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.

*"synopsis" may belong to another edition of this title.*

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.

"John Burgess' *Rigor and Structure* is an enjoyable read. Given the weight of its topics, it is almost breezy...the book is overall quite thought provoking, insightful, and carefully written. It should not be overlooked by philosophers of mathematics who want to make sure that they are asking the questions that are most interesting to contemporary mathematics." -- *Metascience*

"It will be no surprise to those familiar with Burgess's other work that this book is written with exceptional clarity. And it is packed full of Burgess's astute insights into the history of mathematics and its current practice...Overall, mathematicians and philosophers alike will gain much from Burgess's specific insights about particular parts of mathematical practice; but they will also find his larger picture of modern mathematics extremely illuminating." --

*"About this title" may belong to another edition of this title.*

US$ 52.14

**Shipping:**
FREE

From United Kingdom to U.S.A.

Published by
Oxford University Press, United Kingdom
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Oxford University Press, United Kingdom, 2015. Hardback. Condition: New. Language: English . Brand New 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. Seller Inventory # AOP9780198722229

Published by
Oxford University Press, United Kingdom
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Oxford University Press, United Kingdom, 2015. Hardback. Condition: New. Language: English . Brand New 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. Seller Inventory # AOP9780198722229

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Quantity Available: 3

Seller:

Rating

**Book Description **Condition: New. Seller Inventory # 22036098-n

Published by
OUP Oxford 2015-02-19, Oxford
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
Quantity Available: 5

Seller:

Rating

**Book Description **OUP Oxford 2015-02-19, Oxford, 2015. hardback. Condition: New. Seller Inventory # 9780198722229

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Quantity Available: 1

Seller:

Rating

**Book Description **2015. HRD. Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Seller Inventory # VU-9780198722229

Published by
OUP Oxford 2015-02-01
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Quantity Available: 5

Seller:

Rating

**Book Description **OUP Oxford 2015-02-01, 2015. Condition: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Seller Inventory # NU-OUP-00085927

Published by
Oxford University Press
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Oxford University Press, 2015. HRD. Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Seller Inventory # FU-9780198722229

Published by
Oxford University Press
(2015)

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
First Edition
Quantity Available: 1

Seller:

Rating

**Book Description **Oxford University Press, 2015. Condition: New. John P. Burgess presents an illuminating study of the nature of mathematical rigor and of mathematical structure, and above all of the relation between them. He considers recent developments in the field including experimental mathematics and computerized formal proofs, and surveys many historical developments in mathematics, philosophy, and logic. Num Pages: 240 pages. BIC Classification: HPL; PBB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 148 x 223 x 20. Weight in Grams: 436. . 2015. 1st Edition. Hardcover. . . . . . Seller Inventory # V9780198722229

Published by
OUP Oxford

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
Quantity Available: 5

Seller:

Rating

**Book Description **OUP Oxford. Hardcover. Condition: New. New copy - Usually dispatched within 2 working days. Seller Inventory # B9780198722229

Published by
Oxford University Press

ISBN 10: 0198722222
ISBN 13: 9780198722229

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Oxford University Press. Condition: New. John P. Burgess presents an illuminating study of the nature of mathematical rigor and of mathematical structure, and above all of the relation between them. He considers recent developments in the field including experimental mathematics and computerized formal proofs, and surveys many historical developments in mathematics, philosophy, and logic. Num Pages: 240 pages. BIC Classification: HPL; PBB. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 148 x 223 x 20. Weight in Grams: 436. . 2015. 1st Edition. Hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9780198722229