The Origin of the Logic of Symbolic Mathematics

The Origin of the Logic of Symbolic Mathematics

Edmund Husserl and Jacob Klein
Burt C. Hopkins
Distribution: World
Publication date: 8/19/11
Format: cloth 592 pages
6 x 9
ISBN: 978-0-253-35671-0
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Description

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Author Bio

Burt C. Hopkins is Professor of Philosophy at Seattle University. He is author of Intentionality in Husserl and Heidegger and The Philosophy of Husserl. He is founding editor (with Steven G. Crowell) of The New Yearbook for Phenomenology and Phenomenological Philosophy and is permanent secretary of the Husserl Circle.

Reviews

"A striking, original study . . . for the history of mathematics, our understanding of Husserlian phenomenology, and the concepts of formality and formalization." —Robert B. Pippin, University of Chicago

"
The Origin of the Logic of Symbolic Mathematics initiates a radical clarification of François Vieta’s 17th century mathematical introduction of the formal-symbolic, which marks the revolution that made and continues to make possible modern mathematics and logic. Through a philosophically subtle, clarifying, and exacting elaboration of Jacob Klein’s Greek Mathematical Thought and the Origin of Algebra, Hopkins reveals flaws (and strengths) in Edmund Husserl’s thinking about numbers, the formal-symbolic, and the phenomenological foundation of the mathesis universalis." —Robert Tragesser, Author of Phenomenology and Logic and Husserl and Realism in Logic and Mathematics

"The Origin of the Logic of Symbolic Mathematics is a very important work. From an exegetical point of view it presents careful readings of an amazing amount of texts by Plato, Aristotle, Diophantus, Vieta, Stevin, Wallis, and Descartes and shows at the same time a profound knowledge of Husserl’s earlier and later texts . . . ." —History and Philosophy of Logic

"This much needed book should go a long way both toward correcting the under-appreciation of Jacob Klein's brilliant work on the nature and historical origin of modern symbolic mathematics, and toward eliciting due attentio to the significance of that work for our interpretation of the modern scientific view of the world." —Notre Dame Philosophical Reviews

"Hopkins brings all of the myriad concepts of Klein’s analysis of the origins of logic and symbolic mathematics into play as he elucidates the significance of the roles algebra, logic, and symbolic analysis generally have played in the development of modern mathematics" —Mathematical Reviews

"Hopkins’ detailed and careful readings of the texts make his book a source of numerous insights, and its erudition is breathtaking." —Husserl Studies

"This book serves not only as the first major contribution to scholarship on the thought of Jacob Klein, but also as a significant contribution to that of Husserl as well." —The Review of Metaphysics

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Table of Contents

Preface by Eva Brann

Introduction: The Subject Matter, Thesis, and Structure of the Study
Part One. Klein on Husserl’s Phenomenology and the History of Science
1. Klein’s and Husserl’s Investigations of the Origination of Mathematical Physics
2. Klein’s Account of the Essential Connection between Intentional and Actual History
3. The Liberation of the Problem of Origin from its Naturalistic Distortion: The Phenomenological Problem of Constitution
4. The Essential Connection between Intentional History and Actual History
5. The Historicity of the Intelligibility of Ideal Significations and the Possibility of Actual History
6. Sedimentation and the Link between Intentional History and the Constitution of a Historical Tradition
7. Klein’s Departure from the Content but Not the Method of Husserl’s Intentional-Historical Analysis of Modern Science
Part Two. Husserl and Klein on the Method and Task of Desedimenting the Mathematization of Nature
8. Klein’s Historical-Mathematical Investigations in the Context of Husserl’s Phenomenology of Science
9. The Basic Problem and Method of Klein’s Mathematical Investigations
10.Husserl’s Formulation of the Nature and Roots of the Crisis of European Sciences
11. The “Zigzag” Movement Implicit in Klein’s Mathematical Investigations
12. Husserl and Klein on the Logic of Symbolic Mathematics
Part Three. Non-Symbolic and Symbolic Numbers in Husserl and Klein
13. Authentic and Symbolic Numbers in Husserl’s Philosophy of Arithmetic
14. Klein’s Desedimentation of the Origin Algebra and Husserl’s Failure to Ground Symbolic Calculation
15. Logistic and Arithmetic in Neoplatonic Mathematics and in Plato
16. Theoretical Logistic and the Problem of Fractions
17. The Concept of ᾿Αριθμός
18. Plato’s Ontological Conception of ᾿Αριθμοί
19. Klein’s Reactivation of Plato’s Theory of ᾿Αριθμοὶ Εἰδητικοί
20. Aristotle’s Critique of the Platonic Chorismos Thesis and the Possibility of a Theoretical Logistic
21. Klein’s Interpretation of Diophantus’s Arithmetic
22. Klein’s Account of Vieta’s Reinterpretation of the Diophantine Procedure and the Consequent Establishment of Algebra as the General Analytical Art
23. Klein’s Account of the Concept of Number and the Number Concepts in Stevin, Descartes, and Wallis
Part Four. Husserl and Klein on the Origination of the Logic of Symbolic Mathematics
24. Husserl and Klein on the Fundamental Difference between Symbolic and Non-Symbolic Numbers
25. Husserl and Klein on the Origin and Structure of Non-Symbolic Numbers
26. Structural Differences in Husserl’s and Klein’s Accounts of the Mode of Being of Non-Symbolic Numbers
27. Digression: The Development of Husserl’s Thought, after Philosophy of Arithmetic, on the “Logical” Status of the Symbolic Calculus, the Constitution of Collective Unity, and the Phenomenological Foundation of the Mathesis Universalis
28. Husserl’s Accounts of the Symbolic Calculus, the Critique of Psychologism, and the
29. Husserl’s Critique of Symbolic Calculation in his Schröder Review
30. The Separation of Logic from Symbolic Calculation in Husserl’s Later Works
31. Husserl on the Shortcomings of the Appeal to the “Reflexion” on Acts to Account for the Origin of Logical Relations in the Works Leading Up to the Logical Investigations
32. Husserl’s Attempt in the Logical Investigations to Establish a Relationship between “Mere” Thought and the “In Itself ” of Pure Logical Validity by Appealing to Concrete, Universal, and Formalizing Modes of Abstraction and Categorial Intuition
33. Husserl’s Account of the Constitution of the Collection, Number, and the ‘Universal Whatever’ in
Experience and Judgment
34. Husserl’s Investigation of the Unitary Domain of Formal Logic and Formal Ontology in Formal and Transcendental Logic
35. Klein and Husserl on the Origination of the Logic of Symbolic Numbers
Coda: Husserl’s “Platonism” within the Context of Plato’s Own Platonism
Glossary
Bibliography
Index of Names
Index of Subjects
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