Berkeleys Philosophy of Mathematics

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $55.35
Usually ships in 1-2 business days
(Save 44%)
Other sellers (Hardcover)
  • All (5) from $55.35   
  • New (3) from $96.32   
  • Used (2) from $55.35   


In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution.

Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst.

By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.

Read More Show Less

Product Details

Meet the Author

Douglas M. Jesseph is assistant professor of philosophy at North Carolina State University.

Read More Show Less

Table of Contents

Preface Works Frequently Cited Introduction
1. Abstraction and the Berkeleyan Philosophy of Mathematics Aristotelian and Scholastic Background Seventeenth-Century Background Berkeley's Case against Abstract Ideas Sources of Berkeley's Antiabstractionism
2. Berkeley's New Foundations for Geometry The Early View Abstraction and Geometry in the Principles
Geometry in the New Theory of Vision
Geometry and Abstraction in the Later Works
3. Berkeley's New Foundations for Arithmetic Geometry versus Arithmetic Numbers as Creatures of the Mind The Nonabstract Nature of Numbers Berkeley's Arithmetical Formalism Algebra as an Extension of Arithmetic The Primacy of Practice over Theory Berkeley's Formalism Evaluated
4. Berkeley and the Calculus: The Background Classical Geometry and the Proof by Exhaustion Infinitesimal Mathematics The Method of Indivisibles Leibniz and the Differential Calculus The Newtonian Method of Fluxions
5. Berkeley and the Calculus: Writings before the Analyst
The Calculus in the Philosophical Commentaries
The Essay "Of Infinites"
The Principles and Other Works
6. Berkeley and the Calculus: The Analyst
The Object of the Calculus The Principles and Demonstrations of the Calculus The Compensation of Errors Thesis Ghosts of Departed Quantities and Other Vain Abstractions The Analyst Evaluated
7. The Aftermath of the Analyst
Berkeley's Disputes with Jurin and Walton Other Reponses to Berkeley The Significance of the Analyst
Conclusions Bibliography Index

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)