This book analyses the role of diagrammatic reasoning in Plato’s philosophy: the readers will realize that Plato, describing the stages of human cognitive development using a diagram, poses a logic problem to stimulate the general reasoning abilities of his readers. Following the examination of mental models in this book, the readers will reflect on what inferences can be useful to approach this kind of logic problem. Plato calls for a collaboration between writer and readers. In this book the readers will examine the connection between diagrams and discovery, realizing the important epistemic role of visualization. They will recognize the crucial role that diagrams play in problem solving. The logic problem elaborated by Plato is addressed considering the epistemic function of mental models. These models introduce to an advanced stage of cognitive development, in which reasoning uses in its investigations a higher-level of mathematical complexity, represented by structuralism.

Proceedings of the 4th International Conference on Theory and Application of Diagrams, Stanford, CA, USA in June 2006. 13 revised full papers, 9 revised short papers, and 12 extended abstracts are presented together with 2 keynote papers and 2 tutorial papers. The papers are organized in topical sections on diagram comprehension by humans and machines, notations: history, design and formalization, diagrams and education, reasoning with diagrams by humans and machines, and psychological issues in comprehension, production and communication.

The first reference on rationality that integrates accounts from psychology and philosophy, covering descriptive and normative theories from both disciplines. Both analytic philosophy and cognitive psychology have made dramatic advances in understanding rationality, but there has been little interaction between the disciplines. This volume offers the first integrated overview of the state of the art in the psychology and philosophy of rationality. Written by leading experts from both disciplines, The Handbook of Rationality covers the main normative and descriptive theories of rationality—how people ought to think, how they actually think, and why we often deviate from what we can call rational. It also offers insights from other fields such as artificial intelligence, economics, the social sciences, and cognitive neuroscience. The Handbook proposes a novel classification system for researchers in human rationality, and it creates new connections between rationality research in philosophy, psychology, and other disciplines. Following the basic distinction between theoretical and practical rationality, the book first considers the theoretical side, including normative and descriptive theories of logical, probabilistic, causal, and defeasible reasoning. It then turns to the practical side, discussing topics such as decision making, bounded rationality, game theory, deontic and legal reasoning, and the relation between rationality and morality. Finally, it covers topics that arise in both theoretical and practical rationality, including visual and spatial thinking, scientific rationality, how children learn to reason rationally, and the connection between intelligence and rationality.

Advanced visual analysis and problem solving has been conducted successfully for millennia. The Pythagorean Theorem was proven using visual means more than 2000 years ago. In the 19th century, John Snow stopped a cholera epidemic in London by proposing that a specific water pump be shut down. He discovered that pump by visually correlating data on a city map. The goal of this book is to present the current trends in visual and spatial analysis for data mining, reasoning, problem solving and decision-making. This is the first book to focus on visual decision making and problem solving in general with specific applications in the geospatial domain - combining theory with real-world practice. The book is unique in its integration of modern symbolic and visual approaches to decision making and problem solving. As such, it ties together much of the monograph and textbook literature in these emerging areas. This book contains 21 chapters that have been grouped into five parts: (1) visual problem solving and decision making, (2) visual and heterogeneous reasoning, (3) visual correlation, (4) visual and spatial data mining, and (5) visual and spatial problem solving in geospatial domains. Each chapter ends with a summary and exercises. The book is intended for professionals and graduate students in computer science, applied mathematics, imaging science and Geospatial Information Systems (GIS). In addition to being a state-of-the-art research compilation, this book can be used a text for advanced courses on the subjects such as modeling, computer graphics, visualization, image processing, data mining, GIS, and algorithm analysis.

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important or creative changes in theories and concepts. It includes revised contributions presented during the international conference on Model-Based Reasoning (MBR’015), held on June 25-27 in Sestri Levante, Italy. The book is divided into three main parts, the first of which focuses on models, reasoning and representation. It highlights key theoretical concepts from an applied perspective, addressing issues concerning information visualization, experimental methods and design. The second part goes a step further, examining abduction, problem solving and reasoning. The respective contributions analyze different types of reasoning, discussing various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of historical, epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies in experimental research, this part aims at fostering new discussions and stimulating new ideas. All in all, the book provides researchers and graduate students in the field of applied philosophy, epistemology, cognitive science and artificial intelligence alike with an authoritative snapshot of current theories and applications of model-based reasoning.

Australia and New Zealand boast an active community of scholars working in the field of history, philosophy and social studies of science. Australasian Studies in History and Philosophy of Seien ce aims to provide a distinctive publication of essays on a connected outlet for their work. Each volume comprises a group theme, edited by an Australian or a New Zealander with special expertise in that particular area. In each volume, a majority of the contributors is from Australia or New Zealand. Contributions from elsewhere are by no means ruled out, however, and are indeed actively encouraged wherever appropriate to the balance of the volume in question. Earlier volumes in the series have been welcomed for significantly advancing the discussion of the topics they have dealt with. I believe that the present volume will be greeted equally enthusiastically by readers in many parts of the world. R. W Horne General Editor Australasian Studies in History and Philosophy of Science ix LIST OF ILLUSTRATIONS Frontispiece. Andreas Vesalius, Sixth Plate ofthe Muscles, woodcut, designed by Jan Steven van Kalkar, from De humani corporis fabrica (Basel, 1543). (Photo. Scientific Illustration; repr. by kind permission of the University of New South Wales Library. ) In: GUY FREELAND, 'Introduction: In Praise of Toothing-Stones' Fig. 1. Michael Esson, Vesalian Interpretation 3 (1992). (Repr. by kind permission ofthe Artist. ) Fig. 2. Reliefs, University of Padua.

For almost 2,500 years, the Western concept of what is to be human has been dominated by the idea that the mind is the seat of reason - humans are, almost by definition, the rational animal. In this text a more radical suggestion for explaining these puzzling aspects of human reasoning is put forward.

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.

Modeling complex systems is a difficult challenge and all too often one in which modelers are left to their own devices. Using a multidisciplinary approach, The Art of Software Modeling covers theory, practice, and presentation in detail. It focuses on the importance of model creation and demonstrates how to create meaningful models. Presenting three self-contained sections, the text examines the background of modeling and frameworks for organizing information. It identifies techniques for researching and capturing client and system information and addresses the challenges of presenting models to specific audiences. Using concepts from art theory and aesthetics, this broad-based approach encompasses software practices, cognitive science, and information presentation. The book also looks at perception and cognition of diagrams, view composition, color theory, and presentation techniques. Providing practical methods for investigating and organizing complex information, The Art of Software Modeling demonstrates the effective use of modeling techniques to improve the development process and establish a functional, useful, and maintainable software system.