Synthese

, Volume 186, Issue 1, pp 387–409

Diagrams as sketches

Article

Abstract

This article puts forward the notion of “evolving diagram” as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter “diagrams*”) in the context of “sketch theory,” a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively.

Keywords

Mathematical diagrams Pictorialism Categorical diagrams Sketch theory Formal proof Semantics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Département de Philosophie (IREPH)Université Paris OuestNanterreFrance
  2. 2.SPHERE (UMR 7219), Université Paris-DiderotParisFrance

Personalised recommendations