to recognize the part that the psychological concept plays in the whole process of acquiring logical concepts is vicious in either or both of two ways:

to

It leads one to suppose that he is getting a complete psychology of the concept when a very vital part, that of the psychological concept, is left out. As a psychology of the concept it would be, if not false, at least very misleading. Psychological and logical concepts need to be distinguished and their functional relation to each other clearly kept in mind. Particularly is it necessary recognize that logical concepts rest back upon psychological concepts and these in turn are an unreflective outgrowth of perceptual experiences, and it must not be supposed that logical concepts are derived directly from a comparison of scattered, isolated, and independent individual notions, without any previous generalization having taken place. Whole sections of pedagogical works are vitiated by being based upon this handy but misleading psychology of the concept, which has its origin in the analysis of the finished products of mental action.

b. It gives one no basis for understanding the real nature and dynamic connection of the series of steps involved in the process which we have outlined as that by which logical concepts are attained. These steps become purely formal. But when we presuppose that the process has its origin in the breakdown of some psychological concept, which sets a definite problem, then the steps of further observation, of comparison, abstraction, and generalization become vital and dynamic, and their relation to one another is that of organic and necessary connection as phases within one continuous process directed steadily toward the solution of a definite problem.

5. THE LOGICAL CONCEPT NOT FINAL.

The logical concept, once constructed, becomes a tool of the mind used freely and flexibly and without hesitation, until perchance doubt is thrown upon it again by reason of some failure to meet our needs in the control of action or of thought, when it is again subject to investigation and reconstruction. Thus a logical concept at any given time or point in our experience is not necessarily final. In certain phases of our experience, particularly the mathematical, logical concepts once attained are apt to become fixed. It may be instructive to point out that even in this sphere there are logical concepts that have to be reconstructed.

The logical concept of exponent attained in the study of arithmetic is adequate to the needs of that subject. There we think of an exponent as a small figure placed to the right and a little above a number to indicate how many times it is taken as a factor. But in algebraic problems there arise situations to which we apply the laws of exponents which satisfied us for arithmetic and we get into trouble with our concept of exponent. Take the following simple cases:

Here the law of exponents demands that in the process of division the exponent of the divisor be subtracted from that of the dividend to determine the exponent of the quotient. The quotient is one that can be easily interpreted under the prevailing concept of an exponent as indicating how many times a quantity is to be used as a factor. But let us go right on consistently applying our law of exponents to the following cases:

Now apply the concept of exponent to the resulting quotients. Is it intelligible to say that a is to be used zero

-

times as a factor, or that a is to be used -I or -2 times as a factor? Our concept of exponent breaks down at this point. We must either refuse to apply any further the law of exponents applicable to division and say that it is not a universal law, or we must reconstruct our concept of exponent. We do the latter and admit zero and negative exponents, giving them an interpretation in harmony with the facts as seen from another principle of diviaR according to this other principle

sion. Because

- = I,

6 a

of division, we say that a must equal 1; and because

according to this other law of division, we say

I

that a-2 must equal Thus we reinterpret and recon

a'

struct our concept of exponent to make it harmonize with a new set of facts, to make it a tool which we may employ to control new situations more adequately than they could otherwise be controlled. Mathematics furnishes illustration after illustration of this breaking down of concepts which are adequate at one level and their reconstruction to make them adequate at another and higher level in the attainment of control.

The progress of all our sciences has involved the reconstruction of many logical concepts. What a tremendous reconstruction of logical concepts in every department of human thought has been provoked by the application of the idea of evolution! This lack of finality to our logical concepts need not worry us in the least, if we look upon them from the functional point of view as tools of the mind for controlling thought, and through thought ultimately action. Why should it not be a source of satisfaction that humanity may improve the tools of thought as well as the tools of commerce and industry? In fact, one might say that the only way that we can improve the tools of

commerce, of industry, of practical benevolence, of religion, and in general of everything on which the progress of humanity depends, is by improving the tools of thought.

6. SIGNIFICANCE AND FUNCTION OF THE CONCEPT IN THE THINKING PROCESS.

The concept is the most important element of technique in thinking. It is the great simplifier of mental processes. Just as habit reduces the multiplicity of muscular movements to a few simple methods of reaction that can be used for a variety of like situations, so the concept reduces to methods that apply to a large number of individual cases the interpretative and guiding function of consciousness. A concept is a sort of mental habit. This is of great significance for the process of thinking. Concepts furnish certain organized centers for the control of the thinking process. The concept is, as it were, the pivot on which the whole thinking process turns. The pivotal character of the concept may be worked out in two directions.

(1) The concept central between individuals which are problematic and individuals brought under control.

In thinking, we are either analyzing and comparing individuals as a phase of the process of perfecting some concept, either reflectively or unreflectively; or we are taking concepts for granted and are using them to interpret and control individuals. The concept thus occupies a central position between individuals which are problematic, and hence cannot be controlled adequately, and individuals which are properly interpreted and hence can be controlled. This thought is sometimes expressed by saying that in thinking we proceed from individuals to individuals by way of the concept. In actual life it is always individual things or situations which we have to control. The problem is always particular. The concept is not, then, the ultimate goal of thinking; it is rather the tool of thinking in dealing with individuals.

The thought just developed can be clarified by the analogy of a machine, say the reaper. In harvesting grain the problem is always one of controlling some particular situation, of reaping some particular field. There is in human experience no such thing as harvesting in general. Yet, it is just as truly a part of the harvesting function to perfect the reaper as to use it. We perfect the reaper, however, not for its own sake; it is not ultimate, the goal. It is only an instrument for the more adequate control of the individual harvesting situation. But this machine, when it is perfected, has this great significance, that its method of operation is general, and hence this same machine can be used to control other individual harvesting situations, to reap other fields of grain or to reap the same field another year. The movement has been from individual harvesting situations which were problematic to machine and from machine to the control of individual harvesting situations. Now, just as the reaper arises out of the need of individual situations and, when perfected, functions in the more adequate control of those individual situations, so it is with the concept.

The analogy holds true at another point also. The machine is not fixed, but it is subject to modification at such points as inadequacy may be discovered in actual use. So it is with the concept. The concept, then, is to be viewed as a tool of thinking, and its central position in the thinking process is due to the fact that thinking, like industry, is either moving in the direction of perfecting its tools or in that of making use of them.

(2) Another way of expressing the idea that the concept is pivotal in the thinking process.

The concept represents a certain core of meaning, and that core of meaning, if thought of from different points of view, may be analyzed into the various elements which are bound together in the complex. For example, take the case of orange. If the child is hungry, one meaning in the com