November 15, 2022: HiPhis Conference – Diagrammatic Proofs – Old and New Challenges

Tuesday, November 15, 2022,from5:30 p.m.to7:30 p.m.,UM Faculty of Sciences,Classroom SC-10.01, free admission

(Triolet Campus, Building 10, Place Eugène-Bataillon)

Diagrammatic Evidence—Old and New Challenges

Valeria Giardino
  Philosopher of mathematics, CNRS researcher at the Jean-Nicod Institute (CNRS/ENS/EHESS), École Normale Supérieure, Paris

Abstract:
  In this presentation, we will analyze the concept of diagrammatic proof and its validity in the context of mathematical practice. We will first clarify what a “diagrammatic proof” is, then present the philosophical arguments that were put forward in the late^19thand early^{20th centuries against}its validity. We will then outline the reasons that might lead to a reevaluation of these arguments. Next, we will show that the practice of mathematics involves “trafficking in heterogeneity,” to borrow the term used by Emily Grosholz in her critique of the tradition in logic inspired by Russell and Carnap. Finally, we will examine several examples of diagrammatic proofs in both Euclidean geometry and contemporary mathematics that have been discussed in the literature. To conclude, we will consider the implications for a philosophy of mathematical practice of accepting diagrammatic proofs as valid proofs.