The project investigates the mathematical and philosophical roots of mathematical structuralism. Its focus is on several historical developments in nineteenth century mathematics and early twentieth century philosophy: the first one concerns several conceptual changes in geometry between 1860 and 1910 that eventually led to a “structural turn” in the field. This includes the gradual implementation of model-theoretic techniques in geometrical reasoning, the study of geometrical theories by group-theoretic methods as well as the successive consolidation of formal axiomatics. The second development considered here concerns the beginnings of the philosophical reflection on structural mathematics between 1900 and 1940. This includes different attempts by thinkers such as Rudolf Carnap, Edmund Husserl, and Ernst Cassirer (among others) to spell out the philosophical implications of the new structuralist methodologies at work in modern geometry. The principal objective of the project is to provide a first comparative investigation of these early contributions to structuralism and of their immediate mathematical background. The second aim is to connect these early contributions with more recent debates on mathematical structuralism. Specifically, the project aims to provide new systematic insights relevant to contemporary structuralism, in particular a new understanding of notions such as mathematical structure, structural abstraction, and structural properties, as well as of their significance for the philosophy of mathematical practice.
The Roots of Mathematical Structuralism is a five-year project, funded by the European Research Council (03/2017-02/2022) no. 715222. The project is located at the University of Vienna under the direction of Georg Schiemer (Department of Philosophy).