A few findings from our laboratory are provided as evidence favoring “isomrphism” in filling-in. One is the responsivity of macaque-cortical area V1 cells to a stimulus designed for surface filling-in at the blind spot. Another is a phenomenological observation of motion aftereffect confined within a filled-in surface at the blind spot. Our recent study on the monkey's perception of surface filling-in at a scotoma is also mentioned.

Analytical isomorphism is an instance of the demand for a transparent relation between vehicle and content, which is central to the mind-body problem. One can abandon transparency without begging the question with regard to the mind-body problem.

Implicit and explicit filling-in phenomena should be distinguished. Blind spot phenomena and mechanisms of boundary completion can be accounted for by implicit filling-in. Surface regions are “painted” with perceptual quantities, such as brightness, by explicit filling-in. “Filling-in” and “finding-out” relate to different computational tasks. Mechanisms of purposive computation (e.g., for navigation) evaluate local measurements, thus “finding out”; whereas mechanisms for grasping might require passive reconstruction, thus “filling in.”

(1) The purported evidence for neural filling-in is not evidence for filling-in, but just for long-range dynamic interactions. (2) Vision is perhaps not an “illusion,” but at any rate it is not “pictorial.” (3) The idea of the “world as an outside memory” as well as MacKay's “conditional readiness for action” may help approach an “enactive” theory of vision.

The case against analytical isomorphism is made within an evolutionary framework. The relevance to neural filling-in is discussed. Homomorphism is argued for as a conceptually superior substitute for isomorphism, and the implications for the personal/subpersonal distinction are explored.

Pessoa et al. fail to make a clear distinction between visual perception and subjective visual awareness. Their most controversial claims, however, concern subjective visual awareness rather than visual perception: visual awareness is externalized to the “personal level,” thus denying the view that consciousness is a natural biological phenomenon somehow constructed inside the brain.

Discriminating behavior depends on neural representations in which the sensory activity patterns guiding different responses are decorrelated from one another. Visual information can often be parsimoniously transformed into these behavioral bridge-locus representations within neuro-computational visuo-spatial maps. Isomorphic inverse-optical world representation is not the goal. Nevertheless, such useful transformations can involve neural filling-in. Such a subpersonal representation of information is consistent with personal-level vision theory.

Findings in dynamic unit formation suggest that completion processes reflect the optics of our world. Dynamic unit formation may depend on patterns of motion signals that are consistent with the causes of optical changes. In addition, dynamic completion conforms to a local curvature minimization constraint. Such relational aspects of vision are important to consider in linking perceptual experience and neural activity.

Filled-in sensations exhibit a distinctive mélange of causal features, resembling perceptual sensations in some respects and imagery in others. This commentary identifies several of these shared causal features and advances the hypothesis that filled-in sensations may constitute the primordial species of imagery, the evolutionary neurofunctional precursor of paradigmatic forms of imagery.

It is fruitful to think of the representational and the organism-centered approaches as complementary levels of analysis, rather than mutually exclusive alternatives. Claims to the contrary by proponents of the organism-centered approach face what we call the “basketball problem.”

Pessoa et al. provide a valuable taxonomy of perceptual completion phenomena, but it is not yet clear whether these phenomena are mediated by one kind of neural mechanism or more. We suggest three possible neural mechanisms of long-range interaction to stimulate further perceptual and neurophysiological investigation of perceptual completion and filling-in.

It is argued that the notion of bridge locus is compatible with distributed representation and brain interconnectivity. Isomorphism is not a dogmatic condition on explanatory adequacy but a refutable hypothesis, superior to Dennett's proposed alternatives. The assumption of type-type neuro-perceptual correspondences is more parsimonious than multiple realizability.

Although Pessoa, Teller & Noë make excellent points concerning the need for a mechanism of filling-in, they throw out the baby of neural specificity with the bathwater of isomorphism and the homuncular observer. The core act of perception is sensory processing by a stationary observer and does not require overt behavioral interaction with the environment. The complexity of intracortical interconnectivity does not preclude local specificity in the representation of higher-order stimulus properties.

Pessoa, Thompson & Noë present compelling evidence in support of their central claims about the diversity of filling-in, but they embed those claims within a larger framework that rejects analytical isomorphism and uses the personal/subpersonal distinction to challenge the explanatory importance of filling-in. The latter views seem more problematic.

The target article concludes that it is essential to introduce the personal level in cognitive science. We propose to take this conclusion one step further. The personal level should consist of first-person accounts of specific, contextualized experiences, not abstract or imagined cases. Exploring first-person accounts at their own level of detail calls for the refinements of method that can link up with neural accounts.

The taxonomy proposed by Pessoa et al. should be extended to include “pathological” completion phenomena in patients with unilateral brain damage. Patients with visual field defects (hemianopias) may “complete” whole figures, while patients with parietal lobe damage may “complete” partial figures. We argue that the former may be consistent with the brain “filling-in” information, and the latter may be consistent with the brain ignoring the absence of information.

(1) In the everyday situation of seeing a uniform patch on a variegated background, filling-in does seem to require a mechanism. (2) Our attempts to make matches to such a patch make us appreciate anew the elusiveness of the phenomenon.

Differences and similarities between modal and amodal completions can only be understood by considering the goals of visual completion: unity, shape, and perceptual quality. Pessoa et al. cannot reject representational accounts of vision because of flaws with isomorphic representations of perceptual quality: representations and processes for perceptual quality (modal completion) and most likely dissociable from those for unity and shape (nonmodal completions).

The following points are discussed in response to the commentaries: (1) A taxonomy of perceptual completion phenomena should rely on both phenomenological and mechanistic criteria. (2) Certain forms of perceptual completion are caused by topographically organized neural processes – neural filling-in. (3) The bridge locus, understood as the final site of perceptual experience in the brain, should be replaced by the principle that each token percept has a neural substrate that is nomically sufficient for it, all else being equal. (4) Analytic isomorphism – the view that there must be a pictorial or spatial neural-perceptual isomorphism at the bridge locus – should be rejected. Although more abstract kinds of isomorphism are central to the neural-perceptual mapping, the perceptual cannot be exhaustively explained in terms of the neural, and therefore the explanation of perception cannot be reduced to uncovering neural-perceptual isomorphisms. (5) The task of vision is to guide action in the world, not to construct a detailed world-model in the head. (6) Neural filling-in facilitates the integration of information and thereby helps the animal find out about its environment. (7) Perceptual content needs to be understood at the level of the person or animal interacting in the world.

Working memory limits are best defined in terms of the complexity of the relations that can be processed in parallel. Complexity is defined as the number of related dimensions or sources of variation. A unary relation has one argument and one source of variation; its argument can be instantiated in only one way at a time. A binary relation has two arguments, two sources of variation, and two instantiations, and so on. Dimensionality is related to the number of chunks, because both attributes on dimensions and chunks are independent units of information of arbitrary size. Studies of working memory limits suggest that there is a soft limit corresponding to the parallel processing of one quaternary relation. More complex concepts are processed by “segmentation” or “conceptual chunking.” In segmentation, tasks are broken into components that do not exceed processing capacity and can be processed serially. In conceptual chunking, representations are “collapsed” to reduce their dimensionality and hence their processing load, but at the cost of making some relational information inaccessible. Neural net models of relational representations show that relations with more arguments have a higher computational cost that coincides with experimental findings on higher processing loads in humans. Relational complexity is related to processing load in reasoning and sentence comprehension and can distinguish between the capacities of higher species. The complexity of relations processed by children increases with age. Implications for neural net models and theories of cognition and cognitive development are discussed.