Extension and measurement: A constructivist program from Leibniz to Grassmann

This paper traces what I see as a Leibniz-inspired constructivist program through the eyes of the 19th century philosopher-mathematicians Herbart, Riemann and Grassmann, and then uses Grassmann’s algebra of points to build up levels of extension algebraically. The connection between extension and measurement is investigated in line with this constructivist program.

► A 19th century Leibniz-inspired program for constructing extension is identified.
► Extension is not a structureless intuition but a conceptual construction.
► Herbart, Riemann and Grassmann are identified with this constructive tradition.
► A new interpretation of the algebra and its relation to issues of measurement is proposed.