Online research in philosophy

What is difficult to imagine is also surprising to perceive. This indicates that active visual imagery is an integral part of active visual perception. Erroneous mental transformations provide clues to prior assumptions in visual imagery, just as visual illusions provide clues to perceptual assumptions. Visual imagery and perception share generic assumptions about invariants in images of rigid objects.

"This collection of classic essays in the study of visual culture fills a major gap in this new and expanding intellectual field. Its major strength is its insistence on the importance of three central aspects of the study of visual culture: the sign, the institution and the viewing subject. It will provide readers, teachers and students with an essential text in visual and cultural studies." - Janet Wolff, University of Rochester Visual Culture: The Reader provides an invaluable resource of over 30 key statements from a wide range of disciplines. Although underpinned by a focus on contemporary cultural theory, this reader puts issues of visual culture and the rhetoric of the image at centre stage. Divided into three parts, The Culture of the Visual, Regulating Photographic Meaning, Looking and Subjectivity, this reader enables students to make hitherto unmade connections across art, film and photography history and theory, semiotics, history, semiotics and communications, media studies, and cultural theory. The key statements are from the work of: Visual Culture: The Reader sets the agenda for the study of Visual Culture and will be an essential sourcebook for researchers and students alike. This is the reader for the module The Image and Visual Culture (D850) - part of The Open University Masters in Social Sciences Programme.

The present paper has two, interrelated objectives. The first is to analyze the different senses in which arguments are characterized as persuasive in the extant writings of Sextus Empiricus. The second is to examine the Pyrrhonist’s therapeutic use of arguments in the discussion with his Dogmatic rivals – more precisely, to determine the sense and basis of Sextus’ distinction between therapeutic arguments that appear weighty and therapeutic arguments that appear weak in their persuasiveness.

Book description: This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams, etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.

O'Regan & Noë mistakenly identify visual processing with visual experience. I outline some reasons why this is a mistake, taking my data and arguments mainly from the literature on subliminal processing.

This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical constructions. Therefore, they are legitimate components of the theory (combinatorial and geometric group theory) and the pictures of Cayley graphs are a part of practical mathematical procedures.

It has often been assumed that when we use vision to become aware of an object or event in our surroundings, this must be accompanied by a corresponding visual experience (i.e., seeing). The studies reported here show that this assumption is incorrect. When observers view a sequence of displays alternating between an image of a scene and the same image changed in some way, they often feel (or sense) the change even though they have no visual experience of it. The subjective difference between sensing and seeing is mirrored in several behavioral differences, suggesting that these are two distinct modes of conscious visual perception.

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this “crisis” as follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano.

Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.

Brought together for the first time, these writings by visual artist and writer Yve Lomax are united by a common thread: they place writing itself--the written image--into the repertoire of visual art. The book both proposes and demonstrates this development. It also has a twofold purpose and function: it can be read and enjoyed as performance, often resembling poetry, thick with ideas, images and metaphors. It is also an original contribution to theoretical writing on the visual, particularly relating to the image and difference, celebrating and referring to the work of Michel Serres, Gilles Deleuze, Luce Irigaray and others in pursuit of its own strategy of introducing the written image into the theoretical text.