This thesis challenges a general prejudice against visualization in the history of logic and mathematics, by providing a semantic analysis of two graphical representation systems--a traditional Venn diagram representation system and an extension of it. While Venn diagrams have been used to solve problems in set theory and to test the validity of syllogisms in logic, they have not been considered valid proofs but heuristic tools for finding valid formal proofs. ;I present Venn diagrams which have been used in logic (...) as a formal system of representation equipped with its own syntax and semantics. I also show that Venn-I, with the rules of transformation that I specify, is sound and complete. The soundness of Venn-I refutes a worry that mathematicians and logicians have about graphical representation: Fallacies often have arisen from the misuse of diagrams in mathematical proofs, especially in geometry. However, the validity of the transformation rules assures us that the correct application of these rules will not lead to fallacies. ;I extend Venn-I so that this new system has a general way to convey disjunctive information. A new formation rule is introduced and new transformation rules are added. I call this extended system Venn-II. The semantics of Venn-II is formalized as an extension of the semantics of Venn-I. The soundness and completeness of Venn-II are also proven. I then show that Venn-II and a monadic first-order language are equivalent in their expressiveness. ;The analysis of Venn-I and Venn-II leads to interesting issues which have their analogues in other deductive systems. I conclude the thesis with a discussion of some fundamental differences between graphical systems and linguistic systems. (shrink)

Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. (...) Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning. (shrink)

(Open Access article, freely available to download from publisher's site.) Our visual experiences of objects as located in external space, and as having definite three-dimensional shapes, are closely linked to our implicit expectations about what things will look like from alternative viewpoints. What sorts of contents do these expectations involve? One standard answer is that they relate to what things will look like to us upon changing our positions. And what sorts of mental representations do the expectations call (...) upon? A standard answer is that they involve our powers of visual imagery; this answer requires us to allow for the possibility of unconscious visual imagery, however. The current paper presents an alternative model of the contents of our implicit visual expectations, one that regards them as wholly nonreflexive. It also argues that, once we ascribe the relevant contents to the expectations, there is no longer any reason for holding that they involve our powers of visual imagery. (shrink)

The on-going debate over the ‘admissible contents of perceptual experience’ concerns the range of properties that human beings are directly acquainted with in perceptual experience. Regarding vision, it is relatively uncontroversial that the following properties can figure in the contents of visual experience: colour, shape, illumination, spatial relations, motion, and texture. The controversy begins when we ask whether any properties besides these figure in visual experience. We argue that ‘ensemble properties’ should be added to the list of visually (...) admissible properties. Ensemble properties are features that belong to a set of perceptible objects as a whole as opposed to the individuals that constitute that set. They include such features as the mean size of an array of shapes or the average emotional expression of an array of faces. Recent work in vision science has yielded compelling evidence that the visual system routinely encodes such properties. We argue that epistemological considerations provide strong reasons to think that these properties figure in visual experience. Judgements about ensemble properties are immediately warranted by our perceptual experience, and the only plausible way that a perceptual experience could confer this warrant is if it confers awareness of ensemble properties. (shrink)

Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise cognitively inaccessible. Despite their important functional roles in scientific practices, philosophers of science have more or less neglected visual representations in their analyses of epistemic methods and tools (...) of reasoning in science. This book is meant to fill this gap. It presents a detailed investigation into central conceptual issues and into the epistemology of visual representations in science. (shrink)

Let me start by saying that I had the privilege of witnessing the birth of Jon Barwise's new research on heterogeneous logic and its subsequent developments. I entered the Stanford philosophy graduate program in the Fall of 1987, became Barwise and Etchemendy's first research assistant on the project of diagrammatic/heterogeneous reasoning during summer of 1989, and under their guidance completed my thesis, “Valid reasoning and visual representation,” in August, 1991. With this experience I would like to focus (...) on the more personal and informal aspects of Jon's research on heterogeneous logic which may not be conveyed by his articles. (Accordingly, I have written this paper without footnotes or other references except to Jon's work.) The present article can only hint at the depth and the influence of Jon's work in this area.In the first section, I single out an important feature of the project on heterogeneous logic Jon founded together with John Etchemendy about 15 years ago. I title it “resolving conflicts” since the research, I strongly believe, grew out of Jon's personal attitude toward how to resolve a tension between opposite extremes.The second section focuses on how teaching logic itself was shaped as part of Barwise and Etchemendy's research agenda. It is worthwhile noting that their textbookLanguage, Proof, and Logicconstitutes part of their research and, hence, the success of the book vindicates the goal of the overall project. (shrink)

