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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