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)

Thomas Reid argued that the geometrical properties of visible figures equal the geometrical properties of their projections on the inside of a sphere centred around the eye. In recent scholarship there are only a few suggestions of which sources might have inspired Reid. I point to a widely ignored body of early eighteenth-century literature – introductions into projective geometry, the use of celestial globes and astronomy – in which the model of the eye in the centre of a sphere was (...) immensely popular. Moreover, I argue that Reid's account results naturally from some astronomical doctrines in conjunction with George Berkeley's theory of vision. (shrink)

Thomas Reid's Geometry of Visibles, according to which the geometrical properties of an object's perspectival appearance equal the geometrical properties of its projection on the inside of a sphere with the eye in its centre allows for two different interpretations. It may (1) be understood as a theory about phenomenal visual space – i.e. an account of how things appear to human observers from a certain point of view – or it may (2) be seen as a mathematical model of (...) viewpoint-relative but mind-independent relational properties of objects. This paper makes a systematic and a historical claim. I shall argue, first, that given certain features of the human visual system phenomenal visual space differs in several aspects from Reidean visual space. Secondly, I suggest that, since Reid was aware of some of these empirical facts, we should interpret Reid as endorsing the second interpretation of the Geometry of Visibles. (shrink)

Thomas Reid (1710–1796) presented a two-dimensional geometry of the visual field in his Inquiry into the human mind (1764), whose axioms are different from those of Euclidean plane geometry. Reid’s ‘geometry of visibles’ is the same as the geometry of the surface of the sphere, described without reference to points and lines outside the surface itself. Interpreters of Reid seem to be divided in evaluating the significance of his geometry of visibles in the history of the discovery of non-Euclidean geometries. (...) The question will be reexamined with particular attention given to his unpublished manuscripts. These include comments on Saccheri’s work and Reid’s repeated attempts to derive Euclid’s parallel postulate from the axioms of incidence. (shrink)