ABSTRACT

WHEN we compare the development of class structures and that of asymmetrical transitive relations we find a paradox. On the one hand, it seems that seriation (which is an additive arrangement of asymmetrical transitive relations) is more intuitive than an additive sequence of class-inclusions, because it corresponds to a far simpler perceptual configuration. On the other hand, the multiplication of classes seems to correspond to a fairly simple perceptual configuration, so that matrix tests can be solved independently of any operational methods, while the multiplication of asymmetrical transitive relations (involving a matrix with series ordered along the horizontal and vertical axes) may well be much more complicated because it involves a double asymmetry. However, without proceeding to an actual experiment, we cannot be sure of this. We do know that serial correspondence, as opposed to serial multiplication, is just as easy as simple seriation. In other words, a child who can build a single series can also build two or three! <¿4 <C <C C j… A 2 C 2 · · · A$ <C C… and he can tell that C corresponds with C2 and C3, etc. 2 But the correspondence between series is symmetrical in this structure. It does not involve a new asymmetry in a different dimension. What we need is an investigation on the multiplication of asymmetrical transitive relations, so that we can properly compare its development with that of multiplicative cross-classification. We have in fact carried out such an enquiry on 52 subjects.