The Philosophical Status of Diagrams (Center for the Study of Language and Information - Lecture Notes)

Greaves, Mark

ISBN 10: 1575862948 / ISBN 13: 9781575862941

Published by Center for the Study of Language and Inf, 2001

About this Item

This text explores the reasons why diagrams have been ignored in modern formal theories of axiomatic systems. By looking at the use of diagrams in logic and geometry it concludes that it is not technical incompatibility, but history and philosophy that restricts the use of diagrams in these fields. Series: Center for the Study of Language and Information Publication Lecture Notes. Num Pages: 250 pages, Ill. BIC Classification: HPL; PBB; PBM. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 229 x 152 x 12. Weight in Grams: 312. . 2001. Paperback. . . . . Books ship from the US and Ireland.

Seller Inventory # V9781575862941

Bibliographic Details

• Title: The Philosophical Status of Diagrams (Center for the Study of Language and Information - Lecture Notes)
• Publisher: Center for the Study of Language and Inf
• Publication Date: 2001
• Language: English
• ISBN 10: 1575862948
• ISBN 13: 9781575862941
• Binding: Soft cover
• Condition: New

About this title

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.