In Kenneth Winkler (ed.), Philosophical Review. Cambridge University Press. pp. 126-128 (1995)

Authors
Douglas Jesseph
University of South Florida
Abstract
The dissertation is a detailed analysis of Berkeley's writings on mathematics, concentrating on the link between his attack on the theory of abstract ideas and his philosophy of mathematics. Although the focus is on Berkeley's works, I also trace the important connections between Berkeley's views and those of Isaac Barrow, John Wallis, John Keill, and Isaac Newton . The basic thesis I defend is that Berkeley's philosophy of mathematics is a natural extension of his views on abstraction. The first chapter is devoted to a consideration of Berkeley's treatment of abstraction, including his arguments against the doctrine of abstract ideas and his own account of how the explanatory ideas traditionally assigned to abstract ideas can be filled by a non-abstractionist account of human knowledge. In chapter two I investigate the details of Berkeley's proposed new foundations for geometry, showing how his rejection of abstract ideas led him to a critique of the traditional conception of geometry . Of particular importance in this context is Berkeley's denial of infinite divisibility and his attempts to show that a satisfactory account of geometry does not require that geometric magnitudes be infinitely divisible. Chapter three is concerned with Berkeley's treatment of arithmetic and algebra. Here I argue that Berkeley's denial of the claim that arithmetic is the science of abstract ideas of number ultimately results in his advocacy of a strongly nominalistic conception of arithmetic which has strong similarities to modern fomalism. In chapter four I discuss Berkeley's famous critique of the calculus in The Analyst and other works, concluding that his criticism of the calculus is essentially correct, although his attempted explanation of the success of infinitesimal methods is unconvincing
Keywords Mathematics   Berkeley, George
Categories (categorize this paper)
Reprint years 2005
Buy the book Find it on Amazon.com
ISBN(s) 0226398978 (alk. paper)  
DOI 10.2307/2186018
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 62,343
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Standards of Equality and Hume's View of Geometry.Emil Badici - 2011 - Pacific Philosophical Quarterly 92 (4):448-467.

View all 9 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
39 ( #273,944 of 2,445,356 )

Recent downloads (6 months)
6 ( #122,518 of 2,445,356 )

How can I increase my downloads?

Downloads

My notes