Rigor and Structure

Name: Rigor and Structure
Brand: Oxford University Press
SKU: 9780198822677
Price: 4388.0 INR
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by John P. Burgess

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ISBN13: 9780198822677
Binding: Paperback
Subject: N/A
Publisher: Oxford University Press
Publisher Imprint: Oxford University Press
Publication Date: July 1, 2020
Pages: 232
Original Price: USD 41.99
Language: English
Edition: N/A
Item Weight: 273 grams
BISAC Subject(s): Logic

About The Book

While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.

About The Author

John P. Burgess, Princeton University

John P. Burgess joined the philosophy department at Princeton University shortly after receiving his Ph.D. in logic from Berkeley, and has remained there ever since, serving for many years as director of undergraduate studies. He is the author or co-author of seven previous books and over a hundred papers and reviews in mathematical and philosophical logic, philosophy of mathematics and of language, and history of analytic philosophy.

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