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- Robert French (1987). The Geometry of Visual Space. Noûs 21 (June):115-133.
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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 (...)
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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.
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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 (...)
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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 (...)
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 (...)
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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 (...)


