Conventionalism in Reid's 'geometry of visibles'
Studies in History and Philosophy of Science Part A 34 (3):467-489 (2003)
| Abstract | 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 (where a 'metric' can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid's GOV, it is only one of many different geometrical structures that a GOV can possess. Angell's theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid's theory and the alleged non-Euclidean nature of the GOV, in respectively, the focus will turn to the tacit role of conventionalism in Daniels' reconstruction of Reid's GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell (). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid's GOV that does not violate his avowed 'direct realist' theory of perception, since this epistemological thesis largely prompted his formulation of the GOV. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesJames Van Cleve (2002). Thomas Reid's Geometry of Visibles. Philosophical Review 111 (3):373-416.
Emil Badici (2010). On the Compatibility Between Euclidean Geometry and Hume's Denial of Infinite Divisibility. Hume Studies 34 (2):231-244.
Ragnar Fjelland (1991). The Theory-Ladenness of Observations, the Role of Scientific Instruments, and the Kantian a Priori. International Studies in the Philosophy of Science 5 (3):269 – 280.
David Stump (1991). Poincaré's Thesis of the Translatability of Euclidean and Non-Euclidean Geometries. Noûs 25 (5):639-657.
Gideon Yaffe (2002). Reconsidering Reid's Geometry of Visibles. Philosophical Quarterly 52 (209):602-620.
Phillip John Meadows (2011). Contemporary Arguments for a Geometry of Visual Experience. European Journal of Philosophy 19 (3):408-430.
Gordon Belot (2003). Remarks on the Geometry of Visibles. Philosophical Quarterly 53 (213):581–586.
Norman Daniels (1974). Thomas Reid's Inquiry: The Geometry of Visibles and the Case for Realism. New York,B. Franklin.
Amit Hagar (2002). Thomas Reid and Non-Euclidean Geometry. Reid Studies 5 (2):54-64.
Norman Daniels (1972). Thomas Reid's Discovery of a Non-Euclidean Geometry. Philosophy of Science 39 (2):219-234.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads10 ( #106,175 of 548,984 )Recent downloads (6 months)2 ( #37,320 of 548,984 )How can I increase my downloads? |
My notes
Discussion