It is argued that there is no fallacy in the reasoning in the example of the thirsty blindsight subject, on one reconstruction of that reasoning. Neither the case of orgasm nor the case of a visual versus an auditory experience as of something overheard shows that phenomenal content is not representational.

This book's activities highlight the important cycle of exploration, conjecture, and justification in all five mathematical strands. Students recognize patterns and make conjectures, learn the value of a counterexample, explore the strengths and weaknesses of visual proofs, discover the power of algebraic representations, and learn that theoretical approaches can substantiate empirical results. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. --publisher description.

Understanding what is distinctive about the role of models in science requires characterizing broad patterns in how these models evolve in the face of experimental results. That is, we must examine not just model statics—how the model relates to theory, or represents the world, at some point in time—but also model dynamics—how the model both generates new experimental results and is modified in response to them. Visual representations of structure play a central role in the theoretical reasoning (...) of organic chemists. Not surprisingly, these representations have changed in important ways–in response to experimental and theoretical developments– throughout the history of organic chemistry. In many cases it is appropriate to understand the visual representations used by organic chemists as models. The evolution of the structural representations of organic chemists therefore provides a clear example of the dynamics of scientific modeling. In this paper I use a conception of scientific modeling drawn from the work of Mary Hesse to examine how the concept of a molecular conformation was incorporated into the visual representations of structure used by organic chemists. (shrink)

Philosophers and neuroscientists often suggest that we perceptually represent objects and their properties. However, they start from very different background assumptions when they use the term “perceptual representation”. On the one hand, sometimes philosophers do not need to properly take into consideration the empirical evidence concerning the neural states subserving the representational perceptual processes they are talking about. On the other hand, neuroscientists do not rely on a meticulous definition of “perceptual representation” when they talk about this empirical evidence that (...) is supposed to show that we perceptually represent such and such properties. It seems that, on both sides, something is missed. My aim is to show that, in the light of empirical evidence from neuroscience, the case of action properties is a good candidate in order to properly talk of perceptually represented properties. My claim is that the neurophysiological states encoding action properties are perceptual processes and that these perceptual processes are representational processes. That is, in the case of those neurophysiological states involved in the detection of action properties, it is correct to speak of perceptual representational states, and hence, ipso facto, of perceptually represented properties. First, I describe a reasonable and widely agreed upon conception of perceptual representation in the philosophical literature. Then, I report evidence from vision and motor neuroscience concerning the perception of action properties, which is subserved by the ventro-dorsal stream, a portion of the dorsal visual system. Finally, I show that a strong connection can be found between the philosophical idea of perceptual representation I have reported before and the neuroscientific evidence concerning the activity of the ventro-dorsal stream, whose job is, as said, to detect action properties. (shrink)

Knowledge Representation and Reasoning (KR&R) is based on the idea that propositional content can be rigorously represented in formal languages long the province of logic, in such a way that these representations can be productively reasoned over by humans and machines; and that this reasoning can be used to produce knowledge-based systems (KBSs). As such, KR&R is a discipline conventionally regarded to range across parts of artificial intelligence (AI), computer science, and especially logic. This standard view of (...) KR&R’s participating fields is correct — but dangerously incomplete. The view is incomplete because, as we explain herein, sophisticated KR&R must rely heavily upon philosophy. Encapsulated, the reason is actually quite straightforward: Sophisticated KR&R must include the representation of not only simple properties, but also concepts that are routine in the formal sciences (theoretical computer science, mathematics, logic, game theory, etc.), and everyday socio-cognitive concepts like mendacity, deception, betrayal, and evil. Because in KR&R the representation of such concepts must be rigorous in order to enable machine reasoning (e.g., machine-generated and machine-checked proofs that a is lying to b) over them, philosophy, devoted as it is in no small part to supplying analyses of such concepts, is a crucial partner in the overall enterprise. To put the point another way: When the knowledge to be represented is such as to require lengthy formulas in expressive formal languages for that representation, philosophy must be involved in the game. In addition, insofar as the advance of KR&R must allow formalisms and processes for representing and reasoning over visual propositional content, philosophy will be a key contributor into the future. (shrink)

