David Corfield The Idea of Space

Taking R G Collingwood’s idea of metaphysics as the study of the changing presuppositions of a science (construed broadly, to include history), what would we include in a study of the presuppositions of geometry? In other words, what would a successor look like to Robert Toretti’s Philosophy of Geometry from Riemann to Poincaré and Jeremy Gray, Ideas of Space: Euclidean, Non-Euclidean, and Relativistic or Worlds Out of Nothing?

• Klein, Erlanger Program

• Lie,

• Poincare

• Hilbert

• Noether, Alexandrov, algebraic topology

• Grothendieck, n-groupoids

• Connes, noncommutative geometry

• Cartier’s Mad Day’s Work

• Other noncommutative geometry

• Lurie, Toen, derived algebraic geometry, higher geometry

• space

• Space and Quantity

• $\infty$-space

• geometry