Abstract

This is an in-depth study of 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.” Professor Dr. Marco Ivaldo “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