Cognitive impenetrability (CI) of a large part of visual perception is taken for granted by those of us in the field of computational vision who attempt to recover descriptions of space using geometry and statistics as tools. These tools clearly point out, however, that CI cannot extend to the level of structured descriptions of object surfaces, as Pylyshyn suggests. The reason is that visual space – the description of the world inside our heads – is a (...) nonEuclidean curved space. As a consequence, the only alternative for a vision system is to develop several descriptions of space–time; these are representations of reduced intricacy and capture partial aspects of objective reality. As such, they make sense in the context of a class of tasks/actions/plans/purposes, and thus cannot be cognitively impenetrable. (shrink)

Some recently popular accounts of perception account for the phenomenal character of perceptual experience in terms of the qualities of objects. My concern in this paper is with naturalistic versions of such a phenomenal externalist view. Focusing on visual spatial perception, I argue that naturalistic phenomenal externalism conflicts with a number of scientific facts about the geometrical characteristics of visual spatial experience.

The empirical study of visual space has centered on determining its geometry, whether it is a perspective projection, flat or curved, Euclidean or non-Euclidean, whereas the topology of space consists of those properties that remain invariant under stretching but not tearing. For that reason distance is a property not preserved in topological space whereas the property of spatial order is preserved. Specifically the topological properties of dimensionality, orientability, continuity, and connectivity define “real” space as studied (...) by physics and are the spatial properties that characterize the physical universe as being an integral whole. By contrast the geometrical analysis of VS has taken little cognizance of its topology. Instead such properties have been presupposed a priori rather than being established a posteriori by empirical means, perhaps because these properties are self-evident. Applying the method of coordinative definition expounded by Hans Reichenbach for determining geometrical and topological properties of physical space, it can be shown that VS fulfills the topological criteria of being a “real” space sui generis. Though theorized to be produced by the brain, the topology of VS is not topologically equivalent with the structure and activity of the brain because, as will be shown, the topology of VS cannot be formed from the topology of the brain without tearing and/or cutting and pasting. (shrink)

Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features (...) of this contraction are not the same as would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

A meta-analysis and an experiment show that the degree of compression of the in-depth dimension of visual space relative to the frontal dimension increases quickly as a function of the distance between the stimulus and the observer at first, but the rate of change slows beyond 7 m from the observer, reaching an apparent asymptote of about 50 %. In addition, the compression of visual space is greater for monocular and reduced cue conditions. The pattern of (...) compression of the in-depth dimension as a function of distance is similar to the ratio of in-depth to frontal visual angles of stimuli, but is not as extreme as this ratio would suggest, implying that observers are incapable of fully ignoring size information provided by cues to depth. Size and distance judgments may be described by an Affine transformation of physical space; however, the compression parameter in this model changes as a function of distance from the observer and other experimental conditions. (shrink)

In the philosophy of perception, direct realism has come into vogue. Philosophical authors assert and assume that what their readers want, and what anyone should want, is some form of direct realism. There are disagreements over precisely what form this direct realism should take. The majority of positions in favor now offer a direct realism in which objects and their material or physical properties constitute the contents of perception, either because we have an immediate or intuitive acquaintance with those objects (...) and properties, or because our perceptual states have informational content that represents the properties of those objects (and which is not itself an object of perception and has no specifically subjective aspect). This paper considers various forms of perceptual realism, including, for purposes of comparison, the largely abandoned indirect or representative realism. After surveying the variety of perceptual realisms and considering their various commitments, I introduce some considerations concerning the phenomenology of visual space that cause trouble for most forms of direct realism. These considerations pertain to the perception of objects in the distance and, secondarily, to the perception of shapes at a slant. I argue that one of the lesser known varieties of perceptual realism, critical direct realism, can meet the challenges offered by the facts of spatial perception. (shrink)

