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484 Jean Piaget
later at these mechanisms. As to which of these two fundamental lines of
approach will eventually prevail, it is not for us to say. For the moment we
should merely note the rather striking convergences becoming apparent between
schools of thought which may be described by the very general name of genetic
structuralism in psychological research on development, in the study of ‘genera-
tive grammars’ in linguistics, and in certain analyses, outwardly very different,
in economics and Marxist-inspired sociology.
6. Systems of Rules
The third problem we have raised (under c) often finds a possible solution in the
following form: when following the formation of a structure one observes on its
completion some modifications in the subject’s behaviour which are difficult to
explain otherwise than by that completion itself, in other words by the ‘closure’
of the structure. These are fundamental facts which are translated in the consciousness~4
of the subject by feelings of obligation or of ‘normative necessity’
and in his behaviour by obedience to ‘rules’. Let us recall that according to the
habitual, if not general, terminology of experts in the study of ‘normative facts’15
a rule is recognised by the fact that it imposes an obligation but can be either
violated or respected, contrary to a causal ‘law’ or determination which suffers
no exceptions unless it be by reason of contingency variations due to a mixture
of causes.
An example should explain this r61e of the closure of structures.IB A child
of 4 or 5 years is generally unable to deduce that A < Cif he has noted separately
that A < B and then that B < C (but without having seen A and C together).
Moreover, he is unable to construct a seriation of slightly differentiated
objects A < B < C < D . or manages to do so only by groping. On the other
hand when he later achieves a flawless construct consisting in the successive
placing of the smallest of the remaining elements (hence comprehension of the
fact that an element E is simultaneously greater than the preceding elements,
E > D, C, etc., and smaller than the following elements, E < F, G, etc.), he
resolves by so doing the problem of transitivity and will no longer judge A < C
as undecidable or simply probable, but as necessary (‘it’s got to be’, etc.) if he
has seen that A < B and B < C. This feeling of logical necessity, difficult to
evaluate like all states of consciousness, will be translated in behaviour by the
use and recognition of transitivity.
Many other examples could be quoted in other fields of individual development,
such as the emergence of a sense of justice as a highly imperative norm
succeeding a morality of obedience at the age where relations of reciprocity are
structured outside or in opposition to relations of subordination. In the historical
development of societies it seems clear likewise that democratic ideals have
gained currency as a function of changes in structures, etc.
Thus the study of rules or normative facts constitutes an important sector of
the study of structures, the more so as it provides a link between structuralism
and the actual behaviour of subjects. Moreover, such rules are observed in all the