David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Oxford University Press (2007)
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||categorize this paper)|
|Buy the book||$59.99 new (38% off) $100.00 direct from Amazon $102.46 used Amazon page|
|Call number||QA8.4.G534 2007|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Elijah Chudnoff (2013). Is Intuition Based On Understanding? Philosophy and Phenomenological Research 86 (1):42-67.
Catherine Legg & James Franklin (2015). Perceiving Necessity. Pacific Philosophical Quarterly 96 (3).
Tyler Marghetis & Rafael Núñez (2013). The Motion Behind the Symbols: A Vital Role for Dynamism in the Conceptualization of Limits and Continuity in Expert Mathematics. Topics in Cognitive Science 5 (2):299-316.
Angela Breitenbach (2015). Beauty in Proofs: Kant on Aesthetics in Mathematics. European Journal of Philosophy 23 (4):955-977.
Marianna Antonutti Marfori (2010). Informal Proofs and Mathematical Rigour. Studia Logica 96 (2):261-272.
Similar books and articles
Qasim Zaidi & A. Fuzz Griffiths (2002). Generic Assumptions Shared by Visual Perception and Imagery. Behavioral and Brain Sciences 25 (2):215-216.
Jeremy Avigad (2009). Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. Philosophia Mathematica 17 (1):95-108.
Matthew Inglis & Juan Pablo Mejía-Ramos (2009). On the Persuasiveness of Visual Arguments in Mathematics. Foundations of Science 14 (1-2):97-110.
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.
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.
Antti Revonsuo (1998). Visual Perception and Subjective Visual Awareness. Behavioral and Brain Sciences 21 (6):769-770.
Fred W. Mast (2005). Mental Images: Always Present, Never There. Behavioral and Brain Sciences 28 (6):769-770.
Rudolf Arnheim (1970). Visual Thinking. London,Faber.
Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. British Journal for the Philosophy of Science 45 (3):789-813.
Added to index2009-01-28
Total downloads71 ( #51,123 of 1,781,359 )
Recent downloads (6 months)12 ( #64,755 of 1,781,359 )
How can I increase my downloads?