VISUALIZATION, EXPLANATION AND REASONING STYLES IN MATHEMATICS by Paolo Mancosu (Editor), Klaus Frovin Jorgensen (Editor), Stig Andur Pedersen (Editor) ( 9781402033346 )

Item Details

Title:

VISUALIZATION, EXPLANATION AND REASONING STYLES IN MATHEMATICS

By:

Paolo Mancosu (Editor), Klaus Frovin Jorgensen (Editor), Stig Andur Pedersen (Editor)

Format:

Hardback

List price:	£119.99
We currently do not stock this item, please contact the publisher directly for further information.

ISBN 10:

1402033346

ISBN 13:

9781402033346

Publisher:

SPRINGER-VERLAG NEW YORK INC.

Pub. date:

4 April, 2005

Edition:

2005 ed.

Series:

Synthese Library v. 327

Pages:

300

Description:

Contains contributions to the philosophical analysis of mathematical practice. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification?

Synopsis:

In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert's program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics.Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

Illustrations:

biography

Publication:

Imprint:

Springer-Verlag New York Inc.

Returns:

Returnable

Some other items by this author:

A COMPANION TO THE PHILOSOPHY OF TECHNOLOGY