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

554 Raymond Boudon
particular migration phenomena would prove to be explainable by reference to
a law of the Newtonian type. Thus it was postulated that the migratory flux
between two poles could be considered in general terms as proportional to the
product of their respective masses (defined by their respective populations)
and inversely proportional to the square of the distance:
MM'
Migratory flow = a - DZ
It was very soon realized that this function was unusable and under the best
circumstances yielded only the roughest answers. The law was accordingly
suppled, this time by introducing two free parameters adjustable at discretion
to the particular situations being studied, giving the function :
MM'
Migratory flow = a -
OB
The results were little better than before, and migration theory marked time
until it was realized that the particular aspects of the situations analysed also
had to be axiomatized if one wanted to arrive at valid results. The most impor-
tant contribution in this connexion is represented by the researches of Stouffer26
which demonstrate more particularly that the axioms must be varied according
as the researcher is concerned with intra-urban or inter-city migration and that
the structural characteristics of the poles of the migration (e.g. the characteris-
tics of their social composition) can in some cases be ignored, and in others
must be taken into consideration, depending on the scale of the observation.
This doctrine gave Stouffer distinctly better results than were obtained by his
predecessors. But it has one important implication, namely that the idea of a
general law expressing the phenomena must be abandoned and that achieving
an efficient model in a given situation means the adjunction to the general
axioms of particular axioms differing from one case to another.
In the confidence of after knowledge, it can, no doubt, be asserted that such a
conclusion is obvious. From another angle, however, it is indisputable that the
idea of resorting to a mathematical formalization to express a reality particular
in character is utterly at variance with the epistemological model offered by
classical physics, to which the social and human sciences clung slavishly through-
out the whole of the nineteenth century and part of the twentieth.
Of course the analysis presented above does not exhaust the difficulties of
the notion of model. Yet it certainly suffices to show why an entirely new
notion took the place of the notions of theory and law: because the latter
imply properties such as unicity, generality, verifiability, they are in most cases
unsuitable for describing the results of the attempted formalizations applied
to the analysis of human phenomena.
The notion of struct~re.~7
The notion of structure, like the notion of model,
is somewhat obscure and bears different meanings according to the context in
which it is used.
Nevertheless, as in the case of the model, the uses made of the idea permit us