The Philosophical Status of Diagrams - Couverture souple

Greaves, Mark

Couverture souple

ISBN 10 : 1575862948 ISBN 13 : 9781575862941

Editeur : Centre for the Study of Language & Information, 2001

Synopsis

The use of diagrams in logic and geometry has encountered resistance in recent years. For a proof to be valid in geometry, it must not rely on the graphical properties of a diagram. In logic, the teaching of proofs depends on sentenial representations, ideas formed as natural language sentences such as "If A is true and B is true...." No serious formal proof system is based on diagrams.

This book explores the reasons why structured graphics have been largely ignored in contemporary formal theories of axiomatic systems. In particular, it elucidates the systematic forces in the intellectual history of mathematics which have driven the adoption of sentential representational styles over diagrammatic ones. In this book, the effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are traced from antiquity to the early twentieth-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems.

Détails de l'édition

• Éditeur: Centre for the Study of Language & Information
• Date d'édition: 2001
• Langue: anglais
• ISBN 10: 1575862948
• ISBN 13: 9781575862941
• Reliure: Broché
• Nombre de pages: 221
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible