The empirical study of visual space has centered on determining its geometry, whether it is a perspective projection, flat or curved, Euclidean or non-Euclidean, whereas the topology of space consists of those properties that remain invariant under stretching but not tearing. For that reason distance is a property not preserved in topological space whereas the property of spatial order is preserved. Specifically the topological properties of dimensionality, orientability, continuity, and connectivity define “real” space as studied by physics and are the (...) spatial properties that characterize the physical universe as being an integral whole. By contrast the geometrical analysis of VS has taken little cognizance of its topology. Instead such properties have been presupposed a priori rather than being established a posteriori by empirical means, perhaps because these properties are self-evident. Applying the method of coordinative definition expounded by Hans Reichenbach for determining geometrical and topological properties of physical space, it can be shown that VS fulfills the topological criteria of being a “real” space sui generis. Though theorized to be produced by the brain, the topology of VS is not topologically equivalent with the structure and activity of the brain because, as will be shown, the topology of VS cannot be formed from the topology of the brain without tearing and/or cutting and pasting. (shrink)

In the 1930s Otto Selz developed a novel approach to the psychology of perception which he called “synthetic psychology of wholes”. This “synthetic psychology” is based on a phenomenological description of the structural relationships between elementary items building up integral wholes. The present article deals with Selz’s account of spatial cognition within this general framework. Selz Zeitschrift für Psychologie, 114, 351–362 argues that his approach to spatial cognition delivers answers to the long-discussed question of the epistemological status of the laws (...) of geometry. More specifically he tries to derive the Euclidean axioms from the structural laws valid for phenomenal space. After a brief description of the discussion of the status of geometry in the 1920s/1930, the present article explains Selz’s understanding of “phenomenology”. Section 4 then deals with Selz’s attempt to derive the Euclidean laws from the structural phenomenological laws of space. Selz’s attempted derivation suffers from some formal shortcomings, which however can be repaired. The question arises, though, whether the necessary improvements do not rely upon more intricate geometric intuitions and thus render Selz’s attempt to base geometry upon the phenomenology of spatial cognition circular. (shrink)

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own conceptions (...) of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such.. (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)

Two theses appear to be central to Reid’s view of the visual field. By sight, we do not originally perceive depth or linear distance from the eye. By sight, we originally perceive the position that points on the surface of objects have with regard to the centre of the eye. In different terms, by sight, we originally perceive the compass direction and degree of elevation of points on the surface of objects with reference to the centre of the eye. I (...) consider various problems about distance perception and perception of position with regard to the centre of the eye raised by Reid’s texts. These questions are relevant to Reid’s description of the geometry of visibles as the “intrinsic” geometry of the surface of the sphere. (shrink)

Drawing on work done by Helmholtz, I argue that Reid was in no position to infer that objects appear as if projected on the inner surface of a sphere, or that they have the geometric properties of such projections even though they do not look concave towards the eye. A careful consideration of the phenomena of visual experience, as further illuminated by the practice of visual artists, should have led him to conclude that the sides of visible appearances either look (...) straight, in which case their angles appear to approximate Euclidean measures, or their angles do not appear to approximate Euclidean measures for straight line figures, in which case their sides do not look straight. (shrink)

Thomas Reid’s epistemological ambitions are decisively at the center of his work. However, if we take such ambitions to be the whole story, we are apt to overlook the theory of mind that Reid develops and deploys against the theory of ideas. Reid’s philosophy of mind is sophisticated and strikingly contemporary, and has, until recently, been lost in the shadow of his other philosophical accomplishments. Here I survey some aspects of Reid’s theory of mind that I find most interesting. I (...) examine whether Reid is a mysterian about the mind, whether Reid has a direct realist theory of perception, and whether Reid has a higher-order, or “inner-sense,” view of consciousness. Along the way I will mention portions of the secondary literature that examine these aspects and point out whether and to what degree I part ways with the interpretations present in the literature. (shrink)

Over the history of the study of visual perception there has been great success at discovering countless visual illusions. There has been less success in organizing the overwhelming variety of illusions into empirical generalizations (much less explaining them all via a unifying theory). Here, this article shows that it is possible to systematically organize more than 50 kinds of illusion into a 7 × 4 matrix of 28 classes. In particular, this article demonstrates that (1) smaller sizes, (2) slower speeds, (...) (3) greater luminance contrast, (4) farther distance, (5) lower eccentricity, (6) greater proximity to the vanishing point, and (7) greater proximity to the focus of expansion all tend to have similar perceptual effects, namely, to (A) increase perceived size, (B) increase perceived speed, (C) decrease perceived luminance contrast, and (D) decrease perceived distance. The detection of these empirical regularities was motivated by a hypothesis, called “perceiving the present,” that the visual system possesses mechanisms for compensating neural delay during forward motion. This article shows how this hypothesis predicts the empirical regularity. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)