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

556 Raymond Boudon
larly causal relationships. The most frequent instance of a control mechanism is
the thermostat. When the temperature of the system reaches a maximum NI,
the thermostat cuts off the heat-source. The system then cools down progressive-
ly until the thermostat turns on the heat-source when the temperature in the
system falls to a minimum temperature N2. By complicating this basic control
schema considerably, satisfactory representations say, of certain economic
systems, can be got.
However, the logic of the systems dealt with by cybernetics is too simple to
represent certain other systems, notably those capable of learning. The fact is
that, if we define learning as the possibility of making new responses to specified
situations, a ‘cybernetic’ system is incapable of learning : the responses are
predetermined. Cybernetic systems, therefore, are more advanced than the
mechanical systems characterized by unidirectional causality - without being
sufficiently developed to permit of the representation of systems capable of
learning.
For some years past these ‘higher’ systems have been the subject of sustained
research which is given the blanket title general systems theory. These
researches are recorded more particularly in the General Systemsza series.
111. THE DIFFERENT TYPES OF MODELS
As was said at the beginning, it is impossible to cover all the applications of
mathematics in the social and human sciences in the space available. However,
it will be useful to provide a more direct account of the methods and models
used in the social and human sciences than can be got from what has gone before.
It is difficult to classify the mathematical models used by the social and human
sciences according to criteria acceptable to all thedisciplines. Thus the economists
attach great importance to the distinction between dynamic and static models, or
open-ended and closed models. Psychological measurement theory, on the other
hand, distinguishes between deterministic and probabilistic models. The ethnologists
are emphatic in separating statistical and ‘mechanical’ models, a distinction
which does not coincide with that made by the economists, while the biologists
and sociologists insist on the difference between stochastic and nonstochastic
models. But we can also contrast descriptive and inductive models;
distinguish between predictive and explicative models like the economists and
sociologists ; or emphasize the importance of the models defining asymmetric
relations on a set of ordered variables like the sociological survey methodologists.
In short, it is impossible to use the criteria of a particular discipline to classify
the models used by the others.
Moreover it is little to the point to rely on a classification based on the type
of mathematics used.
The difficulty in establishing a satisfactory classification comes from the fact
that each model can be characterized according to a multitude of criteria whose
significance varies with the case and the discipline. Take for example Arrow’s29
analysis of the notion of the general interest: we can say that it is ‘theoretical’