Online research in philosophy

In his 'Inquiry', Reid claims, against Berkeley, that there is a science of the perspectival shapes of objects ('visible figures'): they are geometrically equivalent to shapes projected onto the surfaces of spheres. This claim should be understood as asserting that for every theorem regarding visible figures there is a corresponding theorem regarding spherical projections; the proof of the theorem regarding spherical projections can be used to construct a proof of the theorem regarding visible figures, and vice versa. I reconstruct Reid's argument for this claim, and expose its mathematical underpinnings: it is successful, and depends on no empirical assumptions to which he was not entitled about the workings of the human eye. I also argue that, although Reid may or may not have been aware of it, the geometry of spherical projections is not the only geometry of visible figure.

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.

The subject of this investigation is the role of conventions in the formulation of Thomas Reid's theory of the geometry of vision, which he calls the 'geometry of visibles'. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid's 'geometry of visibles' and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid's direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish 'common-sense' school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid's alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the 'geometry of visibles'. In summarizing the importance of Reid's philosophy in this area, Daniels is led to conclude that 'there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry'; while Angell, similarly inspired by Reid, draws a much stronger inference: 'The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...' The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid's name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.Implicit in the recent work on Reid's 'geometry of visibles', or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric 'conventions', especially of the metric sort, in the formulation of the GOV (

Independently of any eighteenth century work on the geometry of parallels, Thomas Reid discovered the non-euclidean "geometry of visibles" in 1764. Reid's construction uses an idealized eye, incapable of making distance discriminations, to specify operationally a two dimensional visible space and a set of objects, the visibles. Reid offers sample theorems for his doubly elliptical geometry and proposes a natural model, the surface of the sphere. His construction draws on eighteenth century theory of vision for some of its technical features and is motivated by Reid's desire to defend realism against Berkeley's idealist treatment of visual space.

Chapter I: The Geometry of Visibles 1 . The N on- Euclidean Geometry of Visibles In the chapter "The Geometry of Visibles" in Inquiry into the Human Mind, ...

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.