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Conceptual Harmonies

The Origins and Relevance of Hegel’s Logic

A new reading of Hegel’s Science of Logic through the history of European mathematics.

Conceptual Harmonies develops an original account of G. W. F. Hegel’s perplexing Science of Logic from a simple insight: philosophical and mathematical thought have shaped each other since classical times. Situating Science of Logic within the rise of modern mathematics, Redding stresses Hegel’s attention to Pythagorean ratios, Platonic reason, and Aristotle’s geometrically inspired logic. He then explores how later traditions shaped Hegel’s world, through both Leibniz and new forms of algebraic geometry. This enlightening reading recovers an overlooked stream in Hegel’s philosophy that remains, Redding argues, important for contemporary conceptions of logic.

328 pages | 28 line drawings | 6 x 9 | © 2023

History: History of Ideas

Philosophy: General Philosophy, History and Classic Works, Logic and Philosophy of Language

Reviews

"In making his case, Redding places Hegel's discussion of logic and mathematics in a broad historical context, ranging from Plato's academy through Kepler, Newton, Leibniz, Frege, Boole, and Peirce. . . The book will be of interest to Hegel's scholars, not least of all for the challenge it mounts to Robert Brandom's contention that Hegel is best understood within the project of analytic philosophy."

Choice

"In this book, Paul Redding offers his most comprehensive answer to a question that is at the heart of his work: what is the relationship between Hegelian logic and 'what is commonly called logic?'"
 

Archives of Philosophy | Hegelian Bulletin

"The argument of Conceptual Harmonies is . . . a further, if not definitive, sign that the debate on Hegel’s metaphysics is finally changing."

Journal of Transcendental Philosophy

"Conceptual Harmonies is the best kind of history of philosophy. In it, Paul Redding uncovers a neglected tradition of Greek mathematics and shows its importance for Hegel’s theory of logical categories. Redding thus finds a new vocabulary in which to paraphrase some of Hegel’s most idiosyncratic formulations, but a vocabulary with a rich history of which Hegel was more aware than are we contemporary readers of him."

Critical Horizons

“The erudition and scope of Redding’s new book are staggering. This is a very fine book on the history of ancient logic and mathematics and its modern German reception, and it is also a major contribution to Hegel studies and philosophy. We finally have a clear and compelling answer to the question, What did Hegel actually think logic was? Redding has shown us the deep philosophical importance of that answer.”

Robert B. Pippin, University of Chicago

Conceptual Harmonies powerfully challenges a long-standing barrier to a full appreciation of Hegel’s logic: the assumption that, given his trenchant critique of all ‘formalisms,’ Hegel’s logic is in no way mathematical. With his characteristic erudition and insight, Redding guides readers through a history of logic and mathematics from Plato to the twentieth century, toward an entirely new understanding of Hegelian logic. Redding’s latest is a must-read for anyone interested in Hegel and the history of logic, proving once again that Redding is one of the most original, rigorous, and historically sensitive interpreters of Hegel writing in any language.”

Karen Ng, Vanderbilt University

“In Conceptual Harmonies, Redding makes a breathtakingly original case for a new understanding of Hegel’s Logic. Expanding the examination of Hegel’s sources well beyond the standard Aristotelian and Kantian texts, Redding rewrites the history of logic to show that Hegel anticipated many developments in the mid-nineteenth century and beyond. This is a major achievement that opens up a new line of research into Hegel’s though

Dean Moyar, Johns Hopkins University

Table of Contents

Hegel’s Texts: Translations and Abbreviations
Preface
Introduction

Beginning: Hegel’s Classicism
1 Logic, Mathematics, and Philosophy in Fourth-Century Athens
2 Hegel and the Platonic Origins of Aristotle’s Syllogistic
3 The General Significance of Neoplatonic Harmonic Theory for Hegel’s Account of Magnitude

Middle: Classical Meets Modern
4 Geometry and Philosophy in Hegel, Schelling, Carnot, and Grassmann
5 The Role of Analysis Situs in Leibniz’s Modernization of Logic
6 Hegel’s Supersession of Leibniz and Newton: The Limitations of Calculus and Logical Calculus

End: The Modern as Redetermined Classical
7 Exploiting Resources within Aristotle for the Rehabilitation of the Syllogism
8 The Return of Leibnizian Logic in the Nineteenth Century: From Boole to Heyting
9 Hegel among the New Leibnizians: Judgments
10 Hegel beyond the New Leibnizians: Syllogisms
Conclusion: The God at the Terminus of Hegel’s Logic
Acknowledgments
Notes
Bibliography
Index

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