Representation and Productive Ambiguity in Mathematics and the Sciences
| Author | : | |
| Rating | : | 4.90 (668 Votes) |
| Asin | : | 0199299730 |
| Format Type | : | paperback |
| Number of Pages | : | 332 Pages |
| Publish Date | : | 2014-08-19 |
| Language | : | English |
DESCRIPTION:
Representation and Productive Ambiguity in Mathematics and the Sciences. Emily R. Grosholz. 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 understand
"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
Grosholz is Professor of Philosophy at Pennsylvania State University.. Emily R
Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience. 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. Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Focusing on geometri