Shepard's approach is regarded as an attempt to rescue, within an evolutionary perspective, an empiricist theory of mind. Contrary to this, I argue that the structure of perceptual representations is essentially co-determined by internal aspects and cannot be understood if we confine our attention to the physical side of perception, however appropriately we have chosen our vocabulary for describing the external world. Furthermore, I argue that Kubovy and Epstein's “more modest interpretation” of Shepard's ideas on motion perception is based on unjustified assumptions. [Kubovy & Epstein; Shepard]

The probabilistic analysis of functional questions is maturing into a rigorous and coherent research paradigm that may unify the cognitive sciences, from the study of single neurons in the brain to the study of high level cognitive processes and distributed cognition. Endless debates about undecidable structural issues (modularity vs. interactivity, serial vs. parallel processing, iconic vs. propositional representations, symbolic vs. connectionist models) may be put aside in favor of a rigorous understanding of the problems solved by organisms in their natural environments. [Shepard; Tenenbaum & Griffiths]

The evidence for a kinematics of the mind is confounded by uncontrolled properties of pictures. Effects of illumination and of picture-plane geometry may underlie some evidence given for a process of mental rotation. Pictured rotation is confounded by picture similarity, gauged by gray-level correlations. An example is given involving the depicted rotation of Shepard-Metzler solids in depth. [Hecht; Kubovy & Epstein; Shepard; Todorovič]

Kubovy and Epstein distinguish between systems that follow rules, and those that merely instantiate them. They regard compliance with the principles of kinematic geometry in apparent motion as a case of instantiation. There is, however, some reason to believe that the human visual system internalizes the principles of kinematic geometry, even if it does not explicitly represent them. We offer functional resemblance as a criterion for internal representation. [Kubovy & Epstein]

Shepard's article presents an impressive application of the mathematics of symmetry to the understanding of motion. However, there are basic psychological phenomena that the model does not handle well. These include the importance of the orientations of rotational motions to salient reference systems for the understanding of the motions. An alternative model of the understanding of rotations is sketched. [Shepard]

Shepard proposes that the human mind relies on screw displacement because of its adaptive simplicity and uniqueness. I discuss this hypothesis by assessing screw displacement with respect to (1) other plausible spatial transformations, (2) a variety of criteria for adaptive efficiency and utility, and (3) a variety of psychological conditions in which observed responses discriminate amongst alternative spatial procedures. [Shepard]

Recent developments in both evolutionary theory and in our ideas about development suggest that genetic assimilation of environmental regularities may occur on shorter timescales than those considered by Shepard. The nervous system is more plastic and for longer periods than previously thought. Hence, the internal basis of cognitive-perceptual skills is likely to blend ontogenetic and phylogenetic learning. This blend is made more rich and interactive by the special cultural scaffolding that surrounds human development. This being so, the regularities of the environment which have been genetically assimilated during the emergence of modern human beings may themselves be the products of human action. [Shepard]

Shepard's theoretical analysis of generalization is assumed to enable an objective measure of the relation between objects, an assumption taken on board by Tenenbaum & Griffiths. I argue that context effects apply to generalization in the same way as they apply to similarity. Thus, the need to extend Shepard's formalism in a way that incorporates context effects should be acknowledged. [Shepard; Tenenbaum & Griffiths]

Having seen the development of Shepard's program at close hand, I have been inspired by the sophistication of his results. However, his program deals with only half of what is needed: Shepard's research tells what the perception/cognitive process is about, it does not tell how that process is implemented. True, Shepard has recourse to the “how” of process in evolution, but that is not the “how” of everyday implementation. For that we need to know the brain processes with which we can implement Shepard's insights. [Shepard]

Barlow's concept of the exploitation of environmental statistical regularities may be more plausibly related to brain mechanisms than Shepard's notion of internalisation. In our view, Barlow endorses a bottom-up approach to neural coding and processing, whereas we suggest that feedback interactions in the visual system, as well as chaotic correlation dynamics in the brain, are crucial in exploiting and assimilating environmental regularities. We also discuss the “conceptual tension” between Shepard's ideas of law internalisation and evolutionary adaptation. [Barlow; Shepard]

Shepard has challenged psychologists to identify nonarbitrary principles of mind upon which to build a more explanatory and general cognitive science. I suggest that such nonarbitrary principles may fruitfully be sought not only in the laws of physics and mathematics, but also in the logical entailments of different categories of representation. In the example offered here, conceptualizing mental events as indexical with respect to the events they represent enables one to account parsimoniously for a wide range of empirical psychological phenomena. [Shepard]

The perceptual circularity demonstrated by R. Shepard with respect to hue turns out to be a sphericity of color perception based on color excitation vectors of neuronal level. The spherical color model implicitly contains information concerning generalization under color learning. Subjective color differences are “computed” in neuronal nets being represented by amplitudes of evoked potentials triggered by color change. [Shepard]

Shepard promotes the important view that evolution constructs cognitive mechanisms that work with internalized aspects of the structure of their environment. But what can this internalization mean? We contrast three views: Shepard's mirrors reflecting the world, Brunswik's lens inferring the world, and Simon's scissors exploiting the world. We argue that Simon's scissors metaphor is more appropriate for higher-order cognitive mechanisms and ask how far it can also be applied to perceptual tasks. [Barlow; Kubovy & Epstein; Shepard]

The Kubovy-Epstein proposal for the formalization of the relation between kinematic geometry and perception of motion has formal problems in itself. Motion phenomena are inadequately captured by the relational structures and the notion of isomorphism taken over from measurement theory. [Kubovy & Epstein]

The stratification in depth of chromatically homogeneous overlapping figures depends on a minimization rule which assigns the status of being “in front” to the figure that requires the formation of shorter modal contours. This rule has been proven valid also in birds, whose visual neuroanatomy is radically different from that of other mammals, thus suggesting an example of evolutionary convergence toward a perceptual universal. [Shepard]

Shepard's notion of “internalisation” is better interpreted as a simile than a metaphor. A fractal encoding model of visual perception is sketched, in which image elements are transformed in such a way as to maximise symmetry with the current input. This view, in which the transforming system embodies what has been internalised, resolves some problems raised by the metaphoric interpretation. [Hecht; Shepard]

Shepard's general approach provides little specific information about the implementation of laws in brains. Theories that turn on an isomorphism between some domain and the brain, of which Shepard's is one, do not provide specific detail about the implementation of the structures they propose. But such detail is a necessary part in an explanation of mind. [Shepard]

Roger Shepard's description of an abstract representational space defined by landmark objects and kinematic transformations between them fails to successfully capture the essence of the perceptual tasks he expects of it, such as object recognition. Ultimately, objects are recognized in the context of events. The dynamic nature of events is what determines the perceived kinematic behavior, and it is at the level of dynamics that events can be classified as types. [Shepard]

Kubovy and Epstein's main quarrel is with the concept of “internalization.” I argue that they underestimate the aptness of this metaphor. In particular, an emulator which predicts unfolding events can be described as an internalization of external structures. Further, an emulator may use motoric as well as perceptual resources, which lends support to Hecht's proposal. [Hecht; Kubovy & Epstein]

Hoffman is worried that perception itself leaves no time for the computation and compilation of statistics, but this has never been proposed. It is the underlying mechanisms that are thought to have evolved in response to the statistics of sensory stimulation, and which are capable of adjusting their parameters in response to changes in these statistics.