Origin of the Logic of Symbolic Mathematics

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.

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 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) [The Origin of the Logic of Symbolic Mathematics] contains a very precise thesis and claim, which can only be tackled by applying the technical terms and methods from the tradition in which it originated.June 2014(Philosophia Mathematica)

• Preface by Eva BrannIntroduction: The Subject Matter, Thesis, and Structure of the StudyPart One. Klein on Husserl's Phenomenology and the History of Science1. Klein's and Husserl's Investigations of the Origination of Mathematical Physics2. Klein's Account of the Essential Connection between Intentional and Actual History3. The Liberation of the Problem of Origin from its Naturalistic Distortion: The Phenomenological Problem of Constitution4. The Essential Connection between Intentional History and Actual History5. The Historicity of the Intelligibility of Ideal Significations and the Possibility of Actual History6. Sedimentation and the Link between Intentional History and the Constitution of a Historical Tradition7. Klein's Departure from the Content but Not the Method of Husserl's Intentional-Historical Analysis of Modern SciencePart Two. Husserl and Klein on the Method and Task of Desedimenting the Mathematization of Nature8. Klein's Historical-Mathematical Investigations in the Context of Husserl's Phenomenology of Science9. The Basic Problem and Method of Klein's Mathematical Investigations10.Husserl's Formulation of the Nature and Roots of the Crisis of European Sciences11. The "Zigzag" Movement Implicit in Klein's Mathematical Investigations12. Husserl and Klein on the Logic of Symbolic MathematicsPart Three. Non-Symbolic and Symbolic Numbers in Husserl and Klein13. Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic14. Klein's Desedimentation of the Origin Algebra and Husserl's Failure to Ground Symbolic Calculation 15. Logistic and Arithmetic in Neoplatonic Mathematics and in Plato16. Theoretical Logistic and the Problem of Fractions17. The Concept of 18. Plato's Ontological Conception of 19. Klein's Reactivation of Plato's Theory of 20. Aristotle's Critique of the Platonic Chorismos Thesis and the Possibility of a Theoretical Logistic21. Klein's Interpretation of Diophantus's Arithmetic22. Klein's Account of Vieta's Reinterpretation of the Diophantine Procedure and the Consequent Establishment of Algebra as the General Analytical Art23. Klein's Account of the Concept of Number and the Number Concepts in Stevin, Descartes, and WallisPart Four. Husserl and Klein on the Origination of the Logic of Symbolic Mathematics24. Husserl and Klein on the Fundamental Difference between Symbolic and Non-Symbolic Numbers25. Husserl and Klein on the Origin and Structure of Non-Symbolic Numbers26. Structural Differences in Husserl's and Klein's Accounts of the Mode of Being of Non-Symbolic Numbers27. 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 Universalis28. Husserl's Accounts of the Symbolic Calculus, the Critique of Psychologism, and the 29. Husserl's Critique of Symbolic Calculation in his Schröder Review30. The Separation of Logic from Symbolic Calculation in Husserl's Later Works31. 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 Investigations32. 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 Intuition33. Husserl's Account of the Constitution of the Collection, Number, and the 'Universal Whatever' inExperience and Judgment34. Husserl's Investigation of the Unitary Domain of Formal Logic and Formal Ontology in Formal and Transcendental Logic35. Klein and Husserl on the Origination of the Logic of Symbolic NumbersCoda: Husserl's "Platonism" within the Context of Plato's Own PlatonismGlossaryBibliographyIndex of NamesIndex of Subjects