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

540 Raymond Boudon
heard pronounced or are themselves forming for the first time. Such facts sug-
gest the notion that the corpus of grammatical rules of a natural language is to
be regarded not as an aggregation of arbitrary rules, but as a system of specific
rules following logically from a few basic rules. In other words, the problem is
to show, as in the preceding anthropological example, the real but hidden co-
herence of a set of apparently arbitrary laws.
A later section will analyse in detail how these problems led to the develop-
ment of an elaborate methodology of which was born what it is now appropriate
to call mathematical linguistics.
It should incidentally be noted that the term structural analysis is often
applied to the methods whereby the coherence of systems can be analysed. The
rules on permitted and forbidden marital unions characterizing a society, or
the rules for the formation of grammatically correct utterances in a natural
language are examples of such systems.
c. A third function of mathematical methodology which can be regarded as
recent consists in its increasing application to the problems of experimentation.
Of course, this function only relates to those human or social sciences in which
it is possible to set up experiments on the subject matter, notably psychology
and social psychology.
By way of a first example, social psychology offers an impressive volume of
experiments and investigations of all sorts into the formation and changing of
opinions, attitudes or individual feelings as functions of the changes occurring
in the group or environment to which the subject belongs. Since the work of
Heider and of Festinger in particular, a fact strongly emphasized is that the
individual, when he is obliged to modify one of his feelings or attitudes - as when
he is placed in a situation where he is in a minority of one-reacts by undertaking
a general reorganization of his correlative attitudes and opinions. Summarizing
these theories, one could put it that in a social situation which incites him to
modify one of his opinions, his beliefs, etc., the individual will reorganize the
whole body of his opinions, beliefs, etc. so as to restore at least cost the balance
destroyed.
While, until recently, these theories (Festinger’s theory of cognitive dissonance,
Heider’s theory of cognitive organization, etc.) had given rise to many experi-
ments of the classical type, over the last few years a number of writers, notably
Cartwright and Harary, have been using graph theory to formaIize them, ex-
pressing the notion of equilibrium in the representations by the formal notion
of the balanced graph. This formalization, although still very elementary, has
nevertheless had the twofold effect firstly of explicating the concepts embodied
in the theories discussed above, and secondly of contributing to the formulation
of a precise experimental schema which has subsequently led to intensification
of experimentation in this domain.
The second example, this time from psychology, is provided by the psycholog-
ical theory of learning. This theory has been under continuous study for many
years past and for almost as long there have been some psychologists who were
convinced that the hypotheses relating to learning mechanisms should be given
mathematical expression.