Online research in philosophy

Abstract: In this paper I consider recent attempts to establish that the geometry of visual experience is a spherical geometry. These attempts, offered by Gideon Yaffe, James van Cleve and Gordon Belot, follow Thomas Reid in arguing for an equivalency of a geometry of 'visibles' and spherical geometry. I argue that although the proposed equivalency is successfully established by the strongest form of the argument, this does not warrant any conclusion about the geometry of visual experience. I argue, firstly, that (...) the resistance of this contemporary argument to empirical considerations counts against its plausibility. Moreover, I argue that the contemporary approach provides no compelling reason for supposing that the geometry offered as the geometry of 'visibles' is the correct geometrical description of visual experience. (shrink)

An explication is offered of Reid’s claim (discussed recently by Yaffe and others) that the geometry of the visual field is spherical geometry. It is shown that the sphere is the only surface whose geometry coincides, in a certain strong sense, with the geometry of visibles.

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)

In the chapter “The Geometry of Visibles” in his ‘Inquiry into the Human Mind’, Thomas Reid constructs a special space, develops a special geometry for that space, and offers a natural model for this geometry. In doing so, Reid “discovers” non-Euclidean Geometry sixty years before the mathematicians. This paper examines this “discovery” and the philosophical motivations underlying it. By reviewing Reid’s ideas on visible space and confronting him with Kant and Berkeley, I hope, moreover, to resolve an alleged impasse in (...) Reid’s philosophy concerning the contradictory characteristics of Reid’s tangible and visible space. (shrink)

Abstract: In this paper I offer an account of a particular variety of perception of absence, namely, visual perception of empty space. In so doing, I aim to make explicit the role that seeing empty space has, implicitly, in Mike Martin's account of the visual field. I suggest we should make sense of the claim that vision has a field—in Martin'ss sense—in terms of our being aware of its limitations or boundaries. I argue that the limits of the visual field (...) are our own sensory limitations, and that we are aware of them as such. Seeing empty space, I argue, involves a structural feature of experience that constitutes our awareness of our visual sensory limitations, and thus, in virtue of which vision has a field. (shrink)

Introduction -- Simple shapes : vision and concepts -- Basic geometrical knowledge -- Geometrical discovery by visualizing -- Diagrams in geogmetric proofs -- Mental number lines -- Visual aspects of calculation -- General theorems from specific images -- Visual thinking in basic analysis -- Symbol manipulation -- Cognition of structure -- Mathematical thinking : algebraic v. geometric?

Visual space can be distinguished from physical space. The ?rst is found in visual experi- ence, while the second is de?ned 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 (1) that visual space exhibits contraction in all three dimensions with increasing distance from the observer, (2) that experienced features of this contraction (including (...) the apparent convergence of lines in visual experience that are produced from physically parallel stimuli in ordinary viewing con- ditions) are not the same as would be the experience of a perspective projection onto a fronto- parallel plane, and (3) that such contraction is consistent with size constancy. These properties of visual space are di?erent 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 cor- respondence. 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)