In Reconstructing Reason and Representation, Murray Clarke offers a detailed study of the philosophical implications of evolutionary psychology. In doing so, he offers new solutions to key problems in epistemology and philosophy of mind, including misrepresentation and rationality. He proposes a naturalistic approach to reason and representation that is informed by evolutionary psychology, and, expanding on the massive modularity thesis advanced in work by Leda Cosmides and John Tooby, argues for a modular, adapticist account of misrepresentation and knowledge. Just as (...) the reliability of representation can be defended on the basis of an account of the proper function of cognitive modularity, misrepresentation can be explained through an appeal to the "gap theory," by noting the divergence between the proper and actual domains of cognitive modules in a massively modular mind.Clarke argues for an externalist, modular reliabilism by suggesting that evolution has equipped us with generally reliable inferential systems even if they do not always produce true beliefs. He argues that reliable deductive and inductive inference occurs only when cognitive modules deal with actual domains that are sufficiently similar to their proper domains. This psychologically informed, naturalized adapticism leads to the suggestion that knowledge is a set of natural kinds housed in the modules of a massively modular mind. Typically, the proper function of these cognitive modules is to provide us with truths that enable us to satisfy our basic biological needs. Beyond reasoning modules, other cognitive modules discussed include the ability to orient ourselves in space, and our abilities with language, numbers, object reasoning, and social understanding. Clarke also defends Cosmides and Tooby's massive modularity hypothesis against such critics as Jerry Fodor by demonstrating that these critics consistently misrepresent Cosmides and Tooby's position. (shrink)

This article provides a strategic history of the role assigned by modern historians to visual representation in early modern science, an aspect of historiography that is largely ignored in the scholarly literature. Despite the current undervaluation of images and visual reasoning, historians in the 1940s and 1950s who established the 20th century concept of the Scientific Revolution, also assigned a conspicuous role to images, claiming 15th century art as a chapter in the history of science and identifying (...) the first modern scientists in artists such as Brunelleschi and Leonardo. My analysis of the writings that shaped the discourse on visual representation---by giants such as George Sarton, Herbert Butterfield, and Alexandre Koyré---shows that the handful of concepts introduced in these early discussions formed the foundations of the subsequent scholarly approach to early modern scientific images. However, close scrutiny during the 1970s defined these concepts as interesting but not as key elements for the emergence of modern science proposed earlier. The wave of social studies of science in the 1980s further diminished the importance of images, to the point that recent surveys of early modern science neither consider the role of visual representation nor include figures in their narratives. Several recent publications with suggestive titles such as The Power of Images in Early Modern Science promise to recover a significant role for images in the Scientific Revolution. The present inquiry into the earlier discourse seeks to clarify the historiographic framework into which these new efforts fit. (shrink)

This book examines the logical foundations of visual information: information presented in the form of diagrams, graphs, charts, tables, and maps. The importance of visual information is clear from its frequent presence in everyday reasoning and communication, and also in compution. Chapters of the book develop the logics of familiar systems of diagrams such as Venn diagrams and Euler circles. Other chapters develop the logic of higraphs, Pierce diagrams, and a system having both diagrams and sentences among (...) its well-formed representations. Syntax, semantics, rules of inference and soundness and completeness results are provided for each of the systems. In addition to developing the logic of diagrams, key questions about the status of visual information Hammer discusses, such as the relationship between the language and visually-presented information. (shrink)

In this paper, I take up the conciliatory-steadfast debate occurring within social epistemology in regards to the phenomenon of peer disagreement. I will argue, because the conciliatory perspective al-lows us to understand argumentation pragmatically—as a method of problem-solving within a community rather than as a method for obtaining the truth—that in most cases, we should not simply agree to disagree.

