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

572 Raymond Boudon
the values of aij and ail varying with the run of the tests (combinations of A,
and E,).
It should also be noted that in the whole of the above we have been considering
acquirement situations in their simplest state (constant stimulus). Of
course learning theory also concerns itself with the problems of discrimination,
of generalization, of extinction, etc. Several models, on the lines of those
described, have been devised to analyse these situations. Bush thus, in one of his
models, uses a double series of operators: on the one hand conditioning operators
which modify the probability of an Ai response when Ej has occurred; and
on the other generalization operators, which modify the probability of an At
response when the event Ej has not occurred.
It has been deemed useful to dwell at some length on the models associated
with the theory of learning, for the mathematical theory of learning is surely
ope of the important occurrences in the recent history of the applications of
mathematics to the human and social sciences. A research tradition with hundreds
of investigations already to its credit has been created in less than ten years
and has profoundly modified the nature of the experimentation. Today virtually
any experiment carried out in the domain of 1earning.process research must use
a mathematical formalization. Furthermore, we are witnessing the emergence
in learning theory, at both the research and informational levels, of cumulative
progress rare in the human and social sciences. Lastly, we should note that the
evolution of the theory’s methodology illustrates a general tendency : replacement
of groping after functions by a mathematical translation of the elementary
mechanisms.
Nevertheless, it should be stressed that research in the domain of the learning
process, despite the numbers and cumulative character of the investigations, has
as yet achieved only very elementary results, as the examples given show.
It is difficult to say whether the research strategy illustrated by the theory of
learning can spread to other fields. The writer himself sees no reason why it
should not be applied, for instance, to the analysis of the functioning of groups
in social psychology and of social processes in the domain of sociology or of
demography. That something of the sort is possible is demonstrated by a few
relatively isolated examples already mentioned, such as Cohen’s or Orcutt’s
models.
Znductive models used with observation
The observational sciences such as economics or sociology lack the possibilities
of simplification open to researchers in, say, psychology. This creates more
serious obstacles to the introduction of mathematical formalism. As we saw in
the previous section, experiments like those used by learning theory place the
subject in extremely simple situations. In contrast, the economist or sociologist
is confronted with complex situations which cannot be streamlined.
The inductive methods used by the economist belong essentially to the field
of econometrics, Progress made in econometric research, although consider-
able, cannot be said to exhibit breakthroughs analogous to those found in
psychology (with learning theory or genetic epistemology) or in linguistics