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Visualization, Explanation and Reasoning Styles in Mathematics

  • Book
  • © 2005

Overview

Editors:
  1. Paolo Mancosu

    1. University of California, Berkeley, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Klaus Frovin Jørgensen

    1. Roskilde University, Denmark

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    You can also search for this editor in PubMed   Google Scholar

  3. Stig Andur Pedersen

    1. Roskilde University, Denmark

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  • Unique focus on the relationship between philosophy of mathematics and mathematical practice
  • Contains groundbreaking contributions on visualization, explanation and reasoning styles in mathematics

Part of the book series: Synthese Library (SYLI, volume 327)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • P. Mancosu, K.F. Jørgensen, S.A. Pedersen
    Pages 1-9

  3. Mathematical Reasoning and Visualization

    1. Visualization in Logic and Mathematics

      • Paolo Mancosu
      Pages 13-30

    2. From Symmetry Perception to Basic Geometry

      • M. Giaquinto
      Pages 31-55

    3. Naturalism, Pictures, and Platonic Intuitions

      • James Robert Brown
      Pages 57-73

    4. Mathematical Activity

      • M. Giaquinto
      Pages 75-87

  5. Back Matter

    Pages 295-314
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Keywords

About this book

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.

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)

Editors and Affiliations

  • University of California, Berkeley, USA

    Paolo Mancosu

  • Roskilde University, Denmark

    Klaus Frovin Jørgensen, Stig Andur Pedersen

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