Naturalism in Mathematics
Home > Mathematics and Science Textbooks > Mathematics > Philosophy of mathematics > Naturalism in Mathematics
Naturalism in Mathematics

Naturalism in Mathematics


     0     
5
4
3
2
1



International Edition


Award Winner
Awards Winning
| Winner of the 2002 Lakatos Award
X
About the Book

Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view--realism--is assessed and finally rejected in favour of another--naturalism--which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Table of Contents:
PART I: THE PROBLEM 1: The origins of set theory 2: Set theory as a foundation 3: The standard axioms 4: Independent questions 5: New axiom candidates 6: V = L PART II: REALISM 1: Godelian realism 2: Quinean realism 3: Set-theoretic realism 4: A realist's case against V = L 5: Hints of trouble 6: Indispensability and scientific practice 7: Indispensability and mathematical practic PART III: NATURALISM 1: Wittgensteinian anti-philosophy 2: A second Godelian theme 3: Quinean naturalism 4: Mathematical naturalism 5: The problem revisited 6: A naturalist's case against V = L Conclusion Bibliography Index

About the Author :
Penelope Maddy is Professor of Philosophy at the University of California, Irvine, having previously held positions at the University of Illinois, Chicago, and the University of Notre Dame, Indiana.

Review :
`presentation is clear and concise ... historically informed and comprehensive.' A.M.Coyne, MATH, Vol.931 `An excellent book ... The philosopher's task is not to provide external criticism, but rather to clarify debates in this so-called mathematical community. And Ms Maddy makes some fascinating (and very technical) steps in this direction.' The Economist Review `Maddy's important new idea - mathematical naturalism - is a view about the proper relationship between mathematics and philosophy ... This is a powerful book: wonderfully erudite and a pleasure to read. There is no better introduction to the methodology of modern set theory.' Gideon Rosen, British Journal for the Philosophy of Science 50 (1999) `The book is beautifully written, tightly argued and makes compelling reading. I believe the position Maddy introduces and defends - set theoretic naturalism - is a significant and original addition to the philosophy of mathematics landscape, and one that will certainly attract a great deal of attention ... In summary this a very important book covering some fascinating terrain on the border between philosophy and mathematics. The book will thus be of considerable interest to philosophers of mathematics and mathematicians alike. Indeed, Maddy's engaging style and clear explanations of the more technical material makes this book, like her last, accessible and of interest to the non-specialist as well. Naturalism in Mathematics should enjoy a wide readership and it will no doubt promote fruitful debate on the many important issues it raises.' Mark Colyvan, University of Tasmania, Mind, Vol 108, no 431, July 1999 An excellent book. The Economist (UK), February 2000 The philosopher's task is not to provide external critisism, but rather to clarify debates in this so-called mathematical community. And Ms Maddy makes some fascinating (and very technical) steps in this direction. The Economist (UK), February 2000 `The central problem discussed in the book concerns the foundations of contemporary set theory. Drawing on detailed historical studies on the origins and development of set theory... she shows that the ensuing methodological debates have been settled on mathematical grounds and not on the basis of philosophical considerations.' Eduard Glas, Mathematical Reviews.


Best Sellers


Product Details
  • ISBN-13: 9780198235736
  • Publisher: Oxford University Press
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Weight: 473 gr
  • ISBN-10: 0198235739
  • Publisher Date: 13 Nov 1997
  • Height: 224 mm
  • No of Pages: 264
  • Spine Width: 20 mm
  • Width: 144 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Naturalism in Mathematics
Oxford University Press -
Naturalism in Mathematics
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Naturalism in Mathematics

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!