Synthese

, Volume 186, Issue 1, pp 387–409

Diagrams as sketches

Authors

    • Département de Philosophie (IREPH)Université Paris Ouest
    • SPHERE (UMR 7219), Université Paris-Diderot
Article

DOI: 10.1007/s11229-011-9986-5

Cite this article as:
Halimi, B. Synthese (2012) 186: 387. doi:10.1007/s11229-011-9986-5
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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 diagramsPictorialismCategorical diagramsSketch theoryFormal proofSemantics

Copyright information

© Springer Science+Business Media B.V. 2011