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"Mathesis of the Mind"
A Study of Fichte’s Wissenschaftslehre and Geometry
Series: - Fichte-Studien, Supplementa, Volume: 29
Author:
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 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.”
"The author of this book has accomplished something that no one before him has even attempted. He has demonstrated that Fichte does indeed possess a coherent and original ‘philosophy of mathematics’ and even propounds a ‘new model of geometry,’ one that deserves closer attention than it has received. He also has shown that the connections between geometry and the Wissenschaftslehre are deep and significant, especially significant for an understanding the method of Fichte’s system." – Daniel Breazeale, in: Notre Dame Philosophical Reviews, August 2012
"This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched." – Professor Dr. Marco Ivaldo, University of Naples
"This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious." – Professor Dr. Emmanuel Cattin, Université Blaise-Pascal, Clermont-Ferrand
"This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched." – Professor Dr. Marco Ivaldo, University of Naples
"This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious." – Professor Dr. Emmanuel Cattin, Université Blaise-Pascal, Clermont-Ferrand
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
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