Maurice Merleau-Ponty argued that the seeing of things together (focal figure and background objects) accounted for the sense that things possess unseen depth: they are three-dimensional entities, not facades. I compare this idea to the law of large numbers. In both cases, single entities take on substance, depth, or meaning when assimilated into a large body of comparable instances. Thinking along these lines, Erwin Schrödinger proposed that living processes achieve order by virtue of the multiplicity of their constituent parts, any (...) of which, when considered individually, militate against perception and understanding. He further suggested that those parts take their place as things to be perceived even as they constitute our perceiving faculties, and this is why uncertainty occasions their reality. Thus he offers an instance of Merleau-Ponty’s notion of chiasmic intertwining, which allows for world-body interchange or reversibility beyond the reach of unequivocal apprehension. (shrink)

Maurice Merleau-Ponty argued that the seeing of things together (focal figure and background objects) accounted for the sense that things possess unseen depth: they are three-dimensional entities, not facades. I compare this idea to the law of large numbers. In both cases, single entities take on substance, depth, or meaning when assimilated into a large body of comparable instances. Thinking along these lines, Erwin Schrödinger proposed that living processes achieve order by virtue of the multiplicity of their constituent parts, any (...) of which, when considered individually, militate against perception and understanding. He further suggested that those parts take their place as things to be perceived even as they constitute our perceiving faculties, and this is why uncertainty occasions their reality. Thus he offers an instance of Merleau-Ponty’s notion of chiasmic intertwining, which allows for world-body interchange or reversibility beyond the reach of unequivocal apprehension. (shrink)

In this paper I contrast the geometric structure of phenomenal visual space with that of photographic images. I argue that topologically both are two-dimensional and that both involve central projections of scenes being depicted. However, I also argue that the metric structures of the spaces differ inasmuch as two types of “apparent distortions”—marginal distortion in wide-angle photography and close-up distortions—which occur in photography do not occur in the corresponding visual experiences. In particular, I argue that the absence (...) of marginal distortions in vision is evidence for a holistic metric of visual space that is spherical, and that the absence of close-up distortions shows that the local metric structure possesses a dynamic variable curvature which is dependent upon the distance away of objects being viewed at a given time. (shrink)

In spatial sequence synaesthesia ordinal stimuli are perceived as arranged in peripersonal space. Using fMRI, we examined the neural bases of SSS and colour synaesthesia for spoken words in a late-blind synaesthete, JF. He reported days of the week and months of the year as both coloured and spatially ordered in peripersonal space; parts of the days and festivities of the year were spatially ordered but uncoloured. Words that denote time-units and triggered no concurrents were used in a (...) control condition. Both conditions inducing SSS activated the occipito-parietal, infero-frontal and insular cortex. The colour area hOC4v was engaged when the synaesthetic experience included colour. These results confirm the continued recruitment of visual colour cortex in this late-blind synaesthetes. Synaesthesia also involved activation in inferior frontal cortex, which may be related to spatial memory and detection, and in the insula, which might contribute to audiovisual integration related to the processing of inducers and concurrents. (shrink)

This paper examines Berkeley's attitude toward our perception of spatial relations on the two- dimensional visual field. This is a topic on which there has been some controversy. Historians of visual theory have tended to suppose that Berkeley took "all" spatial relations to be derived in the way our knowledge of depth is: from association of more primitive sensations which are themselves in no way spatial. But many philosophers commenting on Berkeley have supposed that he takes our awareness (...) of two- dimensional visual layout to be directly perceived. I argue that Berkeley's position on this issue is deeply ambivalent and that neither alternative sits well with the rest of his philosophy. (shrink)

The visual system captures a unique contrast between implicit and explicit representation where the same event (location of a visible object) is coded in both ways in parallel. A method of differentiating the two representations is described using an illusion that affects only the explicit representation. Consistent with predictions, implicit information is available only from targets presently visible, but, surprisingly, a two-alternative decision does not disturb the implicit representation.

This paper argues that a common form of representationalism has trouble accommodating empirical findings about visual space perception. Vision science tells us that the visual system systematically gives rise to different experiences of the same spatial property. This, combined with a naturalistic account of content, suggests that the same spatial property can have different veridical looks. I use this to argue that a common form of representationalism about spatial experience must be rejected. I conclude by considering alternatives (...) to this view. (shrink)