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272 Jean Piaget
either unconsciously or deliberately, constantly touching upon these questions
of epistemology and of the foundations of mathematics.
A recent paper by P. Suppes read at a Symposium on ‘Models and Formalizazation
of Behaviour’ is entitled ‘The Psychological Foundations of Mathematics’.
In a recent publication on Mathematical L~arning,~5 in which psychologists
like Cronbach, Kessen, Suppes and Bruner have collaborated with the mathe
matician, Stone, there are constant references to processes of spontaneous
formation which concern the epistemology of mathematics as much as the psychology
of development. The Geneva research has been focused on both these
aspects at once, a point to which I shall return under IV.
m. With regard to physics, its contacts with psychology seem at first sight to be
virtually non-existent, except for the exchanges of methods which were noted in
section 4 in connexion with physical Gestalts (in the direction physics +
psychology) and information theory (in the opposite direction or in both direc-
tions). In fact, the epistemology of physics poses psychological problems for at
least two reasons. First, it raises the question of understanding how intuitions
seemingly fundamental and permanent such as absolute time, simultaneity at a
distance, conservation of the object as a corpuscle, etc., can have been so easily
modified by the theory of relativity and microphysics. Incomprehensible as they
would be if it were a case of innate intuitions or a priori forms in the Kantian
sense, these transformations of cognitive instruments are quite natural from the
standpoint of psychogenetic constructivism, and even the strophe and anti-
strophe of wave and corpuscle in microphysics are reminiscent of the difficul-
ties involved in constituting the schema of the permanent object between 4-5
and 12-18 months, and of the obvious psychological fact that this permanence
is very closely linked from its inception to the possibilities of localization in
space (and to the ‘group of displacements’).
The second reason for linking the two disciplines, is that physicists have
discovered interdependences between the effects produced by the manipula-
tions of the experimentor and the effects due to connexions between the phenom-
ena themselves. This fundamental fact naturally raises the problem of the
nature of objectivity, and conduces to supplementing Bridgman’s operation-
alism by a psychological theory of the development of mental processes
showing that decentering leading to objectivity is but a decentering in relation
to the ego of the observer, and is correlative with a logico-mathematical struc-
turalization due to the activities of the epistemic subject and proceeding from the
coordinations of actions (whence ‘groups’, etc.) and no longer from isolated ac-
tions which are sources of possible illusions. Thus the paradox is removed on
which Planck often dwells in replying to Mach: that although physical knowl-
edge begins with sensation (linked to isolated actions), objectivity consists in
turning one’s back on it and not shutting oneself up in it.
These patent or virtual links between physics and psychology have in fact
brought about certain modest beginnings of collaboration. Two examples come
to mind. The fist is that of the works of Kuhn, a very well-known physics
historian, who created the epistemology of the revolutions in the succession