Truth-functional logic in formal operational thinking: Inhelder and Piaget's evidence.

Abstract

According to Inhelder and Piaget, a fully developed formal operational thinker uses all 16 binary operations of truth-functional logic in solving problems. The only evidence they offered, however, was a single protocol from their physical task, Role of Invisible Magnetism. Using this one protocol and the Inhelder-Piaget method of analysis, the present investigators attempted to duplicate the results of Inhelder and Piaget. They found examples and evidence, however, for only 8 of the 16 operations; and they discovered that 8 of the Inhelder-Piaget analyses were faulty. Several important questions are raised, for example, Do fully developed formal operational thinkers actually use all 16 binary operations of truth-functional logic?1 Requests for reprints should be sent to Terrell

Post-Formal Operations? A Need for Further Conceptualization

“…The usefulness of the INRC group and the 16 binary operations for explaining performance on formal opera tional tasks has come under attack [Bynum et al, 1972;Weitz et a!., 1973]. Broughton [1981], on the other hand, has pointed out some conceptual inadequacies of the ap proach of Bynum et al [1972] and Weitz et al [1973], However, if formal operational structures become integrated into a more en compassing post-formal structure, the nature and validity of the structure underlying for mal operations will certainly have relevance for post-formal operational conceptualiza tions.…”

A Constructivist Interpretation of Formal Operations

“…Their analysis of Gou's protocol has. however, been subjected to negative scrutiny by logicians who use propositional logic to analyse this protocol [Bynum et al" 1972], It is sufficient to notice here that Inhelder and Piaget claim merely that it is possible for a stage III subject to run through all 16 operations, not that this is necessary. In formal operational thinking, an individual has the ability to run through all 16 combinations but it is not necessary for this ability to be completely displayed.…”

Piaget’s Structural Developmental Psychology

“…The prejudgment is that the competence-performance distinc tion has no validity or can safely be ignored. The irony is that, in an endeavor to bring data to bear critically upon theory, such researchers as Bynum et al (1972) and Weitz et al (1973) ignore precisely that conceptual distinction (of competence from performance) which was originally formulated to clarify the relevance of evidence to theoretical models.…”

“…Since Piaget has not explicitly developed concepts like those of deep and surface structure and transformations, it is hard to see even what the equivalent empirical studies might be. Neverthe less, let us consider in some detail the twin papers of Bynum et al (1972) and Weitz et al (1973). These are especially significant because of the collaboration involved between psychologists and logicians, and because they are often cited (e.g., Russell, 1978, p. 207;Neimark, 1975, p. 55%,Ennis, 1978Keating, 1979) as major challenges to Piaget's logical model of cognition and even to the very notion of competence itself.…”

“…In this failure, the studies are quite representative of a body of Anglo-American literature that is critical of Piaget. Bynum et al (1972) did a textual analysis of the single protocol of a 15-year-old subject on Inhelder's invisible magnetization task. They found evidence for only half of the 16 binary propositional operations which Inhelder and Piaget (1958) claimed to have demonstrated in this subject.…”