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Visual Thinking in Mathematics: An Epistemological Study

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Visual Thinking in Mathematics: An Epistemological Study Cover

 

Synopses & Reviews

Publisher Comments:

Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures.

Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.

About the Author

Marcus Giaquinto is a Reader in Philosophy at University College London.

Table of Contents

1. Introduction

2. Simple Shapes: Vision and Concepts

3. Basic Geometrical Knowledge

4. Geometrical Discovery by Visualizing

5. Diagrams in Geometric Proofs

6. Mental Number Lines

7. Visual Aspects of Calculation

8. General Theorems from Specific Images

9. Visual Thinking in Basic Analysis

10. Symbol Manipulation

11. Cognition of Structure

12. Mathematical Thinking: Algebraic v. Geometric?

Product Details

ISBN:
9780199575534
Author:
Giaquinto, Marcus
Publisher:
Oxford University Press, USA
Subject:
Mind & Body
Subject:
PHILOSOPHY / Logic
Subject:
Mathematics
Subject:
Philosophy | Logic & Mathematics
Publication Date:
20111131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
304
Dimensions:
6.2 x 9.1 x 0.7 in 0.988 lb

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Related Subjects

Health and Self-Help » Psychology » General
History and Social Science » Sociology » General
Humanities » Philosophy » General
Humanities » Philosophy » Logic
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Logic and Philosophy

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