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[[!meta title="The Psychology of Intelligence"]]
* Author: Jean Piaget
## Logic and psychology
An axiomatics is an exclusively hypothetico-deductive sci-
ence, i.e., it reduces to a minimum appeals to experience (it even
aims to eliminate them entirely) in order freely to reconstruct its
object by means of undemonstrable propositions (axioms),
which are to be combined as rigorously as possible and in every
possible way. In this way geometry has made great progress,
seeking to liberate itself from all intuition and constructing the
most diverse spaces simply by defining the primary elements to
be admitted by hypothesis and the operations to which they are
subject. The axiomatic method is thus the mathematical method
par excellence and it has had numerous applications, not only in
pure mathematics, but in various fields of applied mathematics
(from theoretical physics to mathematical economics). The use-
fulness of an axiomatics, in fact, goes beyond that of demonstra-
tion (although in this field it constitutes the only rigorous
method); in the face of complex realities, resisting exhaustive
analysis, it permits us to construct simplified models of reality
and thus provides the study of the latter with irreplaceable dis-
secting instruments. To sum up, an axiomatics constitutes a “pat-
tern” for reality, as F. Gonseth has clearly shown, and, since all
abstraction leads to a schematization, the axiomatic method in
the long run extends the scope of intelligence itself.
But precisely because of its “schematic” character, an axiomat-
ics cannot claim to be the basis of, and still less to replace, its
corresponding experimental science, i.e. the science relating to
that sector of reality for which the axiomatics forms the pattern.
Thus, axiomatic geometry is incapable of teaching us what the
space of the real world is like (and “pure economics” in no way
exhausts the complexity of concrete economic facts). No axi-
omatics could replace the inductive science which corresponds
to it, for the essential reason that its own purity is merely a limit
which is never completely attained. As Gonseth also says, there
always remains an intuitive residue in the most purified pattern
(just as there is already an element of schematization in all intu-
ition). This reason alone is enough to show why an axiomatics
will never be the basis of an experimental science and why there
is an experimental science corresponding to every axiomatics
(and, no doubt, vice versa).
-- page 30
It is true that in addition to the individual consistency of
actions there enter into thought interactions of a collective order
and consequently “norms” imposed by this collaboration. But
co-operation is only a system of actions, or of operations, car-
ried out in concert, and we may repeat the preceding argument
for collective symbolic behaviour, which likewise remains at a
level containing real structures, unlike axiomatizations of a
formal nature.
For psychology, therefore, there remains unaltered the prob-
lem of understanding the mechanism with which intelligence
comes to construct coherent structures capable of operational
combination; and it is no use invoking “principles” which this
intelligence is supposed to apply spontaneously, since logical
principles concern the theoretical pattern formulated after
thought has been constructed and not this living process of con-
struction itself. Brunschvicg has made the profound observation
that intelligence wins battles or indulges, like poetry, in a con-
tinuous work of creation, while logico-mathematical deduction
is comparable only to treatises on strategy and to manuals of
“poetic art”, which codify the past victories of action or mind
but do not ensure their future conquests. 1
-- page 34
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