The present contribution offers an overview of the main problems concerning the representation of the planets in the pre-Islamic Iranian world, the origin of their denominations, their astral roles and the reasons behind their demonization in the Zoroastrian and Manichaean frameworks. This is a preliminary attempt to resume the planetary iconography and iconology in western and eastern Iranian sources, involving also external visual data, such as those coming from Dunhuang and the Chinese world. The article offers an intellectual journey (...) into a net of mutual cultural and spiritual relations, focusing on the image of the heaven (and of its celestial beings), thereby proposing a new synthesis and highlighting a number of intercultural contaminations. (shrink)

In today’s science, the output of measurement processes are often visual representations of the data detected. Moreover, we find such visual data as parts of scientific reasoning in different contexts. In this article, we will take a look at two of them. On the one hand, visual representations are used as a kind of surrogate for the real object to ask questions about it – we will call this the exploratory use of visual (...) data. On the other hand, visualisations are often used to communicate research results to scientific peers or to laymen. Instances of the latter case we will subsequently call the explanatory use of visual data. However, in both contexts the question arises what might justify these epistemic practices. Believing without reasons is epistemically irresponsible, it leads to gullibility. Thus, we will try to answer the question whether there are any reasons to support our epistemic practices concerning scientific visualisations in the above-mentioned senses and whether these are good reasons to rely on. (shrink)

This paper argues that a theory of situated vision, suited for the dual purposes of object recognition and the control of action, will have to provide something more than a system that constructs a conceptual representation from visual stimuli: it will also need to provide a special kind of direct (preconceptual, unmediated) connection between elements of a visual representation and certain elements in the world. Like natural language demonstratives (such as `this' or `that') this direct connection allows entities (...) to be referred to without being categorized or conceptualized. Several reasons are given for why we need such a preconcep- tual mechanism which individuates and keeps track of several individual objects in the world. One is that early vision must pick out and compute the relation among several individual objects while ignoring their properties. Another is that incrementally computing and updating representations of a dynamic scene requires keeping track of token individuals despite changes in their properties or locations. It is then noted that a mechanism meeting these requirements has already been proposed in order to account for a number of disparate empiri- cal phenomena, including subitizing, search-subset selection and multiple object tracking (Pylyshyn et al., Canadian Journal of Experimental Psychology 48(2) (1994) 260). This mechanism, called a visual index or FINST, is brie. (shrink)

Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large (...) number of comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations. (shrink)

Today the economic diagram is employed universally in teaching and research by professional economists. Yet the history of its construction shows that much that has been regarded as distinctive of twentieth-century visual culture was prefigured in the nineteenth. This paper will place the construction of the first economic diagrams by Alfred Marshall in the context both of contemporary visual technologies developed in other moral sciences, and of his wider theory of industrial production. The paper will argue that an (...) understanding of the background to the historical graphs, constructed by the Cambridge political economist from the late 1860s onwards, will necessitate a revision of the narrative of modern visual reasoning, as recently advanced by Lev Manovich. (shrink)

The sensorimotor account of vision proposed by O'Regan & Noë (O&N) challenges the classical view of visual cognition as a process of mentally representing the world. Many infant cognition researchers would probably disagree. I describe the surprising ability of young infants to represent and reason about the physical world, and ask how this capacity can be explained in non-representational terms. As a first step toward answering this question, I suggest that recent models of embodied cognition may help illustrate a (...) way of escaping the representational trap. (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)

Orthodox epistemological disjunctivism involves the idea that paradigm cases of visual perceptual knowledge are based on visual perceptual states which are propositional, and hence representational. Given this, the orthodox version of epistemological disjunctivism takes on controversial representational commitments in the philosophy of perception. Must epistemological disjunctivism involve these commitments? I don’t think so. Here I argue that we can take epistemological disjunctivism in a new direction and develop a version of the view free of these representational commitments. The (...) basic idea is that instead of conceiving of knowledge grounding perceptions as states in which one sees that such-and-such is the case, we should instead conceive of them as states or episodes in which one sees a thing, we should conceive of them as thing-seeings. I’ll suggest that we can cast such seeings in a knowledge grounding role without conceiving of them as representational. But this is because we can put thing-seeings to epistemological work, in the framework of epistemological disjunctivism, whilst remaining neutral on whether or not they are propositional, or representational at all. The point, then, is not to replace epistemological disjunctivism’s controversial representational commitments with controversial non-representational commitments. The point is, rather, that epistemological disjunctivism can be developed with fewer commitments in the philosophy of perception than is usually appreciated. (shrink)

