Geometrical Practices between Unification and Purity of Methods

• Applicant: Tabea Rohr
• Subject Area: Theoretical Philosophy
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 426133767

The project aims to demonstrate, at the example of geometry, how philosophical analysis of mathematical knowledge can be broadened by uncovering the particularities of specific branches of mathematics. Therefore, it shall be argued on the basis of an historical analysis of the dispute between analytic and synthetic geometry, that purity of methods, which highly valued by synthetic geometry, has an epistemological significance. Purity of methods is, however, often perceived as opposed to the goal to unify mathematics in order to uncover the foundation of mathmatics. Though it depends on which of the notion of purity and unification discussed in the literature is taken as a basis. It will be discussed which epistemological significance is addresed to unification and purity of methods and be argued that, by the interplay of analytical and synthetical practices, the epistemological values of unification and purity of methods can be combined.The project is thus divided into three tasks: (1) The historical analysis of 19th century synthetic geometry, which the applicant worked out in her dissertation, will be supplemented by a historical analysis of Descartes unificational project and his delimitation criteria for geometry. On this basis the following systematic tasks shall be addressed: (2) A taxonomy of different notions of unification and purity one finds in the present literature shall be set up. (3) The epistemological significance of unification and purity of methods shall be discussed.

• DFG Programme: Research Fellowships
• International Connection: France
• Host: Professor Andrew Arana