John L. Mumma, Philosophy Department, presents "Geometric Diagrams as Proof Symbols"
Diagrams have not been standardly thought to function as legitimate symbols of mathematical proof. In this talk I present recent work in which they do play such a role. I first describe the standard view of rigorous mathematical proof, and explain how by it diagrams can only be understood as external to the reasoning. I then present Eu, a formal analysis of Euclid's Elements where diagrammatic symbols form a part of geometric proofs. Specifically, I discuss the principles behind Eu's analysis, the structure of Eu as a formal system, and finally the way in which Eu ensures the generality of inferences drawn from particular diagrams.
Refreshments will be provided.