.

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.

Knowing involves more than mere thinking.

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.

XVIII
THINKING AND FEELING

There is much contention among men whether thought or feeling is the better; but feeling is the bow and thought the arrow; and every good archer must have both. Alone, one is as helpless as the other. The head gives artillery; the heart, powder. The one aims, and the other fires.

Beecher.

It may be noted that medical men, who are a scientific class, and, therefore, more than commonly aware of the great importance of disinterestedness in intellectual action, never trust their own judgment when they feel the approach of disease. They know that it is difficult for a man, however learned in medicine, to arrive at accurate conclusions about the state of a human body that concerns him so nearly as his own, even though the person who suffers has the advantage of actually experiencing the morbid sensations.

Hamerton.

When pupils are encouraged to make for themselves fresh combinations of things already known, additional progress is certain. Variety of exercise in this way is as attractive to children as many of their games. If, when such exercises are given, the rivalry involved in taking places were discontinued, and all extraneous excitement avoided, the play of intelligence would bring an ample reward. I plead for discontinuance of rivalry in such exercises, because, while it stimulates some, in other cases it hinders and even stops the action of intelligence. If any teacher doubts this, he may subject a class to experiment by watching the faces of the pupils, and next by asking from the child who has been corrected an explanation of the reason for the correction. Hurry in such things is an injury, and so is all commingling of antagonistic motives. All fear hinders intellectual action, and the fear of wounded ambition offers no exception to the rule. The fear of being punished is more seriously detrimental than any other form of fear which can be stirred. It is essentially antagonistic to the action of intelligence. Let mind have free play.

Calderwood.

XVIII
THINKING AND FEELING
Bodily conditions.

In all our thinking it is very important to get a clear and full vision of the thing to be known. This is not always as easy as it seems. Like Nelson in the battle of Copenhagen, we may consciously turn the blind eye towards what we do not like and exclaim, “I do not see it.” The lenses through which we gaze may be green, or smoked, or ill-adjusted, and thus without suspecting it we may see things in false colors or distorted shapes. Our bodily condition may color everything we see and think. In health and high animal spirits every thought is rose-colored. In periods of disease and depression everything we think seems to pass, “like a great bruise, through yellow, green, blue, purple, to black. A liver complaint causes the universe to be shrouded in gray; and the gout covers it with inky pall, and makes us think our best friends little better than fiends in disguise.”

Prejudice.

One of the greatest hinderances to correct thinking is prejudice. Hence all who have presumed to give advice on the conduct of the understanding have had something to say concerning prejudice. Bacon has a chapter on the idols of the mind, and Locke contends that we should never be in love with any opinion. In a charming little volume on the “Art of Thinking,” Knowlson has a chapter in which he enumerates and discusses the prejudices arising from birth, nationality, temperament, theory, and unintelligent conservatism. The list might easily be enlarged. Close analysis must convince any one that feeling strengthens all forms of prejudice, and there are very few, if any, fields of thought in which it is not essential for the attainment of truth to divest ourselves of preconceived notions and the resultant feelings, and to weigh the arguments on both sides of a question before reaching a conclusion.

The wishes of the heart and the conclusions of the intellect.

A student may take up geometry with a feeling of prejudice for or against the study, based upon what he has heard from others concerning its difficulties or the teacher who gives the instruction; but after he has mastered the demonstration of a theorem he does not lie awake at night wishing the opposite were true. In the realms of mathematics the wishes of the heart are not in conflict with the conclusions of the intellect. In the domain of ethical, social, historical, or religious truth the head often says one thing and the heart another. “We see plainly enough what we ought to think or do, but we feel an irresistible inclination to think or do something else.” In most of the instances in which the study of science has led to agnosticism the wish was father to the thought. When two men argue the same question, weighing the same arguments and reaching opposite conclusions, as did Stonewall Jackson and his father-in-law at the outbreak of the Civil War, the inclinations and wishes of the heart must have influenced their thinking.

Feeling an element in all mental activity.

Feeling is an element in all forms of mental activity. The intellect never acts without stirring the emotions. The teacher who reproved a pupil for showing signs of pleasure and delight over the reasoning of Euclid, saying, “Euclid knows no emotion,” must have been a novice in the art of introspection. Who cannot recall the thrill of delight with which he first finished the proof of the Pythagorean proposition? Mathematics is considered difficult; the emotions connected with victory and mastery sustain the student as he advances from conquest to conquest. The effort which some thinkers make to reduce the phenomena of the universe to a few universal principles is, without doubt, sustained and stimulated by a feeling that there must be unity in the midst of the most manifold diversity.

Descartes.

Scientists and philosophers are prone to imagine themselves free from the prejudices which warp the thinking of the common mind. Descartes started to divest himself of all preconceived notions; yet he could not divest himself of the notion that he was immensely superior to other men. “This French philosopher regarded himself as almost infallible, and had a scorn of all his contemporaries. He praised Harvey, but says he only learned a single point from him; Galileo was only good in music, and here he attributed to him the elder Galileo’s work; Pascal and Campanella are pooh-poohed. Here is an instance of how pride in one’s own work may beget a cheap cynicism with regard to the work of others; and how as a feeling it blinds the mind to excellences outside those we have agreed to call our own.” Of men in general Jevons, in his treatise on the “Physical Sciences,”[51] says,—

“It is difficult to find persons who can with perfect fairness register facts for and against their own peculiar views. Among uncultivated observers, the tendency to remark favorable and to forget unfavorable events is so great that no reliance can be placed upon their supposed observations. Thus arises the enduring fallacy that the changes of the weather coincide in some way with the changes of the moon, although exact and impartial registers give no countenance to the fact. The whole race of prophets and quacks live on the overwhelming effect of one success compared with hundreds of failures which are unmentioned or forgotten. As Bacon says, ‘Men mark when they hit, and never mark when they miss.’ And we should do well to bear in mind the ancient story, quoted by Bacon, of one who in Pagan times was shown a temple with a picture of all the persons who had been saved from shipwreck after paying their vows. When asked whether he did not now

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