The allegory of isomorphism

Isomorphism has become a key concept for the analysis of representation in many contexts: perceptual experience, mental imagery, scientific theories, and visual artwork may all be described as standing in isomorphisms to their targets. Yet isomorphism is a technical term from mathematics—how are we to evaluate its use in fields such as philosophy, psychology, neuroscience, or physics? I suggest that we should understand appeals to isomorphism as allegorical; the upshot of this suggestion is that isomorphism claims always operate on two distinct levels of significance, with different standards of precision and evaluation. Recognizing these levels as distinct changes the landscape of debate for isomorphism-based accounts of representation: it both dissolves the well-known triviality objection to these accounts and undermines strong forms of structural realism