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

532 Raymond Boudon
and Cournot’s on those of the law courts. And it must not be forgotten that
the works of statisticians like Poisson, Lexis or Quktelet were born of reflec-
tion on statistical distributions often sociological. Even so, it can be reckoned
that it is only recently that well-established traditions of mathematical research
have developed in sociology, previous to which this discipline has nothing to
show which is comparable with the work of the economists on equilibrium
theory, or that of the psychologists in psychometrics.
If we had to fix the birth-dates of modern mathematical methodologies in the
main human sciences, then, it would have to be the end of the nineteenth cen-
tury for economics, 1g20-1g30 for psychology, and the years following the
Second World War for sociology. In this respect ethnology is probably in the
same situation as sociology.
The history of the applications and uses of mathematics has been more
agitated in the human than in the natural sciences. As there is some doubt as to
whether the modern methodology has completely ironed out the difficulties of
the pre-modern period, it will be as well to give a brief account of the charac-
teristics of that period’s mathematics.
A very striking feature is that for a long time there were three quick separate
types of mathematical approach to human phenomena, with no meeting point
in very many cases. Thus from the very first attempts at a mathematical ap-
proach worth mentioning we get a situation extremely different from that charac-
terizing the natural sciences generally, and physics in particular since Galileo.
Specially notable in the applications of mathematics to the human sciences is
the divorce between the theoretical and the inductive approaches: at the risk of
oversimplifying, it could be said that for the most part the theoretical approaches
remain mostly speculative while the inductive do not embody theoretical
propositions. This situation, which sharply differentiates the methodologies of
the human and the natural sciences, is indisputably typical of the ‘pre-modern’
period. But it is by no means certain that the snag has been completely overcome
even today.
The three types of mathematical approach to human phenomena distinguish-
able throughout the whole pre-modern period are as follows:
a. To begin with, we find a biform theoretical tradition which may be
either normative or speculative. There is a plethora of examples of the normative
theoretical tradition at the end of the eighteenth century in France: the mathe-
matics of Buffon, Laplace and Condorcet are all ethical mathematics. They
reason upon choosing the best lines of action, on the means of regulating the
functioning of juries so as to avoid judicial errors, on the manner of analyzing
voting figures for optimum service of the general interest, etc. In other words,
the earliest applications of probability calculus are aimed at immediate utility :
their point is to direct action. This form of mathematics can, if one wishes, be
deemed to prefigure what today is called operational research.
Alongside this normative tradition, there emerge, rather later, with Cournot
in particular, mathematical theories which can be rated as speculative to the
extent that usually no concern is shown to check them against experience or
observation. Their function is more to analyse the consequences of the axioms