Piaget postulated that one of the fundamental actions of people was to
classify objects and actions. These classifications could be grouped
together on the basis of the number of times these actions coordinate
precursor actions. We call this number the order of hierarchical compl
exity when it refers to task demands and the stage when it refers to p
erformance. Fourteen orders of such complexity have been analyzed. Thi
s paper introduces the notion that equivalence classes can be ordered
according to their hierarchical complexity. Here, an adult task shows
how the identity relations at each stage are used to define equivalenc
e classes of the next stage. Results showed that some adults with post
graduate education detect metasystematic (12th order) equivalence clas
ses.