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

542 Raymond Boudon
social sciences described above are not the only ones which could be pointed out.
Another such function which can be instanced is what might be called quasi-
experimentation. It is particularly important in the case of disciplines like eco-
nomics or sociology which, with some exceptions, cannot conduct experiments.
Where this is so, it is possible to represent a particular real position by a model,
and study the latter’s behaviour under different structural conditions. This is a
typical situation in mathematical economics: since it is usually impossible to
manipulate the economic variables experimentally, to determine the effect of
their variations, the researcher sets about constructing models incorporating the
quantities in which he is interested in the form of parameters, so as to make a
quasi-experimental study of the effects of these parameters on the behaviour of
the system symbolized by the model.
The quasi-experimentation function is not new. However, it has been consid-
erably extended: it is no longer a monopoly of economics; sociology now uses
it on a large scale as is evidenced by the work of Simon or Abelson on group
dynamics, by Rapoport’s researches on the phenomena of diffusion, etc.4
A more general account of the rBle of mathematics in the development of the
human sciences wil be given in Section D below. All that has been sought to do
here is to bring out the diversification in the functions of mathematics which the
human sciences’ recent developments entail.
C. The new fields of research dependent on a mathematical methodology
Although this section covers some of the same ground as the preceding one,
it is as well to recapitulate briefly the main fields of research which have latterly
become accessible to methodologies of a mathematical type.
In psychology and social psychology, we have the considerable development
of test theory and measurement theory. These are such technical areas that
henceforward only the professional mathematician or statistician wil be able
to contribute to them. As we have seen, they provide the main subject matter of
the review Psychometrika; in addition, new works in the field are continually
appearing.5 As well as the long-recognized fields of measurement and test
theory, there is the mathematical theory of learning, of recent, but rapid devel-
opment, on which one or more publications appear each year.6 Again, logic and
mathematics are now resorted to on a large scale in developmental psychology
in general, and genetic psychology in particular.
In economics, there has been a considerable development of econometric
methods both for micro-economic phenomena and for macro-economic phe-
nomena of limited incidence, while important progress has been achieved of
recent years in the field of optimization procedures. Today, linear and dynamic
programming are used extensively on partial phenomena when the utility func-
tion can be defined.
Furthermore, research into optimization at the macro-economic level is
being intensively pursued.
In social psychology and sociology, mathematical models are being used for