Grassmann’s Concept Structuralism

Abstract

After recalling some mathematical contributions that are relevant for the structuralist transformation of mathematics, such as abstract algebra, linear algebra, and number theory, this chapter reconstructs Grassmann’s philosophy of mathematics. It is claimed that he contributed to the development of methodological structuralism inasmuch as he clearly separated the study of the most general properties of connections from pure and applied mathematics, basing them on an understanding of generality as conceptual underdetermination, and on the preeminence of the notion of series over that of function. A brief comparison with contemporary philosophical structuralism will clarify Grassmann’s tendency toward a “concept structuralism” rather than an “object structuralism.”