EQUIVALENCE: A THEORETICAL OR A DESCRIPTIVE MODEL?

Abstract

The question is asked: Ooes the mathematical theory of sets provide a theoretical or a descriptive model of equivalence relations in behavior? The argument is made that mathematical set theory contains generalizations that encompass many real-world phenomena, including relations among the environmental and behavioral c0'!lponents of reinforcement contingencies. If pairs of elements that make up an n-term reinforcement contingency are members of an equivalence relation, then emergent relations between elements of the contingency simply illustrate the reflexive, symmetric, and transitive properties that define equivalence. Mathematical set theory defines the equivalence relation in a way that describes behavioral observations perfectly. The behavioral observations are therefore no more than exemplars of the mathematical generalization. Although the mathematical description of equivalence relations in behavior is characterized by features that a good theory must possess -consistency, coherency, productivity, and parsimony-no behavioral theory is involved in that description.