Abstract

Recent historical studies have located in late nineteenth-century mathematics the first proponents of methodological structuralism. In this talk, I shall attempt to answer the question of whether Giuseppe Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and the axioms of arithmetic and geometry, and distinguish two phases in his axiomatisation of these theories. First, I shall argue that the undefinability of the primitive notions of arithmetic and geometry led Peano to the study of the relational features of the systems of objects that compose these theories. Second, I shall defend that Peano developed a schematic understanding of the axioms of arithmetic which, despite diverging in some respects from Dedekind’s construction of arithmetic, should be considered structuralist.