Justus Grassmann's Contributions to the Foundations of Mathematics: Mathematical and Philosophical Aspects

Abstract

This paper explores Justus Grassmann's ideas concerning the foundations of mathematics as developed between 1806 and 1827. It begins with a discussion of the didactic and philosophical contexts of Grassmann's work. This is followed by an exposition of his ideas on the foundations of geometry and of his 1827 account of the foundations of mathematics. Particular attention is given to Grassmann's concept of construction (synthesis), which represents the basis of his entire thinking. © 2000 Academic Press.