Representation and Productive Ambiguity in Mathematics and the Sciences 1st Edition

by Emily R. Grosholz (Author)

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ISBN-13: 978-0199299737

ISBN-10: 0199299730

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Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience.

Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable fore mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are subtly altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.

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Editorial Reviews

Review

"She has given us a very readable and well-argued series of case studies in the history and philosophy of the sciences. Anyone with an interest in the history of mathematics, the history of science, or the general philosophy of science is bound to find a wealth of interesting material here."--Doug Jesseph, Notre Dame Philosophical Reviews

About the Author

Emily R. Grosholz is affiliated with The Pennsylvania State University.

Product details

Publisher : Clarendon Press; 1st edition (October 18, 2007)
Language : English
Hardcover : 332 pages
ISBN-10 : 0199299730
ISBN-13 : 978-0199299737
Item Weight : 1.44 pounds
Dimensions : 9.3 x 1 x 6.3 inches

Best Sellers Rank: #4,642,795 in Books (See Top 100 in Books)
- #1,385 in Logic (Books)
- #1,852 in Epistemology (Books)
- #3,317 in Mathematics History

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Leo F. Rogers

Representation and Productive Ambiguity in Mathematics and the Sciences. Emily R. Grosholz.

Reviewed in the United States on January 13, 2013

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This is an important and wide-ranging study of creative invention in science and mathematics from the early modern period to the present day, showing how the development of ideas arises from the necessarily semiotic ambiguity in different kinds of representation.

Case studies in geometry, mechanics, topology and algebra, are examined to demonstrate that historical analysis and logical abstraction cooperate in understanding the epistemological processes involved in scientific discovery.

Grosholz’ work will be of interest to philosophers of science and mathematics, and to those who see the history of mathematics and science as an important contribution to informing teaching and motivating learning.

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Representation and Productive Ambiguity in Mathematics and the Sciences 1st Edition

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