Formal Representation of Qualitative and Quantitative Reversible Operations

In this chapter I present an approach using contemporary mathematical models of human judgment to explore the issue of whether the relations among a set of variables are conceptualized reversibly. Specifically, are the judgments of each of a set of variables based on a single, fully reversible set of mental operations?1 This topic is important to psychologists for three reasons. Piaget (1947/1960) proposed that reversible mental operations distinguish true intelligence from intuition and perception. If the transition to reversible thought is an important developmental event, then there is a need for precise representations of knowledge that is reversible. It is equally important to describe states of irreversible and partially reversible knowledge in order to describe the transition from irreversible to reversible thought.

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