Human diagrammatic reasoning and seeing-as

Annalisa Coliva

pp. 121-148

in: John Mumma, Marco Panza, Paul-Gabriel Sandu (eds), Diagrams in mathematics, Synthese 186 (1), 2012.

Abstract

The paper addresses the issue of human diagrammatic reasoning in the context of Euclidean geometry. It develops several philosophical categories which are useful for a description and an analysis of our experience while reasoning with diagrams. In particular, it draws the attention to the role of seeing-as; it analyzes its implications for proofs in Euclidean geometry and ventures the hypothesis that geometrical judgments are analytic and a priori, after all.