Main trends of research in the social and human ... - unesdoc - Unesco

Mathematical models and methods 537
mathematical methodology and the question of computer applications in a
multidisciplinary context. These new ventures and realignments have changed
the situation as regards the question of methodology in the social sciences from
one in which-leaving aside the statistical reviews such as the Journal de la
Sociite‘ de statistique de Paris or the Journal of the American Statistical Associa-
tion - two major journals (Econometrica, founded in I932 and Psychometrika,
founded in 1935) held the field to one when there are between ten and a score
of reviews which are either specifically methodological or carry a large propor-
tion of methodological articles.
B. Differentiation of the functions performed by mathematics
The second main feature of current trends, also very striking, is the diversifica-
tion beginning to appear in the functions performed by mathematics in the
human and social sciences.
As we have said, the pre-modern period is characterized essentially by one
‘pure theory’ tradition, another dominated by mathematical statistics and a
third involving the seeking of curve-fitting models. Today, mathematics is
taking on new functions, of which some examples follow:
a. In disciplines like sociology and psychology, the development of the
observation techniques together with the growing quantity of data collected
have engendered a whole multitude of methods and techniques, the main func-
tion of which is to enable the investigator to get his bearings in a mass of in-
formation exceeding his intuitive grasp.
Let us consider, for instance, the methods of factorial analysis associated with
the names of Thurstone, Hotelling and, more recently, Guttman. Looked at from
the point of view of their principles, they are grading, classifying or typologizing
techniques. In other words, they are intended to replace the intuitive procedures
used in ordinary life and for some scientific problems, and grade or order ob-
jects on the basis of a given number of characteristics observed in them. The
intuitive procedure is the one we are using when we observe the behaviour of
two children in n situations, and then declare the first more intelligent than the
second. It is likewise the procedure used by Max Weber in defining his famous
ideal types. One could put it that the techniques we are discussing are meant to
reproduce the logic of these intuitive procedures, while eliminating the scientific
risks implicit in reliance on intuiticn. Obviously, the inadequacy of intuition
increases with the volume of data collected. In situations like that arising in
psychometrics when dozens of tests are given to a multitude of subjects, it is
obviously impossible to rely on intuitive techniques. Hence the idea of construct-
ing grading, classification or typologizing models. The need for this kind of
model was so strongly felt, notably in disciplines like psychology, social
psychology and sociology, that there is now an extremely voluminous corpus of
mathematical models and methods for solving grading, classification and typo-
logizing problems in observational situations of the utmost diversity.
It was again the limitations of intuition which led sociologists to develop a