The Mathematical Context of Frege’s Early Notion of Function

Joan Bertran San-Millán (Centre of Philosophy of Sciences, University of Lisbon)

7 June 2024, 16:00 (Lisbon Time – WET)

Faculdade de Letras de Lisboa

Sala Mattos Romão [C201.J] (Departamento de Filosofia)

Abstract: Tappenden (1995) and Wilson (1992) describe the rich mathematical and historical setting of Frege’s Grundlagen der Arithmetik (1884). They point to the connections between Plücker and Clebsch’s understanding of functions – in the context of the duality principle in projective geometry – and Frege’s functional approach. However, I think more should be said about Frege’s early conception of function, developed by Frege in Begriffsschrift (1879). In this talk, I first provide new textual evidence to Tappenden and Wilson’s claim that substantial sources of influence on Frege’s early notion of function can be found in Clebsch and Plücker’s works. I then argue that the concept of function developed in Begriffsschrift is instrumental in Frege’s early mathematical project; shapes the syntax, quantification and calculus of the logical system; and should be distinguished from Frege’s later notion of function.