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486 Jean Piaget
abnormal (concepts peculiar to living matter and devoid of meaning in physico-
chemistry), there nevertheless exists a kind of limiting point which both sepa-
rates and unites regulations and operations (see section 5). This point of transition
might well in many cases be that between the individual and the inter-individual.
b. A second general problem which follows on from that we have just said is
that of types of obligations or rules. Logical necessity is translated into coherent
operations capable of constituting deductive structures, but there exist a large
number of obligations and rules without intrinsic consistency, arising essen-
tially from constraints of a more or less contingent or momentary kind, the
extreme case being that of the rules of spelling whose arbitrary nature is
sufficiently demonstrated by history. Even independently from the questions
raised under a, it is evident therefore that not every obligation extends into
possible ‘operations’ in the limited sense in which we have adopted this term
(section 5), but that a certain number of systems of rules do not go beyond the
level of structures of regulations.
The second general problem raised by systems of rules is thus to construct,
by means of interdisciplinary comparisons, a hierarchy of varieties of structures,
starting with operational structures of various forms and ending with those
which are based on regulations, likewise of various forms and involving a greater
or lesser degree of chance.
c. The third great problem raised by systems of rules is that of interference
between rules belonging to different fields. This problem, some examples of
which we shall presently discuss, occurs in two forms. First there is the question
of effective intersections of structures leading to interferences between rules : for
example, a legal system is a body of rules sui generis, that is to say irreducible
to moral or logical rules; but objectively it involves all kinds of interferences
with those other two systems by the mere fact that it must not contradict
either of them (which may be easier in one case than in another).IQ But there are
also intersections due to the subject’s realization of the structure, this realization
perhaps being adequate but partial or distortive as a result of various subjective
influences. Thus the usual grammar of teachers is nothing other than a very
incomplete and in part distortive realization of linguistic structures and general-
ly interferes with obligations of the quasi-moral type.
7, Examples of interferences in the field of logical structures
The case of logical structures is a good example of how impossible it is today
to isolate a form of research which yet is very distinct and possesses every
characteristic that might have made of it a kind of absolute, secure from interdisciplinary
contacts. Formal logic is at present perhaps the most exact of
disciplines in terms of the rigour of its demonstrations. It can be placed at the
starting point of mathematics, so much so that one might hesitate to include it
among the sciences of man and that those responsible for the organization of
the present volume have not included it among the disciplines selected for study.
Above all, logic, using as it does an axiomatic or ‘formalising’ method, ignores the