The Nature of Propositional Deduction—a Piagetian Perspective


operations of thought
propositional reasoning
propositional deduction
Boolean algebra



Logic was once thought to describe the laws of thought; however, a plurality of logics has now replaced classical logic, obscuring rather than clarifying the nature of deduction with an embarrassment of riches. In cognitive science, on the other hand, logic is not thought to be a psychological theory of human reasoning. Research on human reasoning has focussed on deduction, although human reasoning is thought to be much richer, and two competing theories dominate contemporary discourse in cognitive science—the syntactic, formal-rule, and the semantic, mental-model theory. Jean Piaget also proposed a psychological theory of reasoning, and, in contrast to the dominant theories, he advocated an operatory theory. Deduction is an integral part of Piaget’s theory, and, in this paper, I briefly outline Piaget’s operatory theory of propositional reasoning before explicating the nature of deduction embodied in it. I conclude that the nature of propositional deduction according to Piaget lies in the interpropositional grouping, a natural structure at the heart of propositional reasoning constituted by a closed system of operations of thought regulated by laws of transformation. I then argue that the nature of propositional deduction lies specifically in the lattice constituted by the inclusion/order relations between the propositions of the interpropositional grouping. Piaget did not conceive of the interpropositional grouping as a logic; nevertheless, I wind up arguing that a logic conceived as Piaget intimated would complement the plurality of logics with a natural logic.



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