Joan Bertran-San Millán: Frege’s Early Notion of Function

Monday, December 11 2023 @17:00 (CEST)
Online

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, fully developed by Frege in Begriffsschrift (1879). In this talk, I claim that Frege’s early notion of function relies, to a great extent, on Frege’s mathematical work from the late 1870s, and reflects the influence of relevant contributions to projective geometry found in Clebsch and Plücker’s works. In so doing, I provide new textual evidence to Tappenden and Wilson’s account of Frege’s functional approach. 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. The purely syntactical use of the function-argument scheme in the proofs of Frege’s 1879 work shows that the notion of function at play is substantially different to Frege’s mature conception, developed from (1891) on.y. 

Bio
Joan Bertran-San Millán holds a post-doctoral fellowship at the Centro de Filosofia das Ciências da Universidade de Lisboa (CFCUL)