The term law has been applied to any general proposition dealing with the relationship between things or events. So understood, it implies nothing compulsive, nothing active, nothing invariable, but such meanings are not infrequently read into the term. Natural laws are often spoken of as though they were active forces, ruling the universe with imperious sway. Of the same order has been the attitude often taken toward the laws of economics; they are viewed as mysterious forces which govern man's conduct in the industrial sphere, principles which must never be transgressed. Such a view of law, whether natural or social, is, as Dewey says, an animistic survival. A law, as the scientist sees it, does not govern. It is a summary of observed relations, "a brief résumé of experience, "" "a shorthand symbol" which assists in the understanding of a number of related phenomena. Laws are generalizations, not forces.

But not all generalizations are of equal validity. And herein lies the distinction between the mechanical conception of law and that conception which is consistent with the statistical view of nature. According to the mechanical conception, a law is a generalization which is universally true, a description of an invariant relationship. It is implicit in this concept that causal relations are specific, determinate, and of the order of certainties. Effect and cause are linked by iron necessity, unvarying, universally the same. Since such generalizations deal, of necessity, with individual cases, it follows that mechanical laws assume the historical type of knowledge. Such laws are not concerned with averages or probabilities, but with unvarying relationships, holding for every instance. A single exception, a single

"obstreperous fact," and the generalization is invalid. Mechanicalption

This concept of law is quite inconsistent with the statistical view of nature. In the world of practical events historical knowledge, knowledge of all specific instances or events of a given type, is not to be had. We must content ourselves with knowledge of averages, of types, that is to say, with statistical knowledge. But in generalizing with respect to such averages we cannot put our statements into the form of invariant mechanical laws, for our knowledge stops short of all individual cases. We can conceive of such laws, and of the relation of certainty which they imply, but their existence cannot be established by perception. Our generalizations must deal with trends, tendencies, average relationships, relationships which may lie anywhere along the scale from perfect independence to complete dependence. If the relation falls short of complete dependence, the generalization holds not with certainty, but with some degree of probability. In reality, most laws relating to the physical realm and all

laws dealing with social phenomena are of this latter class, describing relationships which do not hold universally, with absolute certainty. To adopt the mechanical view is to confine one's knowledge to but one limit of a whole series of possible relations, a limit so rarely attained in nature as to be virtually a pure concept, not a perceptual fact.

From the statistical point of view, therefore, the notions of invariant mechanical laws, of perfect causal relationship, of complete certainty, represent only extremes or boundaries. They are Pearson's conceptual limits, arising from the necessities of our thinking apparatus, rather than from our actual perceptions. In its attempt to find simplifying principles in a vast and complex environment the mind, with its "all too human love of certainty," conceived of relationships as thus direct and obvious-one cause and one effect. Such a conception has the merit of simplicity, but in its assumptions of absolute sameness and of invariant law it fails to accord with fact.1

In the light of this approach, therefore, we forego the searching for sole causes and, instead, seek to measure the degree of association found in experience between related phenomena. Not the isolation of first and only causes, but the determination of the degree of change in one factor associated with a given change in a correlated factor is the task with which we are generally confronted in a world organized on the statistical plan.

The generalizations which describe relations in such a world, moreover, are never looked upon as necessarily final formulations of truth. Scientific generalizations pass through stages of development, first approximations being improved upon by securing more comprehensive formulae with higher degrees of probability. Thus it would ap

1 The following passage from J. M. Keynes is of interest in connection with the discussion of the statistical view of nature, particularly with reference to the character of natural laws:

"The kind of fundamental assumption about the character of material laws on which scientists appear commonly to act, seems to me to be much less simple than the bare principle of Uniformity. They appear to assume something much more like what mathematicians call the principle of the superposition of small effects, or, as I prefer to call it, in this connection, the atomic character of natural law. The system of the material universe must consist, if this kind of assumption is warranted, of bodies which we may term legal atoms, such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state. We do not have an invariable relation between particular bodies, but nevertheless each has on the others its own separate and invariable effect." A Treatise on Probability, 249.

pear that Einstein, if his theories be correct, has not overthrown but has merely introduced a correctional factor into the Newtonian scheme. This process of growth, which can hardly be reconciled with a thorough-going mechanical view, is quite consistent with the statistical concept of law.

