(l) In parallel with the possible,2 the necessary is relative to the subject's
activities. If the necessity of p is to be defined as the impossibility of not-p,
the impossible at a particular level of psycho-genesis or of the history of
science can become possible at a later level. Earlier connections then turn out
to be retrospective "pseudo-necessities" or "pseudo-impossibilities". Even if
the necessity of p is to be defined by the fact that not-p entails
contradictions, those contradictions might in the sequel be removed or even,
to the contrary, p can lead to contradictions in one system despite its
necessity in some other. Moreover, if the "possible" characterises the
beginnings of a genesis qua differentiation from an initial state, the
"necessary" is no more a priori than the possibles are pre-determined. The
"necessary" is elaborated throughout construction, attaining only terminal
completeness qua expression of integration typical of a system which is more
or less closed, however elementary. But just as there is no absolute
beginning, since each genesis rests upon prior development, neither could
there be termination in an absolute (final) sense. All necessity relies upon
"reasons" (Piaget, 2006) which, however valid, call upon deeper
counterparts. Even in those pure axiomatisations upon which formal logic
today relies, "we are never in the presence of a form which has been
definitively established and which could be envisaged. At each moment, we
are engaged in an upward movement towards form" as Ladri¨¨re (1973, pp.
55-56) puts it, "and that ascent towards form has therefore no assignable
term".

In short, necessity is not an observable,3 giving rise to a reading from
objects. Necessity is always the result of constructions inherent in a subject.
If necessary connections can be designated as "states", these are merely
phases of an endless process that it is imperative to consider in its own right
in its intrinsic dynamism. Hence arises the interest in the study of its
formation during psychogenesis. Notice at the outset, there is a double
interest in that the stages observed in this respect turn out to be parallel to
those which are characteristic of the development of the "possible". There
arises then a progressive interaction between these two modalities. This very
synthesis gives birth to operational structures.

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