Isomorphism in mind
Date of Completion
Many models of the mind, both philosophical and psychological, invoke the mathematician's concept of isomorphism. Various theories posit (i) that representation consists in isomorphism between a representation and that which it represents, (ii) that spatially distributed sensory states are realized in brain states to which they are isomorphic, or (iii) that psychological state spaces are realized in neural state spaces to which they are isomorphic. Among these theories, isomorphism is sometimes used as a methodological guide or constraint, and other times it plays a role in general philosophical accounts. The dissertation proposes a taxonomy of various uses of representation, and examines the usefulness of isomorphism for both the methodological and philosophical enterprises in theories of perception and certain theories of representation. I argue that isomorphism is not a useful guide to methodology, and probably cannot serve as a constraint on theories. Isomorphisms are too common, and some theories face Goodman-style worries about arcane isomorphisms between structures with non-natural properties. Many philosophical theories also require that isomorphism be constrained to be useful. I describe worries for theories of representation on which isomorphism is sufficient for representation. I argue that property realism is not a sufficient constraint to ground a theory of representation according to which isomorphism is sufficient for representation, and describe a stronger sort of realism. Finally I argue that philosophical claims that isomorphism is a necessary feature of representation are either trivially true or matters for empirical work to decide. ^
Whitmyer, Virgil Gale, "Isomorphism in mind" (2000). Doctoral Dissertations. AAI9988049.