This whole conception of the essential problem in scientific study is most effectively summarized in the following passage from Pearson : "That the universe is a sum of phenomena, some of which are more, others less closely contingent on each other is the conception, wider than that of causality, which we may at the present time draw from our widening experience. The aim of science ceases to be the discovery of 'cause' and 'effect'; in order to predict future experience it seeks out the phenomena which are most highly correlated From this standpoint it finds no distinction in kind but only in degree between the data, method of treatment, or the resulting 'laws' of chemical, physical, biological, or sociological investigations. They all provide, or should provide (i) a conceptual routine, which is a functional expression of average experience, and (ii) a measure of the possible or probable deviations from this routine, which is a guide to the amount of variation in experience. Because this is small in some physical experiences, it has been neglected as a matter of little practical value-a routine may vary even considerably without its upsetting conduct. But this neglect is no justification for the assumption that our conceptual routine, a product of the statistical treatment of experience, represents a real functional relationship at the back of phenomena. There is always, in non-organic as in organic phenomena, a residual variation. . . . From this standpoint the universe appears as a universe of variation rather than as a universe controlled by the law of causation in its narrowest sense. No phenomena are causal; all phenomena are contingent, and the problem before us is to measure the degree of this contingency which we have seen lies between the zero of independence and the unity of causation." 1

The technical methods of measuring relationship when the tie is one of contingency and not of certainty need not be discussed here. The point to be emphasized is that these tools are of general scientific interest, that their potentialities are only suggested by the results so far secured in limited fields. They represent a fundamental change in the whole matter of looking at the problem of causal relationship, and an attitude toward natural and social laws which is 1 The Grammar of Science, 173-4.

so far removed from the traditional view as to constitute almost a revolution in thought.

While this view of natural law and of the problem of causal relationship has been presented most clearly and with the keenest appreciation of its significance by Pearson, such a concept is implicit in the writings of other scientists, and has been explicitly developed by several authors. Clerk Maxwell's arguments in favor of the statistical view of nature lead directly to such a conception of natural law. All statements of tendency, Royce has asserted, are attempts to frame laws of this correlational type, but with no explicit statement of the probabilities involved. "The term, tendency,' he writes, "is, in every exact usage which you can give it, an essentially statistical term. To say that a has a tendency to lead to b is to declare that a more or less certainly and definitely known proportion of events of the class a are followed by events of the class b."'1 And again the law for which the statistical method seeks is no longer a law that is ideally statable in terms of an invariant differential equation or in terms of any other timeless invariant. When found, the statistical law is an account of a collection of facts in terms of averages involving many events. Jevons' attitude on the problem of causation is quite in accord with the views expressed above. Of contemporary writers, Henry L. Moore has not only clearly described the essential characteristics of statistical laws but has demonstrated the fruitfulness of the concept when applied to economic problems.

2

4

It is a noteworthy fact that this concept of the nature of laws is in complete agreement with the views of philosophers of the pragmatic school who approach the problem from quite a different angle. John Dewey speaks of generalizations as "not fixed rules. . . but instrumentalities for . . . investigation, methods by which the net value of past experience is rendered available for present scrutiny of new perplexities. . . they are hypotheses to be tested and revised

1 Royce, loc. cit., 559.

2 Ibid., 557.

3 "I have no objections to use the words cause and causation, provided they are not allowed to lead us to imagine that our knowledge of nature can attain to certainty. . . . A cause is not to be distinguished from the group of positive or negative conditions which, with more or less probability, precede an event. In this sense there is no particular difference between knowledge of causes and our general knowledge of the succession of combinations in which the phenomena of nature are presented to us or found to occur in experimental inquiry." The Principles of Science, 226.

4 The Laws of Wages, chap. I.

by their further working."1 And elsewhere he writes, "Nature is not an unchangeable order, unwinding itself majestically from the reel of law under the control of deified forces. It is an indefinite congeries of changes. Laws are not governmental regulations which limit change, but are convenient formulations of selected portions of change followed through a shorter or longer period of time, and then registered in statistical forms that are amenable to mathematical manipulation." 2

In summary: Our useful knowledge of events in the world about us is essentially statistical in character; that is, it is not concerned fundamentally with unique, individual events, but with aggregates of events which may be described in terms of averages, of typical characteristics. In generalizing about such aggregates we are of necessity precluded from speaking in terms of invariant laws. Such laws as may be formulated for the purpose of summarizing past experience must be formulated in terms of averages, and therefore assert not certain relations but only probable and approximate relations, insofar as individual events are concerned. Such a view of the nature of law involves a recognition of the purely imaginary character of the concept of causation, in the sense of a direct and perfect relationship between phenomena. Association and correlation are the terms which replace causation, as probability and approximation replace the concept of certainty.

3. QUANTITATIVE METHOD AND THE LAWS OF ECONOMICS

In the light of this approach we may revert to the data, problems and methods of economics. The discussion above has not been concerned with the materials with which the economist deals, but it bears directly and significantly upon the problems of economics.

No attempt can be made here to classify the data of economics. The economist must concern himself with a complex variety of things and events-with births and deaths, with industrial technology and business practices, with tons of coal produced and barrels of flour consumed, with wages, rents, interest rates and commodity prices, with industrial accidents and days lost through unemployment, with human acts, emotions and judgments. Perhaps the widest single category is that of prices, but this falls far short of including all the

1 Human Nature and Conduct, 240-1.

2 The Influence of Darwinism on Philosophy and Other Essays, 72. Henry L. Moore, in "The Statistical Complement of Pure Economics" (Quart. Jour. Econ., xxiii, 16) has quoted part of this passage, and has called attention to the kinship between the pragmatic and the statistical view.