Second order isomorphism: A reinterpretation and its implications in brain and cognitive sciences

Abstract

Shepard and Chipman's second order isomorphism describes how the brain may represent the relations in the world. However, a common interpretation of the theory can cause difficulties. The problem originates from the static nature of representations. In an alternative interpretation, I propose that we assign an active role to the internal representations and relations. It turns out that a collection of such active units can perform analogical tasks. The new interpretation is supported by the existence of neural circuits that may be implementing such a function. Within this framework, perception, cognition, and motor function can be understood under a unifying principle of analogy.