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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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Visualizing in Mathematics

Visualizing in Mathematics

(p.22) 1 Visualizing in Mathematics
The Philosophy of Mathematical Practice

Marcus Giaquinto (Contributor Webpage)

Oxford University Press

Visual thinking in mathematics (thinking with representations in visual imagination or external diagrams) has a plurality of uses. This chapter assesses the epistemic standing of major uses of visual thinking, concentrating on proving (and following a proof), and discovering, i.e. coming to believe a truth by one's own lights in a way that is reliable and involves no violation of epistemic rationality. Taking into account the sorts of error to which visual thinking is especially vulnerable, it is argued that visual thinking can have a non-superfluous role in proving. The chapter then discusses and illustrates the possibility of discovering mathematical truths visually. Finally, other uses of visual thinking in mathematics are surveyed.

Keywords:   visual thinking, visualizing, diagrams, proving, discovery

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