Overview
- Provides a wider context for the study of visual experience in mathematics
- Compares Peirce’s idea of diagrammatic reasoning with Kant’s transcendental schematism
- Offers a fresh perspective on the relationship between visual experience and language
Part of the book series: Mathematics in Mind (MATHMIN)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical andmathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.
Authors and Affiliations
Bibliographic Information
Book Title: Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics
Authors: Vitaly Kiryushchenko
Series Title: Mathematics in Mind
DOI: https://doi.org/10.1007/978-3-031-23245-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-23244-2Published: 13 May 2023
Softcover ISBN: 978-3-031-23247-3Due: 13 June 2023
eBook ISBN: 978-3-031-23245-9Published: 12 May 2023
Series ISSN: 2522-5405
Series E-ISSN: 2522-5413
Edition Number: 1
Number of Pages: X, 172
Number of Illustrations: 1 b/w illustrations
Topics: Mathematical Logic and Foundations, Mathematics Education, Philosophy of Mathematics