the same type, are not identical. This is particularly true in the realm of economics. Here not only is it impossible to secure comprehensive and exhaustive knowledge of individual events, but such events have significance for us only when considered in the mass. We would have no use for knowledge of the multitude of individual events, even were such knowledge to be had. From this view, the generalizations which we term laws are not to be accepted as statements of invariant mechanical relationships, but as statements of tendencies, of average relations. In fields where the degree of variation is slight, the conception of perfect mechanical relationship-cause and effect linked by invariant ties-approximates the truth, but material error is involved in the strict application of this mechanical concept in fields characterized by wide variation and a multiplicity of causes. This is the situation in the field of economics. Hence even the most exact of the laws of economics must be interpreted in this statistical sense. These facts bear directly upon the question of method in the study of economic problems. While it is recognized that induction and deduction must constantly supplement each other, it is suggested that the relative importance of these methods varies in different scientific fields. The methods of deduction may be expected to be most fruitful in fields characterized by slight variation, in which there is a close approach to the conditions of sameness and invariant relationship which are essential to the validity of the mechanical view. While the test of facts must be met here, it will be satisfied by a relatively small amount of inductive evidence. In fields marked by wider variation, where the generalizations must admit of many exceptions, the fruitfulness of deductive reasoning is more limited, and the direct study of facts, assembled and classified, must play a dominant part in scientific investigation. Induction increases in importance as the causes in operation increase in number, as variation becomes, more pronounced, and as the relations between phenomena depart farther from the simple cause and effect connection which is assumed in the application of mechanical methods. Since a multiplicity of causes and wide variation within classes of phenomena are characteristic of the data of economics, induction must ever be one of the most important tools employed by the economist. To a greater extent than ever before economists are today seeking to secure the accuracy and precision which quantitative methods ensure. Induction in a quantitative science of economics involves the handling of numerical facts in the mass; its methods must be sta 1 tistical. Statistical induction is, in all essential respects, similar to induction of the more general type, except that its results are quantitative in form, and that its generalizations are not necessarily universal. Its conclusions deal with frequencies, averages, or with relationships which hold on the average, or in a certain percentage of cases. Exceptions and limitations are recognized. That is, the generalizations which are the objects of statistical induction are of the type described in discussing the meaning of law from the statistical view. They represent the only valid type of generalization, if this view of nature be correct. Since statistical generalizations hold only with a degree of probability, it is essential that in any given case we determine the reliability of the result by measuring this degree of probability. This necessitates the determination of probabilities empirically. A measure of probability may be secured in this way, but it is a measure to which absolute certainty can never attach. From sheer force of necessity we must employ these empirical methods which furnish approximations to the true probabilities involved; they constitute "the only logic for the practical man. But their approximate character should always be recognized, and every effort should be made to reduce the margin of error. This margin of error may be reduced in two general ways. The first is based upon the assumption that there is some measure of initial probability in favor of an inductive conclusion. The greater this a priori element the more certain we may be that our conclusion has validity, and that the results secured by the method of inverse probabilities are a true measure of the reliability of this conclusion. If the a priori element be entirely absent, and we trust to sheer empiricism, a strong and unmeasurable degree of doubt must attach to the generalization. The second method of increasing the reliability of inductive findings requires the testing of the stability of the statistical ratio or measure of relationship under varied conditions. This purely statistical method of examining the stability of a given result, when the data are re-grouped in significant ways, may serve to increase materially the strength of a statistical argument. This process is more fruitful than that of merely increasing the number of cases. By these two methods the degree of doubt which enters into every inductive argument may be reduced to a minimum, and the probability of error involved in any extension of the results reduced until it approximates the measure derived by ordinary mathematical methods. The development of the statistical method has placed in the hands of the inductive economist a trenchant tool, and has given his results precision and practical utility which in the past they have lacked. Yet a loose employment of this tool constitutes a dangerous pitfall. Because the statistical method presents quantitative results, in the form of mathematical equations and coefficients, an impression of absolute accuracy which is frequently thoroughly misleading is conveyed. It is, therefore, highly essential that the logical limitations of this method be clearly understood, and that all necessary precautions be observed in using statistical results as foundations of inductive arguments. There are dangers in the employment of induction to which the worker in the statistical field is particularly exposed. There is danger that immersion in technique will blind him to unsound assumptions and inherent limitations. And there is the abiding danger of over-emphasis on mere fact gathering, of attempting to find truth through the weight of a multitude of facts alone. Facts must be illuminated by the play of speculative reasoning, by "the light of the idea," before they can have significance, before valid generalizations can be secured. That there is a logical reason for the sterility of unilluminated facts has been emphasized in stressing the need of an initial a priori probability in favor of a given conclusion. This initial probability is perhaps strongest when, in Broad's phrase, we feel that we have got hold of the fundamental ground plan of nature in a given field. We "flounder about in the dark till some man of genius sees what are the really fundamental factors and the really fundamental structure of the region of phenomena under investigation." When we have secured this ground plan, the "limping methods of empiricism" become fruitful, and inductions carry conviction. Yet here we are not harking back to pure deduction as the basic method of science. The understanding of the ground plan which explains and illuminates a wilderness of miscellaneous facts is secured ordinarily only by a study of the facts. It does not leap full-formed out of chaos, but grows in the mind of the man of genius, or in the consciousness of the race, by successive approximations. Facts must furnish the fuel for the light of the idea. Darwin started to assemble facts in true Baconian fashion, he says, and arrived only after years of study and classification at the great generalization which gave meaning to his multitudinous data. It may be that it is only given to the man of genius to arrive at the profound generalizations which shape the course of scientific study for centuries. But such generalizations are, in fact, the products of the labor of thousands of workers who have derived the limited conclusions, the tentative generalizations, the empirical formulae which suggest the all-inclusive generalization that may finally top the structure. The aim of that economic research which would be most fruitful in a practical and immediate way must be the limited generalizations which relate to specific groups and specific conditions. In the derivation of such "laws" quantitative induction based upon statistical results must play a leading part. That the conclusions obtained by statistical methods relate, in general, only to specific cases, and can be generalized only with extreme precaution and careful qualification, is perhaps not altogether unfortunate. Economists who seek all-embracing laws are not unlike philosophers in search of the absolute. Practical and immediate problems are too often neglected in the chase of a rainbow in the shape of a generalization of universal validity. Better immediate knowledge which will help to remedy specific maladjustments than general laws to which there are so many exceptions that they fit nothing. The practical problems facing economists today will be more readily solved and human welfare will be more effectively furthered by quantitative study of specific conditions than by the attempt to apply vague generalizations of doubtful validity. In economics, as in philosophy, "Interest . . . shifts from an ultimate goal of good to the direct increments of justice and happiness that intelligent administration of existent conditions may beget and that present carelessness or stupidity will destroy or forego.' 1 John Dewey, The Influence of Darwinism on Philosophy, and Other Essays, 11. |