According to Pylyshyn, depictive representations can be explanatory only if a certain kind of first-order isomorphism exists between the mental representations and real-world displays. What about a system with second-order isomorphism (similarities between different mental representations corresponding with similarities between different real-world displays)? Such a system may help to address whether “depictive” representations contribute to the visual nature of imagery.

The human visual system is capable of learning both abstract and specific mappings to underlie shape recognition. How could dissimilar shapes be mapped to the same location in visual representation space, yet similar shapes be mapped to different locations? Without fundamental changes, Chorus, like other single-system models, could not accomplish both mappings in a manner that accounts for recent evidence.

Implementational-level evidence of dissociable neural subsystems is a critical element that is missing from the analysis in the Schyns et al. target article. The question of whether fixed or flexible features are used in visual form recognition may have different answers for different subsystems; the evidence that features typically are created during category learning may apply most directly to a specific visual form subsystem.

Studies with humans have failed to produce evidence that any direct causal relation exists between the asymmetry of one function in an individual and the asymmetry of a different function in that individual. Without such evidence, factors external to an individual's nervous system, such as social interactions, may play crucial roles in explaining the directions of all asymmetries at all levels.

Dienes & Perner argue that the explicit representation of an individual to which a property is attributed requires explicit representation of the attributed property. The reasons for this conclusion are similar to the reasons why another of their conclusions may be considered suspect: A property may be explicit without an explicit representation of an individual or the predication of the property to an individual. We question the latter conclusion and draw connections to neurophysiological and cognitive evidence.