We are a Working Group devoted to the discussion of historical and philosophical issues in symbolic logic, mathematics, and science. We meet on occasional Wednesday evenings for a talk and a lively discussion. The group is funded by the Doreen B. Townsend Center for the Humanities and the Department of Philosophy.

All members of the academic community are welcome to attend. We have regular participants in many different fields, including philosophy, mathematics, history of science, and psychology.

The group organizers are Lara Buchak (Philosophy), Wesley Holliday (Philosophy), John MacFarlane (Philosophy), Paolo Mancosu (Philosophy), and Seth Yalcin (Philosophy).

Our next event

September 20, 2017, 6-7:30 PM in 234 Moses Hall

Douglas Marshall (Carleton College)

Impurity of Methods: Finite Geometry in the Early Twentieth Century

My talk aims to assess the reasonableness of various demands for purity of methods in mathematics by means of a historical case study of finite geometry in the early twentieth century. Work done in the foundations of algebra from 1900-1910 paved the way for corresponding advances in finite geometry. In particular, a geometric theorem on finite projective planes (Veblen and Bussey, 1906) was proved only with the help of an algebraic theorem on finite division rings (Wedderburn, 1905; Dickson 1905). In later years, several attempts were made to find a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem, none of them entirely successful (Segre, 1958; Tecklenberg 1987). Given that it has already been proved, what exactly would be accomplished by the discovery of a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem? What considerations favor or disfavor the devotion of research effort to a purely geometric development of finite geometry?