Visual Thinking in Mathematics
Graduate studies at Western
OUP Oxford (2011)
|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||No keywords specified (fix it)|
|Categories||categorize this paper)|
|External links||This entry has no external links. Add one.|
|Through your library||Configure|
Similar books and articles
M. Giaquinto (2007). Visual Thinking in Mathematics: An Epistemological Study. Oxford University Press.
Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. British Journal for the Philosophy of Science 45 (3):789-813.
Jeremy Avigad (2009). Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. Philosophia Mathematica 17 (1):95-108.
Andrew Arana (2009). Visual Thinking in Mathematics • by Marcus Giaquinto. Analysis 69 (2):401-403.
Andrew Arana (2009). Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW] Analysis 69:401-403.
Matthew Inglis & Juan Pablo Mejía-Ramos (2009). On the Persuasiveness of Visual Arguments in Mathematics. Foundations of Science 14 (1-2):97-110.
Mohan Matthen (2007). Defining Vision: What Homology Thinking Contributes. Biology and Philosophy 22 (5):675-689.
Don Fawkes (2003). Critically Thinking Through Visual Arts. Inquiry: Critical Thinking Across the Disciplines 22 (4):13-25.
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.
Qasim Zaidi & A. Fuzz Griffiths (2002). Generic Assumptions Shared by Visual Perception and Imagery. Behavioral and Brain Sciences 25 (2):215-216.
V. di Lollo, James T. Enns & R. Rensink (2000). Competition for Consciousness Among Visual Events: The Psychophysics of Reentrant Visual Processes. Journal Of Experimental Psychology-General 129 (4):481-507.
Antti Revonsuo (1998). Visual Perception and Subjective Visual Awareness. Behavioral and Brain Sciences 21 (6):769-770.
Sorry, there are not enough data points to plot this chart.
Added to index2012-04-15
Total downloads1 ( #292,563 of 740,419 )
Recent downloads (6 months)1 ( #61,680 of 740,419 )
How can I increase my downloads?