Ludwig von Mises
Sociology and History
8. Qualitative and Quantitative Analysis in Economics
Sociology cannot grasp human action in its fullness. It must take the actions of individuals as ultimately given. The predictions it makes about them can be only qualitative, not quantitative. Accordingly, it can say nothing about the magnitude of their effects. This is roughly what is meant by the statement that the characteristic feature of history is concern with the individual, the irrational, life, and the domain of freedom. For sociology, which is unable to determine in advance what they will be, the value judgments that are made in human action are ultimate data. This is the reason why history cannot predict things to come and why it is an illusion to believe that qualitative economics can be replaced or supplemented by quantitative economics. Economics as a theoretical science can impart no knowledge other than qualitative. And economic history can furnish us with quantitative knowledge only post factum.
Social science is exact in the sense that it strives with conceptual rigor for an unequivocally defined and provable system. It is idle to dispute over whether one should make use of mathematical forms of presentation in sociology, and particularly in economics. The problems confronting sociology in all its branches, including economics, present such extraordinary difficulties that, in the eyes of many, even the most perplexing mathematical problems possess the advantage of being more easily visualized. Whoever believes that he cannot do without the help that the reasoning and terminology of mathematics affords him in the mastery of economic problems is welcome to make use of them. Vestigia terrent! Those theorists who are usually designated as the great masters of mathematical economics accomplished what they did without mathematics. Only afterwards did they seek to present their ideas in mathematical form. Thus far, the use of mathematical formulations in economics has done more harm than good. The metaphorical character of the relatively more easily visualized concepts and ideas imported into economics from mechanics, which may be warranted as a didactic and occasionally as a heuristic expedient as well, has been the occasion of much misunderstanding. Only too often the criticism to which every analogy must be subjected has been neglected in this case. Of primary importance is what is set forth in words in the preliminary statement that has to serve as the starting point for further mathematical elaboration. This statement, however, is always nonmathematical. Whether or not its further elaboration in mathematical terms can be useful depends on the correctness of this initial nonmathematical statement. To be sure, if the mathematical elaboration is itself incorrect, it will arrive at incorrect results even though it may start from a correct statement; but mathematical analysis can never expose an error made in an incorrect statement.
Even the mathematical sciences of nature owe their theories not to mathematical, but to nonmathematical reasoning. Mathematics has a significance in the natural sciences altogether different from what it has in sociology and economics. This is because physics is able to discover empirically constant relationships, which it describes in its equations. The scientific technology based on physics is thereby rendered capable of solving given problems with quantitative definiteness. The engineer is able to calculate how a bridge must be constructed in order to bear a given load. These constant relationships cannot be demonstrated in economics. The quantity theory of money, for example, shows that, ceteris paribus, an increase in the quantity of money leads to a decrease in the purchasing power of the monetary unit, but the doubling of the quantity of money does not bring about a fifty percent decline in its purchasing power. The relationship between the quantity of money and its purchasing power is not constant. it is a mistake to think that, from statistical investigations concerning the relationship of the supply of and the demand for definite commodities, quantitative conclusions can be drawn that would be applicable to the future configuration of this relationship. Whatever can be established in this way has only historical significance, whereas the ascertainment of the specific gravity of different substances, for example, has universal validity.
Economics too can make predictions in the sense in which this ability is attributed to the natural sciences. The economist can and does know in advance what effect an increase in the quantity of money will have upon its purchasing power or what consequences price controls must have. Therefore, the inflations of the age of war and revolution, and the controls enacted in connection with them, brought about no results unforeseen by economics. However, this knowledge is not quantitatively definite. For example, economics is not in a position to say just how great the reduction in demand will be with which consumption will react to a definite quantitative increase in price. For economics, the concrete value judgments of individuals appear only as data. But no other science?not even psychology?can do any more here.
To be sure, even the valuations of individuals are causally determined. We also understand how they come about. That we are unable to foretell their concrete configuration is due to the fact that we here come up against a boundary beyond which all scientific cognition is denied to us. Whoever wants to predict valuations and volitions would have to know the relationship of the world within us to the world outside us. Laplace was unmindful of this when he dreamed of his cosmic formula.
 Simmel seeks in an ingenious way to express this singularity of the historical in his discussion of individual causality. Cf. Simmel, op. cit., pp. 100 ff.
 Mitchell shares this illusion with many others. Cf. Mitchell, "Quantitative Analysis in Economic Theory," American Economic Review, XV, 1 ff.
 Cf. Dingler, Der Zusammenbruch der Wissenschaft (Munich, 1926), pp. 63 ff.; Schams, "Die Casselschen Gleichungen und die mathematische Wirtschaftstheorie," Jahrb?cher f?r National?konomie und Statistik, Series III, Vol. LXXII, pp. 386ff. Painlev? aptly states the objection to the mathematical treatment of economics in his preface to the French edition of Jevons' Principles (Paris, 1909), pp. v ff.
 Cairnes, The Character and Logical Method of Political Economy, pp. 118ff.; Eulenburg, "Sind historische Gesetze m?glich?" Hauptprobleme der Soziologie (Munich, 1923), 1, 43.
 Therefore, it would also be a mistake to attempt to attack the statement in the text by referring to the fact that the natural sciences borrowed the statistical method from sociology and now seek to make it serve their own purposes.