On the Compatibility between Euclidean Geometry and Hume’s Denial of Infinite Divisibility

Hume Studies 34 (2):231-244 (2008)
  Copy   BIBTEX

Abstract

It has been argued that Hume’s denial of infinite divisibility entails the falsity of most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem. I argue that Hume’s thesis that there are indivisibles is not incompatible with the Pythagorean theorem and other central theorems of Euclidean geometry, but only with those theorems that deal with matters of minuteness. The key to understanding Hume’s view of geometry is the distinction he draws between a precise and an imprecise standard of equality in extension. Hume’s project is different from the attempt made by Berkeley in some of his later writings to save Euclidean geometry. Unlike Berkeley, who interprets the theorems of Euclidean geometry as false albeit useful approximations of geometrical facts, Hume is able to save most of the central theorems as true.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,247

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

From Inexactness to Certainty: The Change in Hume's Conception of Geometry.Vadim Batitsky - 1998 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 29 (1):1-20.
Standards of Equality and Hume's View of Geometry.Emil Badici - 2011 - Pacific Philosophical Quarterly 92 (4):448-467.
Kant's Views on Non-Euclidean Geometry.Michael Cuffaro - 2012 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 25:42-54.
Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
Hume's Theory of Space and Time in its Sceptical Context.Donald L. M. Baxter - 2009 - In David Fate Norton & Jacqueline Anne Taylor (eds.), The Cambridge Companion to Hume. Cambridge University Press.
The Bifurcation Approach to Hyperbolic Geometry.Abraham A. Ungar - 2000 - Foundations of Physics 30 (8):1257-1282.
Thomas Reid's Discovery of a Non-Euclidean Geometry.Norman Daniels - 1972 - Philosophy of Science 39 (2):219-234.

Analytics

Added to PP
2010-08-16

Downloads
142 (#86,880)

6 months
1 (#415,205)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Emil Badici
Texas A&M University - Kingsville

References found in this work

No references found.

Add more references