Now, every civilized man who is not mentally deficient can perform the fundamental operations of arithmetic. He can add and subtract, multiply and divide. In other words, he can use numbers. The man who has become an accomplished mathematician can use numbers much better; but if we are capable of following intelligently the intricate series of operations that he carries out on the paper before us, and can see the significance of the system of signs which he uses as an aid, we shall realize that he is only doing in more complicated ways what we have been accustomed to do almost from our childhood.
If we are interested, not so much in performing the operations, as in inquiring into what really takes place in a mind when several units are grasped together and made into a new unit—for example, when twelve units are thought as one dozen—the mathematician has a right to say: I leave all that to the psychologist or to the metaphysician; every one knows in a general way what is meant by a unit, and knows that units can be added and subtracted, grouped and separated; I only undertake to show how one may avoid error in doing these things.
It is with geometry as it is with arithmetic. No man is wholly ignorant of points, lines, surfaces, and solids. We are all aware that a short line is not a point, a narrow surface is not a line, and a thin solid is not a mere surface. A door so thin as to have only one side would be repudiated by every man of sense as a monstrosity. When the geometrician defines for us the point, the line, the surface, and the solid, and when he sets before us an array of axioms, or self-evident truths, we follow him with confidence because he seems to be telling us things that we can directly see to be reasonable; indeed, to be telling us things that we have always known.
The truth is that the geometrician does not introduce us to a new world at all. He merely gives us a fuller and a more exact account than was before within our reach of the space relations which obtain in the world of external objects, a world we already know pretty well.
Suppose that we say to him: You have spent many years in dividing up space and in scrutinizing the relations that are to be discovered in that realm; now tell us, what is space? Is it real? Is it a thing, or a quality of a thing, or merely a relation between things? And how can any man think space, when the ideas through which he must think it are supposed to be themselves non-extended? The space itself is not supposed to be in the mind; how can a collection of non-extended ideas give any inkling of what is meant by extension?
Would any teacher of mathematics dream of discussing these questions with his class before proceeding to the proof of his propositions? It is generally admitted that, if such questions are to be answered at all, it is not with the aid of geometrical reasonings that they will be answered.
10. THE SCIENCE OF PSYCHOLOGY.—Now let us come back to a science which has to do directly with things. We have seen that the plain man has some knowledge of minds as well as of material things. Every one admits that the psychologist knows minds better. May we say that his knowledge of minds differs from that of the plain man about as the knowledge of plants possessed by the botanist differs from that of all intelligent persons who have cared to notice them? Or is it a knowledge of a quite different kind?
Those who are familiar with the development of the sciences within recent years have had occasion to remark the fact that psychology has been coming more and more to take its place as an independent science. Formerly it was regarded as part of the duty of the philosopher to treat of the mind and its knowledge; but the psychologist who pretends to be no more than a psychologist is a product of recent times. This tendency toward specialization is a natural thing, and is quite in line with what has taken place in other fields of investigation.
When any science becomes an independent discipline, it is recognized that it is a more or less limited field in which work of a certain kind is done in a certain way. Other fields and other kinds of work are to some extent ignored. But it is quite to be expected that there should be some dispute, especially at first, as to what does or does not properly fall within the limits of a given science. Where these limits shall be placed is, after all, a matter of convenience; and sometimes it is not well to be too strict in marking off one field from another. It is well to watch the actual development of a science, and to note the direction instinctively taken by investigators in that particular field.
If we compare the psychology of a generation or so ago with that of the present day, we cannot but be struck with the fact that there is an increasing tendency to treat psychology as a natural science. By this is not meant, of course, that there is no difference between psychology and the sciences that concern themselves with the world of material things—psychology has to do primarily with minds and not with bodies. But it is meant that, as the other sciences improve upon the knowledge of the plain man without wholly recasting it, as they accept the world in which he finds himself and merely attempt to give us a better account of it, so the psychologist may accept the world of matter and of minds recognized by common thought, and may devote himself to the study of minds, without attempting to solve a class of problems discussed by the metaphysician. For example, he may refuse to discuss the question whether the mind can really know that there is an external world with which it stands in relation, and from which it receives messages along the avenues of the senses. He may claim that it is no more his business to treat of this than it is the business of the mathematician to treat of the ultimate nature of space.
Thus the psychologist assumes without question the existence of an external real world, a world of matter and motion. He finds in this world certain organized bodies that present phenomena which he regards as indicative of the presence of minds. He accepts it as a fact that each mind knows its own states directly, and knows everything else by inference from those states, receiving messages from the outer world along one set of nerves and reacting along another set. He conceives of minds as wholly dependent upon messages thus conveyed to them from without. He tells us how a mind, by the aid of such messages, gradually builds up for itself the notion of the external world and of the other minds which are connected with bodies to be found in that world.
We may fairly say that all this is merely a development of and an improvement upon the plain man's knowledge of minds and of bodies. There is no normal man who does not know that his mind is more intimately related to his body than it is to other bodies. We all distinguish between our ideas of things and the external things they represent, and we believe that our knowledge of things comes to us through the avenues of the senses. Must we not open our eyes to see, and unstop our ears to hear? We all know that we do not perceive other minds directly, but must infer their contents from what takes place in the bodies to which they are referred—from words and actions. Moreover, we know that a knowledge of the outer world and of other minds is built up gradually, and we never think of an infant as knowing what a man knows, much as we are inclined to overrate the minds of infants.
The fact that the plain man and the psychologist do not greatly differ in their point of view must impress every one who is charged with the task of introducing students to the study of psychology and philosophy. It is rather an easy thing to make them follow the reasonings of the psychologist, so long as he avoids metaphysical reflections. The assumptions which he makes seem to them not unreasonable; and, as for his methods of investigation, there is no one of them which they have not already employed themselves in a more or less blundering way. They have had recourse to introspection, i.e. they have noticed the phenomena of their own minds; they have made use of the objective method, i.e. they have observed the signs of mind exhibited by other persons and by the brutes; they have sometimes experimented—this is done by the schoolgirl who tries to find out how best to tease her roommate, and by the boy who covers and uncovers his ears in church to make the preacher sing a tune.
It may not be easy to make men good psychologists, but it is certainly not difficult to make them understand what the psychologist is doing and to make them realize the value of his work. He, like the workers in the other natural sciences, takes for granted the world of the plain man, the world of material things in space and time and of minds related to those material things. But when it is a question of introducing the student to the