Visualization, Explanation and Reasoning Styles in Mathematics / Edition 1

by P. Mancosu, Klaus Frovin Jørgensen, S.A. Pedersen

Overview

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 justification 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 (finitistic reasoning), of the consistency of such formalized theories. While interest in modified 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.

Product Details

ISBN-13:	9789048168378
Publisher:	Springer Netherlands
Publication date:	01/11/2011
Series:	Synthese Library , #327
Edition description:	Softcover reprint of hardcover 1st ed. 2005
Pages:	300
Product dimensions:	6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

Mathematical Reasoning and Visualization.- Visualization in Logic and Mathematics.- From Symmetry Perception to Basic Geometry.- Naturalism, Pictures, and Platonic Intuitions.- Mathematical Activity.- Mathematical Explanation and Proof Styles.- Tertium Non Datur: On Reasoning Styles in Early Mathematics.- The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Prescription of Computation and the Operation as Argumento.- Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice.- The Varieties of Mathematical Explanation.- The Aesthetics of Mathematics: A Study.

Editorial Reviews

From the reviews:

"As its title suggests, the book deals with themes that are of great interest to mathematics educators. … this book is a collection of excellent papers by distinguished authors. It also shows a high standard of book production, in its layout, paper quality, draftsmanship and binding. … this book deserves the attention of all those with an interest in mathematics education." (G. Hanna, Educational Studies in Mathematics, Vol. 64, 2007)

"This fascinating collection of essays is a must-have for those who are interested in the history and philosophy of mathematics … . this is a book that libraries will want to have, particularly if they strive to have good collections on the history and philosophy of mathematics." (Fernando Q. Gouvêa, MathDL, August, 2005)

From the Publisher