Visual Thinking in Mathematics

An Epistemological Study
Erscheinungsjahr 2011
ISBN: 978-0-19-957553-4
Verlag: OUP Oxford

Buch, Englisch, 298 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 456 g

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.

Zielgruppe

Scholars and advanced students of philosophy, mathematics, and psychology. Anyone with an interest in the role of visual thinking in mathematical thought.

Autoren/Hrsg.

Giaquinto, Marcus

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Sozialwissenschaften Psychologie Allgemeine Psychologie Kognitionspsychologie
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik EDV | Informatik Informatik Mensch-Maschine-Interaktion Informationsvisualisierung

Inhaltsverzeichnis

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?

Über Autor(innen)

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

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