Visual Reasoning with Diagrams

Front Cover
Amirouche Moktefi, Sun-Joo Shin
Springer Science & Business Media, Jul 8, 2013 - Mathematics - 200 pages
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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Contents

What is a Logical Diagram?
1
The Geometry of Diagrams and the Logic of Syllogisms
19
A Diagrammatic Calculus of Syllogisms
33
Carrolls Marked Quadriliteral Diagram
55
The Numerical Segment
73
Diagrammatic Reasoning with Classes and Relationships
83
On the Completeness of Spider Diagrams Augmented with Constants
101
A PracticeBased Approach to Diagrams
135
Figures Formulae and Functors
153
Representation of Graphs in Diagrams of Graph Theory
171
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