Visual Thinking in Mathematics: An Epistemological Study
Oxford University Press (2007)
| Abstract | 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 | |||||||||
| Keywords | Mathematics Philosophy Visual perception Information visualization Geometry Arithmetic | |||||||||
| Categories | ||||||||||
| Buy the book | $61.10 used (29% off) $62.55 new (27% off) $65.49 direct from Amazon (23% off) Amazon page | |||||||||
| Call number | QA8.4.G534 2007 | |||||||||
| ISBN(s) | 9780199285945 0199285942 | |||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,865 |
| External links |
  Try with proxy. Try with proxy. |
| Through your library | Configure |
Similar books and articlesQasim Zaidi & A. Fuzz Griffiths (2002). Generic Assumptions Shared by Visual Perception and Imagery. Behavioral and Brain Sciences 25 (2):215-216.
Rudolf Arnheim (1970). Visual Thinking. London,Faber.
Fred W. Mast (2005). Mental Images: Always Present, Never There. Behavioral and Brain Sciences 28 (6):769-770.
Antti Revonsuo (1998). Visual Perception and Subjective Visual Awareness. Behavioral and Brain Sciences 21 (6):769-770.
John Heffner (1976). Some Epistemological Aspects of Recent Work in Visual Perception. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1976:165 - 174.
Andrew Arana (2009). Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW] Analysis 69:401-403.
Andrew Arana (2009). Visual Thinking in Mathematics • by Marcus Giaquinto. Analysis 69 (2):401-403.
Matthew Inglis & Juan Pablo Mejía-Ramos (2009). On the Persuasiveness of Visual Arguments in Mathematics. Foundations of Science 14 (1-2):97-110.
Jeremy Avigad (2009). Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. Philosophia Mathematica 17 (1):95-108.
Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. British Journal for the Philosophy of Science 45 (3):789-813.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads45 ( #25,064 of 556,803 )Recent downloads (6 months)7 ( #11,112 of 556,803 )How can I increase my downloads? |
My notes
Discussion
