to manipulate a
boomerang. The instance merely suggests a kind of skill that he has
never been led to acquire.

Yet it is possible to distinguish intellectual skill, or better skills,
from physical or athletic prowess. Primarily, it is directed at the
formation and use of concepts, and the concept is only a symbol that can
be substituted for experiences. A well-built concept is a part of a
system of concepts where relations have taken the place of real
connections in such a fashion that, forgetting the actuality, it is
possible to present situations that have never occurred or at least are
not immediately given at the time and place of the presentation, and to
substitute them for actual situations in such a fashion that these may
be expediently met, if or when such situations present themselves. An
isolated concept, that is, one not a part of any system, is as mythical
an entity as any savage ever dreamed. Indeed, it would add much to the
clearness of our thinking if we could limit the use of "intelligence" to
skill in constructing and using different systems of concepts, and speak
concretely of mathematical intelligence, philosophical intelligence,
economic intelligence, historic intelligence, and the like. The problem
of creative intelligence is, after all, the problem of the acquisition
of certain forms of skill, and while the general lines are the same for
all knowledge (because the instruments are everywhere symbolic
presentations, or concepts), in each field the situation studied makes
different types of difficulties to be overcome and suggest different
methods of attaining the object.

In mathematics, the formal impulse to reduce the content of fundamental
concepts to a minimum, and to stress merely relations has been most
successful. We saw its results in such geometries as Hilbert's and
Peano's, where the empty name "entity" supplants the more concrete
"point," and the "1" of arithmetic has the same character. In the social
sciences, however, such examples as the "political" and the "economic"
man are signal failures, while, perhaps, the "atom" and the "electron"
approach the ideal in physics and chemistry. In mathematics, all further
concepts can be defined by collections of these fundamental entities
constituted in certain specified ways. And it is worth noting that both
factually and logically a collection of entities so defined is not a
mere aggregate, but possesses a differentiated character of its own
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