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authorSilvio Rhatto <rhatto@riseup.net>2017-09-01 18:45:03 -0300
committerSilvio Rhatto <rhatto@riseup.net>2017-09-01 18:45:03 -0300
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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