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.

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 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 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