Indiana University Bloomington
Indiana University Bloomington
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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.
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.
“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
Preface by Eva Brann
Introduction: 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 Logistic
Fulfilling the Promise
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