Ebook: Visual Reasoning with Diagrams

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.

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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.

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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.
Content:
Front Matter....Pages I-XV
What is a Logical Diagram?....Pages 1-18
The Geometry of Diagrams and the Logic of Syllogisms....Pages 19-31
A Diagrammatic Calculus of Syllogisms....Pages 33-53
Beyond Syllogisms: Carroll’s (Marked) Quadriliteral Diagram....Pages 55-71
A Diagrammatic Bridge Between Standard and Non-standard Logics: The Numerical Segment....Pages 73-81
Diagrammatic Reasoning with Classes and Relationships....Pages 83-100
On the Completeness of Spider Diagrams Augmented with Constants....Pages 101-133
A Practice-Based Approach to Diagrams....Pages 135-151
Figures, Formulae, and Functors....Pages 153-170
Representation of Graphs in Diagrams of Graph Theory....Pages 171-200

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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.
Content:
Front Matter....Pages I-XV
What is a Logical Diagram?....Pages 1-18
The Geometry of Diagrams and the Logic of Syllogisms....Pages 19-31
A Diagrammatic Calculus of Syllogisms....Pages 33-53
Beyond Syllogisms: Carroll’s (Marked) Quadriliteral Diagram....Pages 55-71
A Diagrammatic Bridge Between Standard and Non-standard Logics: The Numerical Segment....Pages 73-81
Diagrammatic Reasoning with Classes and Relationships....Pages 83-100
On the Completeness of Spider Diagrams Augmented with Constants....Pages 101-133
A Practice-Based Approach to Diagrams....Pages 135-151
Figures, Formulae, and Functors....Pages 153-170
Representation of Graphs in Diagrams of Graph Theory....Pages 171-200
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