There is a long-lasting quest of demarcating a minimally representational behavior. Based on neurophysiologically-informed behavioral studies, we argue in detail that one of the simplest cases of organismic behavior based on low-resolution spatial vision–the visually-guided obstacle avoidance in the cubozoan medusaTripedalia cystophora–implies already a minimal form of representation. We further argue that the characteristics and properties of this form of constancy-employing structural representation distinguish it substantially from putative representational states associated with mere sensory indicators, and we reply to some possible (...) objections from the liberal representationalists camp by defending and qualitatively demarcating the minimal nature of our case. Finally, we briefly discuss the implications of our thesis within a naturalistic framework. (shrink)

I recently discovered that work I was doing in the laboratory and in theoretical writings was implicitly taking a position on a set of questions that philosophers had been worrying about for much of the past 30 or more years. My clandestine involvement in philosophical issues began when a computer science colleague and I were trying to build a model of geometrical reasoning that would draw a diagram and notice things in the diagram as it drew it (Pylyshyn, Elcock, (...) Marmor, & Sander, 1978). One problem we found we had to face was that if the system discovered a right angle it had no way to tell whether this was the intersection of certain lines it had drawn earlier while constructing a certain figure, and if so which particular lines they were. Moreover, the model had no way of telling whether this particular right angle was identical to some bit of drawing it had earlier encountered and represented as, say, the base of a particular triangle. There was, in other words, no way to determined the identity of an element (I use the term “element” when referring to a graphical unit such as used in experiments. Otherwise when speaking informally I use the term “thing” on the grounds that nobody would mistake that term for a technical theoretical construct. Eventually I end up calling them “Visual Objects” to conform to usage in psychology) at two different times if it was represented differently at those times. This led to some speculation about the need for what we called a “finger” that could be placed at a particular element of interest and that could be used to identify it as particular token thing (the way you might identify a particular feature on paper by labeling it). In general we needed something like a finger that would stay attached to a particular element and could be used to maintain a correspondence between the individual element that was just noticed now and one that had been represented in some fashion at an earlier time. The idea of such fingers (which.... (shrink)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that (...) one of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.In essence, modal logic is a simple formalism for working with relational structures . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference (...) to individual nodes is possible.But hybrid logic is a rather unusual modal upgrade. It pushes one simple idea as far as it will go: represent all information as formulas. This turns out to be the key needed to draw together a surprisingly diverse range of work . Moreover, it displays a number of knowledge representation issues in a new light, notably the importance of sorting. (shrink)

Ninety-one right brain-damaged patients with left neglect and 43 right brain-damaged patients without neglect were asked to extend horizontal segments, either left- or rightward, starting from their right or left endpoints, respectively. Earlier experiments based on similar tasks had shown, in left neglect patients, a tendency to overextend segments toward the left side. This seemingly paradoxical phenomenon was held to undermine current explanations of unilateral neglect. The results of the present extensive research demonstrate that contralesional overextension is also evident in (...) most right brain-damaged patients without contralesional neglect. Furthermore, they show that in a minority of left neglect patients, the opposite behavior, i.e., right overextension can be found. The paper also reports the results of correlational analyses comprising the parameters of line-extension, line-bisection, and cancellation tasks, as well as the parameters relative to the Milner Landmark Task, by which a distinction is drawn between perceptual and response biases in unilateral neglect. A working hypothesis is then advanced about the brain dysfunction underlying neglect and an attempt is made at finding an explanation of neglect and the links between the mechanisms of space representation and consciousness through the study of the changes induced by unilateral brain lesions in the characteristics of space-coding neurons. Abbreviations: C, control group;GN+91,full group of neglect patients;GN+27,group of neglect patients with relative left overextension;GN+14,group of neglect patients with relative right overextension;GN-43,full group of non-neglect patients;GN-9,group of non-neglect patients with relative left overextension; H canc, H cancellation task; LE, left extension; LE/RE, ratio of left-right extension; N+, neglect patients; N-, non-neglect patients; PB Land-M, perceptual bias on Landmark motor task; PB Land-V, perceptual bias on Landmark verbal task; RB Land-M, response bias on Landmark motor task; RB Land-V, response bias on Landmark verbal task; RE, right extension. (shrink)

