November 15, 2022: HiPhis conference - Diagrammatic evidence - old and new challenges

Tuesday, November 15, 2022from 5:30to7:30 p.m.,UM Faculty of Science, lecture hallSC-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 Institut Jean-Nicod CNRS/ENS/EHESS, École Normale Supérieure, Paris

Abstract:
In this talk, we will analyze the notion of diagrammatic proof and its validity in the context of mathematical practice. First, we'll clarify what a "diagrammatic proof" is, and then present the philosophical arguments that were put forward in the late ^19thand early 20th centuries ^againstits validity. We will then give the reasons why these arguments should be revised. Secondly, we will show that the practice of mathematics involves "trafficking in heterogeneity", to use the term coined by Emily Grosholz in her critique of the tradition in logic inspired by Russell and Carnap. Finally, we'll look at some examples of diagrammatic proofs in both Euclidean geometry and contemporary mathematics that have been discussed in the literature. To conclude, we will consider the consequences for a philosophy of mathematical practice of accepting diagrammatic proofs as valid proofs.