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560 Raymond Boudon
‘theory’ is also given. These set out to analyse well-defined phenomena, but
unlike game theory, they consist of models which are to a large extent independent
of one another from the point of view of logic, as, for instance, with the
‘theory of economic cycles’. This title is made to cover a multitude of models
characterized by a common aim: to analyse the cyclic phenomena which are
features of almost all modern economic systems. The problem of the theory of
cycles, in other words, is to explain why all modern economic systems seem subject
to cyclic phenomena following a definite pattern. Briefly, the models
it is required to construct are not inductive but theoretical. As we see, when we
talk of the theory of economic cycles the word is used in a very different sense
from the one given it in the expression ‘game theory’. The models subsumed
under economic cycle theory are self-contained theorizations between which, on
occasions, the only connexion is their theme, despite the fact that certain of
them may be considered variously complex versions of the same hypothesis
(for example the successive versions of Kalecki’s m0de1).3~
Yet other disciplines have ‘theories’ comparable in logical nature with economic
cycle theory. For instance, in sociology, there is the analysis of diffusion
and migration phenomena, and in anthropology, the analysis of kinship systems.
Finally there are various ‘general theories’ where ‘theory’ is used in a third
sense, one example being the formal theory of grammars. Here we are not
dealing with a collection of more or less independent models, as with the theory
of economic cycles. Nor have we a theory closely tied in with some reality like
game theory (the latter, indeed, is inconceivable without the notion of rational
behaviour, which it endeavours, of course, to formalize, but which is based on
psychological and sociological experience). Rather we have here a true mathematical
theory which has got the same distance away from its ‘raw material’ as
Euclidean geometry from natural circles and lines. This theory has already
been mentioned in passing and at this point an example will give a better understanding
of its nature.
The analysis of natural languages led Chomsky to conceive a rule of grammar
as a rewriting rule. Consider for instance the following rules, where x + y
stands for the expression ‘x can be rewritten y’:
s +AB
A + CD
B +ED
C -+ a, the, another
D -+ ball, boy, girl
E +hit, struck
Applying these rules, we obtain the sentences: ‘a ball hit the girl’, ‘a boy hit
the girl’, both grammatically correct. All we need retain of this is the idea that
a rule of grammar can be expressed in the form x 3 y, where x and y represent
either terms in a non-terminal vocabulary (in this instance such vocabulary is
made up of terms S, A, B, C, D, E.), or terms in a terminal vocabulary (in this
instance: a, the, another, ball, boy, girl, hit, struck). This representation of
grammatical rules led Chomsky and other writers to set themselves problems of
formalization, and to raise the question, for example, of the types of language