The emulation theory of representation is developed and explored as a framework that can revealingly synthesize a wide variety of representational functions of the brain. The framework is based on constructs from control theory (forward models) and signal processing (Kalman filters). The idea is that in addition to simply engaging with the body and environment, the brain constructs neural circuits that act as models of the body and environment. During overt sensorimotor engagement, these models are driven by efference copies in (...) parallel with the body and environment, in order to provide expectations of the sensory feedback, and to enhance and process sensory information. These models can also be run off-line in order to produce imagery, estimate outcomes of different actions, and evaluate and develop motor plans. The framework is initially developed within the context of motor control, where it has been shown that inner models running in parallel with the body can reduce the effects of feedback delay problems. The same mechanisms can account for motor imagery as the off-line driving of the emulator via efference copies. The framework is extended to account for visual imagery as the off-line driving of an emulator of the motor-visual loop. I also show how such systems can provide for amodal spatial imagery. Perception, including visual perception, results from such models being used to form expectations of, and to interpret, sensory input. I close by briefly outlining other cognitive functions that might also be synthesized within this framework, including reasoning, theory of mind phenomena, and language. Key Words: efference copies; emulation theory of representation; forward models; Kalman filters; motor control; motor imagery; perception; visual imagery. (shrink)

Several recent books indicate that the philosophy of art has embarked upon a new alliance with cognitive science. One impetus for this is the move, beginning in the 70s and 80s, away from general aesthetics to a greater concern with the philosophies of the individual arts. Questions about the nature of art, expression, aesthetic experience and aesthetic properties as generic phenomena are still with us but many philosophers now approach them by means of specialized studies of music, literature, film, the (...) visual arts or the performing arts. Some claim that these questions can only be answered, or can best be answered, by studying the individual art forms. This has brought aesthetics into alignment with empirical research, which has always been concerned with individual art forms, for reasons having to do both with experimental design and with views of the mind as functionally differentiated. There is no psychological work on the perception of beauty, for example, but only on the perception of visual beauty, beauty in music and the like. Now that aesthetics is equally specialized, empirical research on the individual arts can be brought to bear upon familiar problems in aesthetics. (shrink)

The importance of working memory in reading and mathematics performance has been widely studied, with recent research examining the components of WM and their roles in these educational outcomes. However, the differing relationships between these abilities and the foundational skills involved in the development of reading and mathematics have received less attention. Additionally, the separation of verbal, visual and spatial storage and processing and subsequent links with foundational skills and downstream reading and mathematics has not been widely examined. The (...) current study investigated the separate contributions of processing and storage from verbal, visual and spatial tasks to reading and mathematics, whilst considering influences on the underlying skills of verbal comprehension and counting, respectively. Ninety-two children aged 7- to 8-years were assessed. It was found that verbal comprehension was predicted by verbal storage and reading was predicted by verbal and spatial storage. Counting was predicted by visual processing and storage, whilst mathematics was related to verbal and spatial storage. We argue that resources for tasks relying on external representations of stimuli related mainly to storage, and were largely verbal and spatial in nature. When a task required internal representation, there was a draw on visual processing and storage abilities. Findings suggest a possible meaningful separability of types of processing. Further investigation of this could lead to the development of an enhanced WM model, which might better inform interventions and reasonable adjustments for children who struggle with reading and mathematics due to WM deficits. (shrink)

The problem of representing the spatial structure of images, which arises in visual object processing, is commonly described using terminology borrowed from propositional theories of cognition, notably, the concept of compositionality. The classical propositional stance mandates representations composed of symbols, which stand for atomic or composite entities and enter into arbitrarily nested relationships. We argue that the main desiderata of a representational system—productivity and systematicity—can (indeed, for a number of reasons, should) be achieved without recourse to the classical, (...) proposition‐like compositionality. We show how this can be done, by describing a systematic and productive model of the representation of visual structure, which relies on static rather than dynamic binding and uses coarsely coded rather than atomic shape primitives. (shrink)

