What does “isomorphism between conscious representations and the structure of the world” mean?

Behavioral and Brain Sciences 25 (3):346-347 (2002)
Abstract
Perruchet & Vinter's provocative article challenges a series of interesting issues, yet the concept of isomorphism is troublesome for a series of reasons: (1) isomorphism entails some sort of dualism; (2) isomorphism does not entail that a piece of the world is a representation; and (3) it is extremely difficult to provide an explanation about the nature of the relation of isomorphism.
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