"Mathesis of the mind" : a study of Fichte's Wissenschaftslehre and geometry
著者
書誌事項
"Mathesis of the mind" : a study of Fichte's Wissenschaftslehre and geometry
（Fichte-Studien-Supplementa, Bd. 29）
Rodopi, 2012
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注記
Originally presented as the author's thesis (Ph.D.)--Ludwig-Maximilians-Universität, Munich, 2009
Bibliography: p. [291]-302
内容説明・目次
内容説明
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 "ursprungliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. Accordingly, this study classifies Fichte's philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or "mathesis of the mind."
目次
Acknowledgements
Introduction: Fichte as the Euclid of Philosophy?
Fichte's Philosophy of Mathematics
A Philosophy of Mathematics in nuce: Fichte's Erlanger Logik
The Contents of a Fichtean Philosophy of Mathematics
Fichte's Theory of "Original" Geometry
"Ordinary" and "Original" Geometry
Fichte's Mathematical Platonism
Axioms, Intuition and Construction
Is Fichte's Grundsatz equivalent to a Geometric Postulate?
Sensible, Mathematical and Intellectual Intuition
Geometrical Construction in the Wissenschaftslehre
The Fichtean Conception of Space
Philosophical Images: Fichte on Fundamental Elements of Geometry
Fichte's Conception of Space
The Relationship between Geometry and the "Wissenschaftslehre"
Geometry as a Propedeutic for the Wissenschaftslehre
Further Similarities and Differences between Wissenschaftslehre and Geometry
The "Wissenschaftslehre" as "Mathesis of the Mind"
Appendix: Johann Gottlieb Fichte: "Original Geometry"
Bibliography
List of Abbreviations
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