can prove anything if you only select your instances rightly. Nothing is easier than to prove that planting in the "up sign" insures a good crop. You only need recall merely those instances where success has followed such planting and forget the rest. Red-headed people are unusually irascible. To prove so note only those cases in which they are. Indeed often large numbers of instances can be marshaled that carry for the point a high degree of plausibility. Unbalanced concepts and groundless generalizations come almost always from the careless use of this Method of Agreement alone. This method must, therefore, be checked by another, the Method of Difference. Method of difference. In this, instead of finding a series of instances to which the supposed cause is common, you select one where that cause is present, and another, exactly like it in all other respects, where it is absent. You endeavor, that is, to make the two differ only in respect to the critical element. If, then, the effect follows where the supposed cause is present, and does not follow where it is absent, you are pretty safe in judging that the element in question is essential to the effect. If the child referred to above had not only recalled instances where the wind and rain occurred together, but had definitely tried to think of occasions where they were not together, he would not have taken the wind to be the cause of the rain. If the person who is justifying the efficacy of the "up sign" would seek for cases where a successful crop had followed planting in another sign, their necessary connection would soon be disproved. It is only because negative instances are not sought, nay are even carefully avoided, that so many shallow and indefensible generalizations can arise so easily and persist so long. If one were trying to prove that light is essential to the growth of a plant he could do so by setting one box containing a plant in the light, and another, exactly like it, in the dark. To determine that air is essential to the carrying of sound one rings a bell first in a jar containing air and then in the same jar with the air exhausted. To prove that water boatmen possess the sense of hearing the scientist Graber first dropped stones into a vessel, in which they were present, which had its bottom covered with mud, and in which, consequently, the dropping of the stones made no noise. Then he put a plate of glass over the mud, so that when dropped upon it the stones would make a noise, and found that in the latter case, but not in the former, the insects took flight, showing that they did possess the sense of hearing. Joint method of agreement and difference. - Ordinarily, however, particularly in our practical affairs outside the laboratory, we use a Joint Method of Agreement and Difference by combining the two. We compare a number of instances where the supposed cause is present with a number in which it is absent. If the effect follows in all of the former series and in none of the latter we conclude that it is the true cause. To prove that the liquor business increases the taxes of a county, through increasing the court and police expenses, we take a large number of typical counties which have saloons and compare them with a large number of typical ones which do not have. If we find the expenses uniformly high in the former case and low in the latter we attribute the result to the liquor business. To test the social effect of Christianity we compare a large number of representative church members with a large number of representative nonmembers. To assure ourselves whether a certain kind of food, or a certain form of dissipation, is injurious to us, we compare our condition on a large number of occasions when we have indulged with our condition on many occasions when we have not, being careful always to select for the two sides instances as nearly as possible alike except for the presence or absence of the element under scrutiny. Concomitant variations. Still a fourth method, however, is available to further strengthen our certainty. It is illustrated by the result of several investigations into the influence of the use of tobacco upon success in school work. A repre sentative inquiry, carried on by one of the high school boys among his schoolmates at Highland Park, Illinois, resulted in the following facts: Average grade of 77 boys who had never smoked Average grade of 24 boys who had quit smoking Average grade of 45 habitual smokers who had left school 84.5% 80.5% 76 % 69 % It showed that, on the average, success in school work varied regularly with the use of tobacco. As the cause of low standing increased the effect increased, and vice versa. The two at every point varied together. Hence the use of tobacco was concluded to be a handicap to successful study. This method of reasoning the logicians call by the rather jaw-breaking name, the Method of Concomitant Variations, that is, of simultaneous or parallel changes. This method is used repeatedly, both in the laboratory and in everyday affairs. From the fact that the mercury in the thermometer rises and falls in exact accord with temperature changes we conclude that the change in temperature causes the change in the length of the mercury column. If investigation shows that the number of deaths rises and falls concomitantly with the rise and fall in the humidity of the atmosphere, a most natural conclusion would be that the humidity is responsible. If the magnetic disturbances on the earth increase and decrease at the exact time, and in the exact proportion, as an increase or decrease in the number and magnitude of spots on the sun, the magnetic storms on the earth may be legitimately attributed to the disturbance on the sun. Two independent elements may sometimes change at the same time; but if they continually vary together, always changing in the same proportion, each reach ing its maximum or its minimum simultaneously with the other, we feel sure that their connection is not accidental but essential. Method of residues. And finally we may use what is called the Method of Residues. This method was used by Archimedes when he demonstrated that the king's crown was not made of pure gold. He weighed it in air and then in water, observing how much of its weight it lost. Then he calculated how much it should have lost had it been of pure gold, and discovered that there still remained some loss unaccounted for. This residual effect he could attribute to the only remaining admissible cause the presence of some light alloy. By a like method the planet Neptune was discovered. Uranus was found not to move in the orbit which the attraction of the known heavenly bodies would require. It was seen that there must, therefore, be, as a remaining cause, some unknown body whose attraction could explain the remaining effect. The position of this required planet was calculated and the result was the discovery of Neptune. Similarly if one had an unusual attack of indigestion and were looking for its cause one would expect to find it outside of those elements of which the effects were known to be otherwise. One would consider that it could not be the bread, or the potatoes, or the meat, for these he had eaten frequently and had experienced no such result. It must, therefore, have been due, one concludes, to the doughnuts, since they are the only remaining possible cause. The methods of clarifying your ideas which have been discussed in this chapter are not, of course, new methods which you have never used before. You have used them all repeatedly. Everybody has. But if they are consciously recognized and brought under control, especially at certain critical times, they can be made much more effective in freeing ideas from the chaos and confusion which usually characterize them. EXERCISES 1. As you think back over your experience do you see that you have always been using the methods here described? What difference, then, could the study of this chapter make in your thinking? 2. The neglect of what factor particularly, do you think, is responsible for a person's clinging to a superstition which he could easily disprove? 3. Can we be absolutely certain that the conclusions reached by the methods described in this chapter are universally true? What are the conditions under which this certainty will be greatest? 4. Do Mill's methods give us our start in finding our cause, or must we begin with the method of hypotheses described earlier? Illustrate. 5. Describe the method by which you would test your supposition that mathematics trains the reasoning powers. Which of the Experimental Methods have you proposed using? Show what precautions must be observed. 6. Tell which method is used in each of the following examples (all taken from Hibben): (a) If a beam of the sun's light is passed through a prism, a colored band nearly five times as long as it is broad results. Newton tried several experiments in which he varied the size of prism, and the quality of the glass; he also passed the beam through various parts of the same prism, and tried other minor suppositions. But in all these cases there was the same color effect produced. (b) Hawksbee, in 1715, first noticed that by striking a bell in the receiver of an air-pump, the bell was heard when the receiver was full of air; but when the receiver was exhausted, no sound was heard. (c) Also it was found that as the air was gradually admitted into the receiver, the sound of the bell grew louder and louder. (d) With various kinds of polished metals, no dew is deposited; but with various kinds of glass, having highly polished surfaces, dew is deposited. Therefore, the deposit of dew is affected by the kind of substances themselves. (e) Nitrogen obtained from various chemical sources is of uniform density; in 1894 Lord Rayleigh and Professor Ramsay, noting the fact that atmospheric nitrogen is about one half per cent heavier, were led to the discovery of a hitherto unknown substance which received the name of argon, K |