The problem of representing the spatial structure of images, which arises in visual object processing, is commonly described using terminology borrowed from propositional theories of cognition, notably, the concept of compositionality. The classical propositional stance mandates representations composed of symbols, which stand for atomic or composite entities and enter into arbitrarily nested relationships. We argue that the main desiderata of a representational system — productivity and systematicity — can (indeed, for a number of reasons, should) be achieved without (...) recourse to the classical, proposition-like compositionality. We show how this can be done, by describing a systematic and productive model of the representation of visual structure, which relies on static rather than dynamic binding and uses coarsely coded rather than atomic shape primitives. (shrink)

The founder of both American pragmatism and semiotics, Charles Sanders Peirce is widely regarded as an enormously important and pioneering theorist. In this book, scholars from around the world examine the nature and significance of Peirce’s work on perception, iconicity, and diagrammatic thinking. Abjuring any strict dichotomy between presentational and representational mental activity, Peirce’s theories transform the Aristotelian, Humean, and Kantian paradigms that continue to hold sway today and, in so doing, forge a new path for understanding the centrality of (...) visual thinking in science, education, art, and communication. The essays in this collection cover a wide range of issues related to Peirce’s theories, including the perception of generality; the legacy of ideas being copies of impressions; imagination and its contribution to knowledge; logical graphs, diagrams, and the question of whether their iconicity distinguishes them from other sorts of symbolic notation; how images and diagrams contribute to scientific discovery and make it possible to perceive formal relations; and the importance and danger of using diagrams to convey scientific ideas. This book is a key resource for scholars interested in Perice’s philosophy and its relation to contemporary issues in mathematics, philosophy of mind, philosophy of perception, semiotics, logic, visual thinking, and cognitive science. (shrink)

This monograph treats the important topic of the epistemology of diagrams in Euclidean geometry. Norman argues that diagrams play a genuine justificatory role in traditional Euclidean arguments, and he aims to account for these roles from a modified Kantian perspective. Norman considers himself a semi-Kantian in the following broad sense: he believes that Kant was right that ostensive constructions are necessary in order to follow traditional Euclidean proofs, but he wants to avoid appealing to Kantian a priori intuition as the (...) epistemological background for these constructions.Norman's main argument is limited to the thesis that certain Euclidean arguments—in particular, that of Proposition 1.32, the internal-angle-sum theorem—require inferences from diagrams. Interestingly, Norman is not committed to the view that these arguments are proofs. This becomes clear only quite late in the book, when he distinguishes argument from proofs, remarking that the argument he has been focusing on is not rigorous, and so is not a proof. Norman does not, however, explicitly classify all Euclidean arguments as non-proofs. His view is that diagrammatic reasoning can in principle feature in rigorous proofs, but he is not committed to the thesis that any particular argument, Euclidean or otherwise, provides an example of this. Rather than proofs in particular, Norman is more interested in the general issue of justification in mathematics.The argument has three components. First, Norman argues against competing accounts of Euclidean arguments such as empiricism, and ‘Leibnizianism’—the view that diagrams play only a heuristic role. Second, he provides a more direct, or positive, argument that the way we actually follow the standard argument for 1.32 does appeal to the diagram. This is an appeal to the phenomenology of following the argument. Third, he articulates and defends his semi-Kantian position against some objections.The book has a very careful and …. (shrink)

Visual analogy is believed to be important in human problem solving. Yet, there are few computational models of visual analogy. In this paper, we present a preliminary computational model of visual analogy in problem solving. The model is instantiated in a computer program, called Galatea, which uses a language for representing and transferring visual information called Privlan. We describe how the computational model can account for a small slice of a cognitive-historical analysis of Maxwell’s reasoning (...) about electromagnetism. (shrink)

Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations and linguistic features. Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: highlighting relevant relations in a micrograph ; sketching the plan for an experiment; and expressing expected visually salient (...) information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as heuristic tools in proof construction ; notational devices; and full-blown proof procedures. Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception. (shrink)