ABSTRACT
WE now propose to study the development of the notion of a complementary class. A complementary class is one which may be combined with a given class, 5, or C to yield the next higher ranking class B, C, or D. For example, if A is the class of ducks, B that of birds and C that of animals, their respective complementary classes are those which we called “secondary” when describing “elementary groupings”: A’ (birds other than ducks) is the complement of A relative to B, B’ (animals which are not birds) is the complement of B relative to C, etc. (Such classes are called “complements of the first kind” in lattice theory.) The importance of this relation lies in the fact that it raises the more general problem of negation. Given a class A, the class not-^ is the complement of A relative to Z, being the largest_class in the system, (i.e. the universe of discourse: Z—A = not -A, or A). The psychologist wants to know how children understand the class not-y4. Does a child think of the class of not-ducks as including pebbles, stars and fairy-tale characters; or does he usually connect it with other birds (A’) or other animals (C—A = A’ + B ‘)?
