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. (shrink)

Thomas Reid was a philosopher who founded the Scottish school of 'common sense'. Much of Reid's work is a critique of his contemporary, David Hume, whose empiricism he rejects. In this work, written after Reid's appointment to a professorship at the university of Glasgow, and published in 1785, he turns his attention to ideas about perception, memory, conception, abstraction, judgement, reasoning and taste. He examines the work of his predecessors and contemporaries, arguing that 'when we find philosophers maintaining that there (...) is no heat in the fire, nor colour in the rainbow … we may be apt to think the whole to be only a dream of fanciful men, who have entangled themselves in cobwebs spun out of their own brain'. Written by one of the Scottish Enlightenment's most important thinkers, this work brings to life the intellectual debates of the time. (shrink)

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, ...

In his account of visual perception, Thomas Reid describes visible figure as both ‘real and external’ to the eye and as the ‘immediate object of sight’. These claims appear to conflict with Reid's direct realism, since if the ‘immediate’ object of vision is also its direct object, then sight would be perceptually indirect due to the role of visible figure as a perceptual intermediary. I argue that this apparent threat to Reid's direct realism may be resolved by understanding visible figure (...) as the set of geometrical properties that holds between an object's visible surfaces and some particular perspective or point of view. On this relational interpretation of visible figure, and once an ambiguity over the use of the term ‘object’ is resolved, Reid's account of vision is both epistemically and perceptually direct, as well as consistent with his account of the other senses and doctrine of signs. (shrink)

In a brief but remarkable section of the Inquiry into the Human Mind, Thomas Reid argued that the visual field is governed by principles other than the familiar theorems of Euclid—theorems we would nowadays classify as Riemannian. On the strength of this section, he has been credited by Norman Daniels, R. B. Angell, and others with discovering non-Euclidean geometry over half a century before the mathematicians—sixty years before Lobachevsky and ninety years before Riemann. I believe that Reid does indeed have (...) a fair claim to have discovered a non-Euclidean geometry. However, the real basis of Reid’s geometry of visibles is subtle and easy to misidentify. My main aim in what follows is to make clear what the real basis is, separating it from several fallacious or irrelevant considerations on which Reid may seem to be relying. A secondary aim is to air the worry that Reid’s case for his geometry can succeed only at the cost of compromising the achievement for which Reid is best known—his direct realist theory of perception. (shrink)

There are issues in Reid scholarship as well as the primary texts that seem to suggest that Reid is not a direct realist about visual perception. In this paper, I examine two key issues ? colour perception and visible figure ? and attempt to defend the direct realism of Reid's theory through an interpretation of ?directness? as well as what Reid calls ?acquired perception?, which is ?mediate? in that it requires prior perception of signs, but nonetheless constitutes direct perception.

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)

The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because all (...) that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense. (shrink)

Reid's Inquiry into the Human Mind on the Principles of Common Sense devotes more space to double vision than to any other topic. In what follows, I examine why this subject was so important to Reid and why he dealt with it as he did. I also consider whether his argument for his position begs the question against his main opponents, Berkeley and Robert Smith. I show that, as Reid presented it, it does, but that he could have said more (...) than he did in reply to Smith. My discussion of why double vision was important for Reid begins with an exposition of the relevance of the theory of vision for one of Reid's principal concerns in the Inquiry: the concern to respond to scepticism concerning our knowledge of an external world. I then turn to consider how Reid's account of double vision contributes to his epistemological realism and why the alternative account offered by Berkeley and Smith challenges it. (shrink)

In a brief but remarkable section of the Inquiry into the Human Mind, Thomas Reid argued that the visual field is governed by principles other than the familiar theorems of Euclid—theorems we would nowadays classify as Riemannian. On the strength of this section, he has been credited by Norman Daniels, R. B. Angell, and others with discovering non-Euclidean geometry over half a century before the mathematicians—sixty years before Lobachevsky and ninety years before Riemann. I believe that Reid does indeed have (...) a fair claim to have discovered a non-Euclidean geometry. However, the real basis of Reid’s geometry of visibles is subtle and easy to misidentify. My main aim in what follows is to make clear what the real basis is, separating it from several fallacious or irrelevant considerations on which Reid may seem to be relying. A secondary aim is to air the worry that Reid’s case for his geometry can succeed only at the cost of compromising the achievement for which Reid is best known—his direct realist theory of perception. (shrink)

Thomas Reid presented a two-dimensional geometry of the visual field in his Inquiry into the Human Mind (1764). The axioms of this geometry are different from those of Euclidean plane geometry. The ‘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. In a recent article, James Van Cleve has argued that Reid can secure a non-Euclidean geometry of visibles only at the cost of (...) abandoning his direct realist theory of perception, and reintroducing sense-data. The question will be reexamined by considering two aspects of Reid’s theory of vision: the claim that we do not directly perceive distance by sight and Reid’s characterization of visible figure as a partial notion of an external object. (shrink)