Kripke’s Category Error: Why There Are No Necessary A posteriori Propositions

Kripke’s main argument against descriptivism is rooted in a category error that confuses statements about the world with statements about models of the world. It is only because of the ambiguity introduced by the fact that a single sentence can frame two different propositions, one necessary and the other a posteriori, that one reaches the mistaken conclusion that there can be necessary a posteriori truths. This ambiguity from language was carried over into modal logic by Kripke. However, we must consider the two different propositions (1) and (2) separately. Doing so reveals that a given proposition is either necessary and a priori or contingent and a posteriori. It cannot be both

Volume completion

The visual system completes image fragments into larger regions when those fragments are taken to be the visible portions of an occluded object. Kellman and Shipley (1991) argued that this ‘‘amodal’ ’ completion is based on the way that the contours of image fragments ‘‘relate.’ ’ Contours relate when their imaginary extensions intersect at an obtuse or right angle. However, it is shown here that contour relatability is neither necessary nor sufficient for completion to take place. Demonstrations that go beyond traditional examples of overlapping flat surfaces reveal that ‘‘mergeable’ ’ volumes, rather than relatable contours, are the critical elements in completion phenomena. A volume is defined as a 3-D enclosure. Typically, this refers to a surface plus the inside that it encloses. Two volumes are mergeable when their unbounded visible surfaces are relatable or the insides enclosed by those surfaces can completely merge. Two surfaces are relatable when their visible portions can be extended into occluded space along the trajectories defined by their respective curvatures so that they merge into a common surface. A volume-based account of amodal completion subsumes surface completion as a special case and explains examples that neither a contour- nor a surface-based account can explain. © 1999 Academic Pres

Complete mergeability and amodal completion

When image fragments are taken to correspond to the visible portions of a single occluded object, the object is said to `amodally complete' behind the occluder. Kellman and Shipley (Kellman, P. J., & Shipley, T. F. (1991). A theory of visual interpolation in objective perception. Cognitive Psychology, 23, 144±221) argued that when the virtual contour extensions of such image fragments subtend an obtuse or right angle, the contours are `relatable ' and therefore complete. However, edge and surface relatability are neither necessary nor sufficient for completion to be perceived (Tse, P. U. (1999) Volume completion. Cognitive Psychology). Evidence is o€ered that completion is not driven directly by image cues such as contour relatability, but is driven, rather, by intermediate representations, such as volumes that are inferred from global image cue relationships. Evidence suggests that several factors, none of which is necessary for amodal completion to occur, contribute to the perceived strength of amodal completion, including similarity of pattern or substance, proximity, and good volume continuation or complete mergeability. Two partially occluded volumes are completely mergeable when they can be extended into occluded space along the trajectory de®ned by their visible surfaces such that they merge entirely with each other. Mergeability is not measurable in the image because it describes an inferred relationship among volumes that must themselve

Amodal completion in the absence of image tangent discontinuities

It has been widely believed since Helmholtz that tangent discontinuities in image contours, such as T-junctions or L-junctions, will occur when one object occludes another. Here we describe a class of occlusion relationships where changes in 'border ownership' and amodal completion take place in the absence of tangent discontinuities in the image. We propose that even subtle curvature discontinuities can be a signal to potential changes in border ownership, and are valid ecological cues for occlusion in certain scenes

The duration of 3D form analysis in transformational apparent motion. Perception

Transformational apparent motion (TAM) occurs when a figure changes discretely from one configuration to another overlapping configuration. Rather than an abrupt shape change, the initial shape is perceived to transform smoothly into the final shape as if animated by a series of intermediate shapes. We find that TAM follows an analysis of form that takes 80–140 msec. Form analysis can function both at and away from equiluminance and can occur over contours defined by uniform regions as well as outlines. Moreover, the forms analyzed can be 3-D, resulting in motion paths that appear to smoothly project out from or into the stimulus plane. The perceived transformation is generally the one that involves the least change in the shape or location of the initial figure in a 3-D sense. We conclude that perception of TAM follows an analysis of 3-D form that takes,100 msec. This stage of form analysis may be common to both TAM and second-order motion. When two nonoverlapping figures are flickered in succession within a certain range of spatiotemporal offsets (Korte, 1915), they appear to comprise a single object jumping rigidly back and forth in translational apparent motion. Because no object actually moves in the world, th