David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophical Review 97 (1):47-69 (1988)
Since both berkeley and hume are committed to the view that a line is composed of finitely many fundamental parts, They must find responses to the standard geometrical proofs of infinite divisibility. They both repeat traditional arguments intended to show that infinite divisibility leads to absurdities, E.G., That all lines would be infinite in length, That all lines would have the same length, Etc. In each case, Their arguments rest upon a misunderstanding of the concept of a limit, And thus are not successful. Berkeley, However, Adds a further ingenious argument to the effect that the standard geometrical proofs of infinite divisibility misread the unlimited representational capacity of geometrical diagrams as a substantive feature of the objects that these diagrams represent. The article concludes that berkeley is right on this matter, And that the traditional proofs of infinite divisibility do not show what they are intended to show
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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.
Citations of this work BETA
Emil Badici (2011). Standards of Equality and Hume's View of Geometry. Pacific Philosophical Quarterly 92 (4):448-467.
Stefan Storrie (2012). What is It the Unbodied Spirit Cannot Do? Berkeley and Barrow on the Nature of Geometrical Construction. British Journal for the History of Philosophy 20 (2):249-268.
Similar books and articles
David M. Levy (1992). Bishop Berkeley Exorcises the Infinite. Hume Studies 18 (2):511-536.
Dale Jacquette (2002). Hume on Infinite Divisibility and the Negative Idea of a Vacuum. British Journal for the History of Philosophy 10 (3):413 – 435.
Dale Jacquette (1996). Hume on Infinite Divisibility and Sensible Extensionless Indivisibles. Journal of the History of Philosophy 34 (1):61-78.
Donald L. M. Baxter (1988). Hume on Infinite Divisibility. History of Philosophy Quarterly 5 (2):133-140.
Dale Jacquette (1994). Infinite Divisibility in Hume's First Enquiry. Hume Studies 20 (2):219-240.
Thomas Holden (2002). Infinite Divisibility and Actual Parts in Hume’s Treatise. Hume Studies 28 (1):3-25.
H. Mark Pressman (1997). Hume on Geometry and Infinite Divisibility in the Treatise. Hume Studies 23 (2):227-244.
Vadim Batitsky (1998). From Inexactness to Certainty: The Change in Hume's Conception of Geometry. [REVIEW] Journal for General Philosophy of Science 29 (1):1-20.
James Franklin (1994). Achievements and Fallacies in Hume's Account of Infinite Divisibility. Hume Studies 20 (1):85-101.
Emil Badici (2010). On the Compatibility Between Euclidean Geometry and Hume's Denial of Infinite Divisibility. Hume Studies 34 (2):231-244.
Added to index2009-01-28
Total downloads30 ( #58,256 of 1,101,683 )
Recent downloads (6 months)6 ( #44,817 of 1,101,683 )
How can I increase my downloads?