Representation and productive ambiguity in mathematics and the sciences

Sinopse

"Emily Grosholz offers an investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. She presents a range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing primarily 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." "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." "Grosholz's arguments, which invoke Descartes, Locke, Hume, and Kant will be of interest to philosophers and historians of mathematics and science, and also have consequences for epistemology and philosophy of language."--Jacket.