Isomorphism in Information Carrying Systems

For the information theorist, the lawful generalizations that subsume instantiations of properties in the environment and instantiations of properties of perceptual representations determine the latter’s content. Perceptual representations are also commonly thought to be isomorphic to what they represent, which presents the information theorist with a puzzle. What role could isomorphism play in perceptual representation when lawful generalizations determine content? I show that in order for the information that they carry to be available to cognition, perceptual representations must be isomorphic with respect to the constituent structure of the properties that they represent. Isomorphism therefore plays an important role in the information theorist’s account of perceptual representation, even though it plays no role in determining content.