Erich Reck

Affiliation: 

University of California

On the Pre-History of Mathematical Structuralism

The symposium will investigate the historical roots of mathematical structuralism, one of the most prominent positions in current philosophy of mathematics. At the position’s core lies the suggestion that mathematical theories describe abstract structures: Peano arithmetic describes the natural number structure, analysis the real number structure, geometry the structure of (Euclidian) space, and so on. Precise elaborations, or formal explications, of that suggestion have been provided in terms of a number of different versions of structuralism by now.

Structuralist themes in the early Husserl

In the late 1890s and early 1900s, Husserl devoted considerable efforts toward developing a “theory of manifolds [Mannigfaltigkeitslehre]”. There are evidently ties to developments in 19th-century mathematics, e.g., Bernhard Riemann’s novel approach to geometry. In the