Inquiry into Inquiries: Essays in Social Theory

By Arthur F. Bentley; Sidney Ratner | Go to book overview

CHAPTER FIVE
Sociology and Mathematics

I
THE COMMON PROBLEM OF ANALYSIS

When a paper is offered upon the subject of sociology and mathematics, one may reasonably expect it to discuss those many mathematical techniques which have so usefully been taken over by the social sciences, such as series, graphs, correlations, probabilities, and other statistical methods; or, if not these, then those mathematical constructions of demand, price, money, and competition which are known as pure economics. We shall have here, however, no concern with any of these topics.

Such mathematical techniques and constructions require, before they can be put to use, the provision by the social sciences of the statistical data, or, alternatively, of the postulational elements, with which they are to deal. These data and postulational elements in their turn require, before they can be assembled, or before they can be given precision, an analysis of the general situation to be investigated, and the determination of a scheme of classification. Mathematical techniques contribute nothing directly to the analysis; and the wider values of the results secured through the techniques are always dependent upon the adequacy of the antecedent classifications and postulatory fixations which the analysis has furnished,1 though it is of course true that work of this kind may often stimulate a return to the preliminary procedures of analysis.

Sociology is much more than a manipulation of data assumed as factually well established and adequately provided for its use. Mathematics is much more than a compendium of technical devices.

Mathematics is itself the great science of rigorous analysis; and to

____________________
1
In making this statement I have directly in mind the present status of mathematical technique as exhibited, for example, by Griffith C. Evans in his Mathematical Introduction to Economics, 1930, and by Irving Fisher, in his Willard Gibbs' lecture, "The Application of Mathematics to the Social Sciences," Bulletin of the American Mathematical Society, April, 1930. For an appraisal of the important work of Professor Evans, see Part II, Section 6, of this chapter.
From The Sociological Review, Vol. XXIII, No. 2 ( July, 1931), pp. 85-107; No. 3 ( October, 1031), pp. 149-72.

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