| Description |
1 online resource (iii, 304 pages) : illustrations |
| Series |
Fichte-Studie-Supplementa ; Bd. 29 |
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Fichte-Studien-Supplementa ; Bd. 29.
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| Contents |
Cover; Title Page; Copyright Page; Table of Contents; Acknowledgements; Introduction: Fichte as the Euclid of Philosophy?; a. Fichte and Mathematics; b. Theses and Methodology; c. Contemporary Reception and Influences on Fichte; d. Current State of Research; Chapter One: Fichte's Philosophy of Mathematics; 1. A Philosophy of Mathematics in nuce: Fichte's Erlanger Logik; a. The Nature of the Erlangen Text; b. What is a Philosophy of Mathematics?; c. Situating the Erlanger Logik among Fichte's other Texts on Mathematics; 2. The Contents of a Fichtean Philosophy of Mathematics |
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A. Nine Elements of a Philosophy of Mathematics in the Erlanger Logik 1805i. Geometry; ii. Arithmetic; iii. Algebra; iv. Theory of Infinity; v. Archetypal Elements; vi. Transcendentalism; vii. The Parallel Problem; viii. Dimensions of Space; ix. Language of Mathematics; Chapter Two: Fichte's Theory of "Original" Geometry; 1. "Ordinary" and "Original" Geometry; a. Synthetic and Analytic in Geometry; b. Kant's Conception of Geometry; c. Fichte's Theory of "Original" Geometry; d. Where to Place Fichte's Theory in the History of Geometry?; 2. Fichte's Mathematical Platonism |
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A. Formalism, Logicism and Intuitionismb. Fichte's Mathematical Platonism ; c. Platonism, Neo-Platonism and the Wissenschaftslehre; Chapter Three: Axioms, Intuition and Construction; 1. Is Fichte's Grundsatz equivalent to a Geometric Postulate?; a. Definitions, Axioms and Postulates: The First Principles of Geometry; b. Fichte's Grundsatz and the Postulates of Geometry; c. Wissenschaftslehre more geometrico?; 2. Sensible, Mathematical and Intellectual Intuitio; a. From Kant's Sensible Intuition to Fichte's Intellectual Intuition; b. What is Geometrical Intuition? |
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C. Fichte on the Intelligible Intuitions of Mathematics3. Geometrical Construction in the Wissenschaftslehre; a. Fichte's Understanding of Construction; b. Geometrical Construction in Fichte's Sonnenklarer Bericht (1801) and Einleitung in die Wissenschaftslehre (1813); Chapter Four: The Fichtean Conception of Space; 1. Philosophical Images: Fichte on Fundamental Elements of Geomet; a. The Euclidean and Fichtean Definitions of the Point; b. The Point and das Bild des Ich; c. The Euclidean and Fichtean Definitions of the Geometric Line |
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D. The Drawing of the Line and das Bild des Lebens -- Fichte's Transformation of Euclid's First Postulate2. Fichte's Conception of Space; a. Kant's Theory of Space; b. Differences Between the Fichtean and Kantian Theories of Space; c. Fichte on Time and Original Space; d. Geometry as the Science of Space; Chapter Five: The Relationship between Geometry and the "Wissenschaftslehre"; 1. Geometry as a Propedeutic for the Wissenschaftslehre; a. Pestalozzi's Influence and the Teaching of Mathematics; b. The Path from Geometry to the Fichtean System of Philosophy |
| Summary |
This is the first major study in any language on J.G. Fichte's philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to "ordinary" Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an "ursprüngliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or in |
| Bibliography |
Includes bibliographical references |
| Notes |
Based on the author's thesis (Ph. D.)--Ludwig-Maximilians-Universität, Munich, 2009 |
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Print version record |
| Subject |
Fichte, Johann Gottlieb, 1762-1814.
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| SUBJECT |
Fichte, Johann Gottlieb, 1762-1814 fast |
| Subject |
Geometry -- Philosophy
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Mathematics -- Philosophy.
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PHILOSOPHY -- History & Surveys -- Modern.
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Geometry -- Philosophy
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Mathematics -- Philosophy
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| Form |
Electronic book
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| ISBN |
9789401207683 |
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9401207682 |
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