Wood D. Mathesis of the Mind: A Study of Fichte's Wissenschaftslehreand Geometry

Amsterdam: Rodopi, 2012. — 314 p. — ISBN-10: 9042034912; ISBN-13: 978-9042034914 — ( Fichte-Studien-Supplementa. Book 29)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. 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."Introduction: Fichte as the Euclid of Philosophy?Fichte and Mathematics
Theses and Methodology
Contemporary Reception and Influences on Fichte
Current State of ResearchFichte’s Philosophy of MathematicsA Philosophy of Mathematics in nuce: Fichte’s Erlanger LogikThe Nature of the Erlangen Text
What is a Philosophy of Mathematics?
Situating the Erlanger Logik among Fichte’s other Texts on MathematicsThe Contents of a Fichtean Philosophy of MathematicsNine Elements of a Philosophy of Mathematics in the Erlanger Logik 1805Fichte’s Theory of »Original« Geometry"Ordinary" and "Original" GeometrySynthetic and Analytic in Geometry
Kant’s Conception of Geometry
Fichte’s Theory of »Original« Geometry
Where to Place Fichte’s Theory in the History of Geometry?Fichte’s Mathematical PlatonismFormalism, Logicism and Intuitionism
Fichte’s Mathematical Platonism
Platonism, Neo-Platonism and the WissenschaftslehreAxioms, Intuition and Construction

[b][i]Is Fichte’s Grundsatz equivalent to a Geometric Postulate?

[i]Definitions, Axioms and Postulates: The First Principles of Geometry
Fichte’s Grundsatz and the Postulates of Geometry
Wissenschaftslehre more geometrico?Sensible, Mathematical and Intellectual IntuitionFrom Kant’s Sensible Intuition to Fichte’s Intellectual Intuition
What is Geometrical Intuition?
Fichte on the Intelligible Intuitions of Mathematics
Geometrical Construction in the Wissenschaftslehre
Fichte’s Understanding of Construction
Geometrical Construction in Fichte’s Sonnenklarer Bericht (1801) and Einleitung in die Wissenschaftslehre (1813)[b]The Fichtean Conception of SpacePhilosophical Images: Fichte on Fundamental Elements of GeometryThe Euclidean and Fichtean Definitions of the Point
The Point and das Bild des Ich
The Euclidean and Fichtean Definitions of the Geometric Line
The Drawing of the Line and das Bild des LebensFichte’s Transformation of Euclid’s First PostulateFichte’s Conception of SpaceKant’s Theory of Space
Differences Between the Fichtean and Kantian Theories of Space
Fichte on Time and Original Space
Geometry as the Science of SpaceThe Relationship between Geometry and the "Wissenschaftslehre"Geometry as a Propedeutic for the WissenschaftslehrePestalozzi’s Influence and the Teaching of Mathematics
The Path from Geometry to the Fichtean System of PhilosophyFurther Similarities and Differences between Wissenschaftslehre and Geometry[/i]Similarities: Evidenz, Determinacy and Irrefutability
Differences: Formal Languages and Freiheit[/i]Conclusion: The "Wissenschaftslehre" as "Mathesis of the Mind"Fichte’s New Philosophical MathesisJohann Gottlieb Fichte: »Original Geometry« – Translated excerpt from: Erlanger Logik (1805)Works of Johann Gottlieb Fichte
Classical and Contemporary Sources
Other Authors